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  • Digitale Medien  (738)
  • 1995-1999  (738)
  • 1995  (738)
  • Engineering General  (737)
  • Physics
  • 1
    Digitale Medien
    Digitale Medien
    Axial and lateral resolution of rotational intravascular ultrasound: In vitro observations and diagnostic implications (1995)
    Springer
    CardioVascular & interventional radiology 18 (1995), S. 239-242 
    Details
    ISSN: 1432-086X
    Schlagwort(e): Ultrasound, intravascular ; Artifact ; Physics
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Medizin
    Notizen: Abstract Purpose: To determine the axial and lateral resolution of a rotating intravascular ultrasound system and the diagnostic implications for the diagnosis of early artherosclerosis. Methods: The resolution of a 20 MHz rotating transducer was tested in a specially designed high-resolution phantom and in five aortic autopsy specimens with varying degrees of early atherosclerosis. Results: The best lateral resolution is at the minimal distance between transducer and object. Measurements in the wire phantom showed this to be better than 0.43 mm. This is less than the axial resolution which is better than 0.13 mm. Decreasing lateral resolution with increasing distance between transducer and object is manifested by arcing and overestimation of the extent of focal atherosclerotic lesions. Conclusion: Axial resolution is significantly better than lateral resolution. Rapid deterioration of lateral resolution affects the diagnostic ability to characterize the extent of early atherosclerosis. Eccentric positioning of the transducer tip, particularly in larger vessels, will therefore influence diagnostic accuracy in vivo.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00239419
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  • 2
    Digitale Medien
    Digitale Medien
    A modified direct preconditioner for indefinite symmetric Toeplitz systems (1995)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 2 (1995), S. 415-429 
    Details
    ISSN: 1070-5325
    Schlagwort(e): indefinite ; inverse ; preconditioning ; symmetric ; Toeplitz ; Trench algorithm ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: A modification is presented of the classical O(n2) algorithm of Trench for the direct solution of Toeplitz systems of equations. The Trench algorithm is stable for symmetric matrices that are positive definite, but can be unstable for the indefinite case (and for general matrices). Our modification permits extension of the algorithm to compute approximate inverses of indefinite symmetric Toeplitz matrices, for which the unmodified algorithm breaks down when principal submatrices are singular. As a preconditioner, the approximate inverse has an advantage that only matrix - vector multiplications are required for the solution of a linear system, without forward and backward solves. The approximate inverse so obtained can be sufficiently accurate, moreover, that, when it is used as a preconditioner for the applications investigated, subsequent iteration may not even be necessary. Numerical results are given for several test matrices. The perturbation to the original matrix that defines the modification is related to a perturbation in a quantity generated in the Trench algorithm; the associated stability of the Trench algorithm is discussed.
    Zusätzliches Material: 1 Tab.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/nla.1680020504
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  • 3
    Digitale Medien
    Digitale Medien
    Conference diary (1995)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 2 (1995), S. 483-485 
    Details
    ISSN: 1070-5325
    Schlagwort(e): Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/nla.1680020509
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  • 4
    Digitale Medien
    Digitale Medien
    Completely parallelizable preconditioning methods (1995)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 2 (1995), S. 447-465 
    Details
    ISSN: 1070-5325
    Schlagwort(e): preconditioned iterative methods ; SSOR factorization ; parallelization ; connection machine ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: A class of parallelizable preconditioned iterative methods for the solution of certain finite difference or finite element linear systems of equations is presented. The methods are based on calculation of approximate inverses of the SSOR factorization. The speed of the methods may be increased by making the approximation of the inverse more accurate. The construction of the preconditioning as well as the solution of the preconditioning systems (realized by matrix-vector multiplication) can be made in parallel over the total amount of meshpoints. The methods are suitable for implementation on massively parallel computers such as connection machines. Problems with constant as well as strongly varying orthotropy are examined and the methods are compared to other parallel techniques with respect to rate of convergence, computational complexity and consumed CM200 computing time. We report a small but significant decrease in computing time compared to the (until now) most frequently used completely parallel preconditioning, the Jacobi method.
    Zusätzliches Material: 7 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/nla.1680020506
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  • 5
    Digitale Medien
    Digitale Medien
    A saxpy formulation for plane rotations (1995)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 2 (1995), S. 533-541 
    Details
    ISSN: 1070-5325
    Schlagwort(e): plane rotation ; shear product ; Saxpy operation ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: An algorithm for pre- or post-multiplication of a matrix by a plane rotation, using only three vector saxpy operations instead of the four vector operations usually considered necessary, is described. No auxiliary storage for overwriting is required. The method is shown to be numerically stable.
    Zusätzliches Material: 6 Tab.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/nla.1680020605
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  • 6
    Digitale Medien
    Digitale Medien
    Multilevel preconditioners for discretizations of the biharmonic equation by rectangular finite elements (1995)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 2 (1995), S. 487-505 
    Details
    ISSN: 1070-5325
    Schlagwort(e): biharmonic equation ; rectangular finite elements ; preconditioning ; multilevel methods ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: Recently, some new multilevel preconditioners for solving elliptic finite element discretizations by iterative methods have been proposed. They are based on appropriate splittings of the finite element spaces under consideration, and may be analyzed within the framework of additive Schwarz schemes. In this paper we discuss some multilevel methods for discretizations of the fourth-order biharmonic problem by rectangular elements and derive optimal estimates for the condition numbers of the preconditioned linear systems. For the Bogner-Fox-Schmit rectangle, the generalization of the Bramble-Pasciak-Xu method is discussed. As a byproduct, an optimal multilevel preconditioner for nonconforming discretizations by Adini elements is also derived.
    Zusätzliches Material: 3 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/nla.1680020603
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  • 7
    Digitale Medien
    Digitale Medien
    Matrix shapes invariant under the symmetric QR algorithm (1995)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 2 (1995), S. 87-93 
    Details
    ISSN: 1070-5325
    Schlagwort(e): QR algorithm ; zero pattern ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: The QR algorithm is a basic algorithm for computing the eigenvalues of dense matrices. For efficiency reasons it is prerequisite that the algorithm is applied only after the original matrix has been reduced to a matrix of a particular shape, most notably Hessenberg and tridiagonal, which is preserved during the iterative process. In certain circumstances a reduction to another matrix shape may be advantageous. In this paper, we identify which zero patterns of symmetric matrices are preserved under the QR algorithm.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/nla.1680020203
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  • 8
    Digitale Medien
    Digitale Medien
    Efficient reduction algorithms for bordered band matrices (1995)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 2 (1995), S. 95-113 
    Details
    ISSN: 1070-5325
    Schlagwort(e): arrowhead matrix ; band matrix ; inverse eigenvalue problem ; givens rotations ; singular value decomposition ; updating ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: Various plane rotation patterns are presented, which provide stable algorithms for reducing a b-band matrix bordered by p rows and/or columns to (b + p)-band form. These schemes generalize previously presented O(N2) reduction algorithms for matrices of order N, b = 1, and p = 1 to the reduction of more general b-band, p-bordered matrices where b ≥ 1 and p ≥ 1. Moreover, by splitting the matrix into two similarly structured submatrices and chasing nonzeros to the corners in two directions, the newly proposed patterns reduce the number of required rotations and hence the computational cost by one half compared to the other existing one-way chasing algorithms. Symmetric, as well as more general matrices, are considered. An example of the first type is the symmetric arrowhead matrix that arises in solving inverse eigenvalue problems. Examples of the second type are found in updating the singular value decomposition (SVD) and the partial SVD.
    Zusätzliches Material: 7 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/nla.1680020204
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  • 9
    Digitale Medien
    Digitale Medien
    On Parlett's matrix norm inequality for the Cholesky decomposition (1995)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 2 (1995), S. 243-250 
    Details
    ISSN: 1070-5325
    Schlagwort(e): Cholesky ; norm inequality ; perturbation ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: We show that a certain matrix norm ratio studied by Parlett has a supermum that is O(\documentclass{article}\pagestyle{empty}\begin{document}$\mathop \[\sqrt n \] $\end{document}) when the chosen norm is the Frobenius norm, while it is O(log n) for the 2-norm. This ratio arises in Parlett's analysis of the Cholesky decomposition of an n by n matrix.
    Zusätzliches Material: 1 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/nla.1680020306
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  • 10
    Digitale Medien
    Digitale Medien
    Optimal backward perturbation bounds for the linear least squares problem (1995)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 2 (1995), S. 271-286 
    Details
    ISSN: 1070-5325
    Schlagwort(e): linear least squares ; backward perturbations ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: Let A be an m × n matrix, b be an m-vector, and x̃ be a purported solution to the problem of minimizing ‖b  -  Ax‖2. We consider the following open problem: find the smallest perturbation E of A such that the vector x̃ exactly minimizes ‖b  -  (A+E)x‖2. This problem is completely solved when E is measured in the Frobenius norm. When using the spectral norm of E, upper and lower bounds are given, and the optimum is found under certain conditions.
    Zusätzliches Material: 1 Tab.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/nla.1680020308
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  • 11
    Digitale Medien
    Digitale Medien
    On the solution of block Hessenberg systems (1995)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 2 (1995), S. 287-296 
    Details
    ISSN: 1070-5325
    Schlagwort(e): block Hessenberg matrix ; block Toeplitz matrix ; linear system ; queue ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: This paper describes a divide-and-conquer strategy for solving block Hessenberg systems. For dense matrices the method is as efficient as Gaussian elimination; however, because it works almost entirely with the original blocks, it is much more efficient for sparse matrices or matrices whose blocks can be generated on the fly. For Toeplitz matrices, the algorithm can be combined with the fast Fourier transform.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/nla.1680020309
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  • 12
    Digitale Medien
    Digitale Medien
    Announcement (1995)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 2 (1995), S. ii 
    Details
    ISSN: 1070-5325
    Schlagwort(e): Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/nla.1680020602
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  • 13
    Digitale Medien
    Digitale Medien
    Implicit Cholesky algorithms for singular values and vectors of triangular matrices (1995)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 2 (1995), S. 507-531 
    Details
    ISSN: 1070-5325
    Schlagwort(e): Cholesky decomposition ; singular values ; eigenvalues ; null spaces ; noise spaces ; URV and ULV factorizations ; QR algorithm ; LR algorithm ; Jacobi methods ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: The implicit Cholesky algorithm has been developed by several authors during the last 10 years but under different names. We identify the algorithm with a special version of Rutishauser's LR algorithm. Intermediate quantities in the transformation furnish several attractive approximations to the smallest singular value.The paper extols the advantages of using shifts with the algorithm. The nonorthogonal transformations improve accuracy.
    Zusätzliches Material: 4 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/nla.1680020604
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  • 14
    Digitale Medien
    Digitale Medien
    Conference diary (1995)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 2 (1995), S. 543-545 
    Details
    ISSN: 1070-5325
    Schlagwort(e): Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/nla.1680020606
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  • 15
    Digitale Medien
    Digitale Medien
    Approximate solutions and eigenvalue bounds from Krylov subspaces (1995)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 2 (1995), S. 115-133 
    Details
    ISSN: 1070-5325
    Schlagwort(e): Krylov subspace ; Lanczos process ; symmetric matrix ; conjugate gradients ; minimum residual ; Lehmann intervals ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: Approximations to the solution of a large sparse symmetric system of equations are considered. The conjugate gradient and minimum residual approximations are studied without reference to their computation. Several different bases for the associated Krylov subspace are used, including the usual Lanczos basis. The zeros of the iteration polynomial for the minimum residual approximation (harmonic Ritz values) are characterized in several ways and, in addition, attractive convergence properties are established. The connection of these harmonic Ritz values to Lehmann's optimal intervals for eigenvalues of the original matrix appears to be new.
    Zusätzliches Material: 3 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/nla.1680020205
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  • 16
    Digitale Medien
    Digitale Medien
    Minimization of the norm, the norm of the inverse and the condition number of a matrix by completion (1995)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 2 (1995), S. 155-171 
    Details
    ISSN: 1070-5325
    Schlagwort(e): condition number ; norm of a matrix ; matrix completion ; dilation theory ; robust regularization of descriptor systems ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: We study the problem of minimizing the norm, the norm of the inverse and the condition number with respect to the spectral norm, when a submatrix of a matrix can be chosen arbitrarily. For the norm minimization problem we give a different proof than that given by Davis/Kahan/Weinberger. This new approach can then also be used to characterize the completions that minimize the norm of the inverse. For the problem of optimizing the condition number we give a partial result.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/nla.1680020207
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  • 17
    Digitale Medien
    Digitale Medien
    Conference diary (1995)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 2 (1995), S. 191-194 
    Details
    ISSN: 1070-5325
    Schlagwort(e): Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/nla.1680020209
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  • 18
    Digitale Medien
    Digitale Medien
    Stability of block LU factorization (1995)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 2 (1995), S. 173-190 
    Details
    ISSN: 1070-5325
    Schlagwort(e): block algorithm ; LAPACK ; level 3 BLAS ; iterative refinement ; LU factorization ; backward error analysis ; block diagonal dominance ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: Many of the currently popular ‘block algorithms’ are scalar algorithms in which the operations have been grouped and reordered into matrix operations. One genuine block algorithm in practical use is block LU factorization, and this has recently been shown by Demmel and Higham to be unstable in general. It is shown here that block LU factorization is stable if A is block diagonally dominant by columns. Moreover, for a general matrix the level of instability in block LU factorization can be bounded in terms of the condition number K(A) and the growth factor for Gaussian elimination without pivoting. A consequence is that block LU factorization is stable for a matrix A that is symmetric positive definite or point diagonally dominant by rows or columns as long as A is well-conditioned.
    Zusätzliches Material: 4 Tab.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/nla.1680020208
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  • 19
    Digitale Medien
    Digitale Medien
    Orthogonal projection and total least squares (1995)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 2 (1995), S. 135-153 
    Details
    ISSN: 1070-5325
    Schlagwort(e): orthogonal projection ; numerical rank ; total least squares ; rank revealing QR factorization ; acute perturbation ; subspace angle ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: Overdetermined linear systems often arise in applications such as signal processing and modern communication. When the overdetermined system of linear equations AX ≍ B has no solution, compatibility may be restored by an orthogonal projection method. The idea is to determine an orthogonal projection matrix P by some method M such that [à B̃] = P[A B], and ÃX = B̃ is compatible. Denote by XM the minimum norm solution to ÃX = B̃ using method M. In this paper conditions for compatibility of the lower rank approximation and subspace properties of à in relation to the nearest rank-k matrix to A are discussed. We find upper and lower bounds for the difference between the solution XM and the SVD-based total least squares (TLS) solution XSVD and also provide a perturbation result for the ordinary TLS method. These results suggest a new algorithm for computing a total least squares solution based on a rank revealing QR factorization and subspace refinement. Numerical simulations are included to illustrate the conclusions.
    Zusätzliches Material: 4 Tab.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/nla.1680020206
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  • 20
    Digitale Medien
    Digitale Medien
    Masthead (1995)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 2 (1995) 
    Details
    ISSN: 1070-5325
    Schlagwort(e): Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/nla.1680020301
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  • 21
    Digitale Medien
    Digitale Medien
    Some inverse eigenproblems for Jacobi and arrow matrices (1995)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 2 (1995), S. 195-203 
    Details
    ISSN: 1070-5325
    Schlagwort(e): Jacobi matrix ; arrow matrix ; inverse problem ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: We consider the problem of reconstructing Jacobi matrices and real symmetric arrow matrices from two eigenpairs. Algorithms for solving these inverse problems are presented. We show that there are reasonable conditions under which this reconstruction is always possible. Moreover, it is seen that in certain cases reconstruction can proceed with little or no cancellation. The algorithm is particularly elegant for the tridiagonal matrix associated with a bidiagonal singular value decomposition.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/nla.1680020302
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  • 22
    Digitale Medien
    Digitale Medien
    Trust regions based on conic functions in linear and nonlinear programming (1995)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 2 (1995), S. 235-241 
    Details
    ISSN: 1070-5325
    Schlagwort(e): interior-point methods ; trust regions ; conic functions ; conjugate gradients ; linear programming ; nonlinear minimization ; Karmarkar's algorithm ; centering ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: An optimization method is developed based on ellipsoidal trust regions that are defined by conic functions. It provides a powerful unifying theory from which can be derived a variety of interesting and potentially useful optimization algorithms, in particular, conjugate-gradient-like algorithms for nonlinear minimization and Karmarkar-like interior-point algorithms for linear programming.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/nla.1680020305
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  • 23
    Digitale Medien
    Digitale Medien
    Progress in the numerical solution of the nonsymmetric eigenvalue problem (1995)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 2 (1995), S. 219-234 
    Details
    ISSN: 1070-5325
    Schlagwort(e): nonsymmetric matrices ; sparse matrices ; eigenvalue problem ; EISPACK ; LAPACK ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: With the growing demands from disciplinary and interdisciplinary fields of science and engineering for the numerical solution of the nonsymmetric eigenvalue problem, competitive new techniques have been developed for solving the problem. In this paper we examine the state of the art of the algorithmic techniques and the software scene for the problem. Some current developments are also outlined.
    Zusätzliches Material: 2 Tab.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/nla.1680020304
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  • 24
    Digitale Medien
    Digitale Medien
    Regions of convergence of the Rayleigh quotient iteration method (1995)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 2 (1995), S. 251-269 
    Details
    ISSN: 1070-5325
    Schlagwort(e): eigenvalues ; eigenvectors ; symmetric matrices ; Rayleigh quotient iteration ; convergence ; basins of attraction ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: The Rayleigh quotient iteration method finds an eigenvector and the corresponding eigenvalue of a symmetric matrix. This is a fundamental problem in science and engineering. Parlett and Kahan have shown, in 1968, that for almost any initial vector in the unit sphere, the Rayleigh quotient iteration method converges to some eigenvector. In this paper, the regions of the unit sphere which include all possible initial vectors converging to a specific eigenvector are studied. The generalized eigenvalue problem Ax = λBx is considered. It is shown that the regions do not change when the matrix is shifted or multiplied by a scalar. These regions are completely characterized in the three-dimensional case. It is shown that, in this case, the area of the region of convergence corresponding to the interior eigenvalue is larger than the area of those corresponding to any extreme one. This can be interpreted, with the appropriate choice of probability distribution, as: the probability of converging to an eigenvector corresponding to the interior eigenvalue is larger than the probability of converging to an eigenvector corresponding to any extreme eigenvalue. It is conjectured that the same is true for matrices of any order. Experiments in higher dimensions are presented which conform with the conjecture.
    Zusätzliches Material: 7 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/nla.1680020307
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  • 25
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    Krylov subspace approximation of eigenpairs and matrix functions in exact and computer arithmetic (1995)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 2 (1995), S. 205-217 
    Details
    ISSN: 1070-5325
    Schlagwort(e): Lanczos method ; spectral Lanczos ; decompostion method ; eigenpairs ; matrix functions ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: Many researchers are now working on computing the product of a matrix function and a vector, using approximations in a Krylov subspace. We review our results on the analysis of one implementation of that approach for symmetric matrices, which we call the spectral lanczos decomposition method (SLDM).We have proved a general convergence estimate, relating SLDM error bounds to those obtained through approximation of the matrix function by a part of its Chebyshev series. Thus, we arrived at effective estimates for matrix functions arising when solving parabolic, hyperbolic and elliptic partial differential equations. We concentrate on the parabolic case, where we obtain estimates that indicate superconvergence of SLDM. For this case a combination of SLDM and splitting methods is also considered and some numerical results are presented.We implement our general estimates to obtain convergence bounds of Lanczos approximations to eigenvalues in the internal part of the spectrum. Unlike Kaniel-Saad estimates, our estimates are independent of the set of eigenvalues between the required one and the nearest spectrum bound.We consider an extension of our general estimate to the case of the simple Lanczos method (without reorthogonalization) in finite computer arithmetic which shows that for a moderate dimension of the Krylov subspace the results, proved for the exact arithmetic, are stable up to roundoff.
    Zusätzliches Material: 1 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/nla.1680020303
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  • 26
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    Announcement and call for papers (1995)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 2 (1995), S. 311-312 
    Details
    ISSN: 1070-5325
    Schlagwort(e): Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/nla.1680020311
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  • 27
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    Conference diary (1995)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 2 (1995), S. 313-315 
    Details
    ISSN: 1070-5325
    Schlagwort(e): Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/nla.1680020312
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  • 28
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    Dynamical analysis of numerical systems (1995)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 2 (1995), S. 297-310 
    Details
    ISSN: 1070-5325
    Schlagwort(e): dynamical systems ; eigenvalues ; QR algorithm ; Francis shift ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: For many years techniques from numerical analysis have been applied fruitfully to the study of dynamical systems. In this paper it is shown that the theory of dynamical systems may be applied to certain computational problems. In particular the question of global convergence of various QR algorithms can be reduced to the study of certain vector iterations derived from Schur forms of matrices. The technique is illustrated in determining the convergence behavior of normal Hessenberg matrices under the Francis and multishift QR iterations.
    Zusätzliches Material: 3 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/nla.1680020310
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  • 29
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    Masthead (1995)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 2 (1995) 
    Details
    ISSN: 1070-5325
    Schlagwort(e): Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/nla.1680020401
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  • 30
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    A comparison result for multisplittings and waveform relaxation methods (1995)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 2 (1995), S. 335-346 
    Details
    ISSN: 1070-5325
    Schlagwort(e): multisplittings ; overlapping ; comparison results ; M-matrices ; waveform relaxation ; parallel algorithms ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: We show that certain multisplitting iterative methods based on overlapping blocks yield faster convergence than corresponding nonoverlapping block iterations, provided the coefficient matrix is an M-matrix. This result can be used to compare variants of the waveform relaxation algorithm for solving initial value problems. The methods under consideration use the same discretization technique, but are based on multisplittings with different overlaps. Numerical experiments on the Intel iPSC/860 hypercube are included.
    Zusätzliches Material: 2 Tab.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/nla.1680020403
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  • 31
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    A spectral algorithm for envelope reduction of sparse matrices (1995)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 2 (1995), S. 317-334 
    Details
    ISSN: 1070-5325
    Schlagwort(e): envelope reduction ; eigenvalues of graphs ; Gibbs - King algorithm ; Gibbs - Poole - Stockmeyer algorithm ; Laplacian matrices ; reordering algorithms ; reverse Cuthill - McKee algorithm ; sparse matrices ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: The problem of reordering a sparse symmetric matrix to reduce its envelope size is considered. A new spectral algorithm for computing an envelope-reducing reordering is obtained by associating a Laplacian matrix with the given matrix and then sorting the components of a specified eigenvector of the Laplacian. This Laplacian eigenvector solves a continuous relaxation of a discrete problem related to envelope minimization called the minimum 2-sum problem. The permutation vector computed by the spectral algorithm is a closest permutation vector to the specified Laplacian eigenvector. Numerical results show that the new reording algorithm usually computes smaller envelope sizes than those obtained from the current standards such as the Gibbs - Poole - Stockmeyer (GPS) algorithm or the reverse Cuthill - McKee (RCM) algorithm in SPARSPAK, in some cases reducing the envelope by more than a factor of two.
    Zusätzliches Material: 5 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/nla.1680020402
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  • 32
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    Digitale Medien
    The RSCG algorithm on distributed memory architectures (1995)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 2 (1995), S. 401-414 
    Details
    ISSN: 1070-5325
    Schlagwort(e): conjugate gradient ; distributed computing ; analytic model ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: In this paper, we demonstrate the scalability of the Reduced System Conjugate Gradient (RSCG) algorithm on distributed memory architectures. We present speed-up results obtained on the Intel iPSC/860 that compare one-, two-, and three-dimensional decompositions of the domain for both positive definite and positive semidefinite test problems. We develop a model for the RSCG algorithm to analyze computational and communication costs. The model is validated using experimental data and then used to examine and predict behavior of the RSCG algorithm as a function of architecture parameters including communication latency and transmission times and memory access costs.
    Zusätzliches Material: 2 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/nla.1680020503
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  • 33
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    Digitale Medien
    Announcement and call for papers (1995)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 2 (1995), S. 481-481 
    Details
    ISSN: 1070-5325
    Schlagwort(e): Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/nla.1680020508
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  • 34
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    On a generalized conjugate gradient orthogonal residual method (1995)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 2 (1995), S. 467-479 
    Details
    ISSN: 1070-5325
    Schlagwort(e): generalized conjugate gradient ; orthogonal residual ; rate of convergence ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Notizen: To solve a linear system of equations with a generally nonsymmetric matrix, a generalized conjugate gradientorthogonal residual method is presented. The method uses all previous search directions (or a truncated set of them) at each step but, contrary to standard implementations of similar methods, it requires storage of only one set with a linearly growing number of vectors (or the number in the truncated set). Furthermore, there is only one vector (the residual), which must be updated using all the vectors in this set, at each step. In this respect it is similar to the popular GMRES method but it has the additional advantage that it can stop at any stage when the norm of the residual is sufficiently small and no extra computation is needed to compute this norm. Furthermore, the new method can be truncated.The rate of convergence of the method is also discussed.
    Zusätzliches Material: 3 Tab.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/nla.1680020507
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  • 35
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    Digitale Medien
    Masthead (1995)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Linear Algebra with Applications 2 (1995) 
    Details
    ISSN: 1070-5325
    Schlagwort(e): Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/nla.1680020601
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  • 36
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    Digitale Medien
    Masthead (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995) 
    Details
    ISSN: 1069-8299
    Schlagwort(e): Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik , Technik allgemein
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/cnm.1640110101
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  • 37
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    Editorial preface for the second decade of Communications in Numerical Methods in Engineering (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. iii 
    Details
    ISSN: 1069-8299
    Schlagwort(e): Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik , Technik allgemein
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/cnm.1640110102
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  • 38
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    Application of the spline prism method to analyse vibration of thick rectangular plates with two opposite edges simply supported (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 1-11 
    Details
    ISSN: 1069-8299
    Schlagwort(e): vibration ; spline prism method ; thick rectangular plate ; 3D elasticity theory ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik , Technik allgemein
    Notizen: The paper presents an application of the spline prism method to analyse vibration of isotropic, thick rectangular plates with two opposite edges simply supported. Three-dimensional spline prism models are formulated by combining B-spline functions with beam eigenfunctions. Because of the orthogonality of the beam functions, three-dimensional problems are reduced to a series of two-dimensional ones. To demonstrate the accuracy and convergence of the semi-numerical method, the results are compared with those obtained by other numerical methods. Good convergence and accuracy are obtained. The effects of the ratio of thickness to width and the aspect ratio on the frequencies of thick rectangular plates with several boundary conditions are analysed, and the results are compared with those calculated by the Mindlin plate theory.
    Zusätzliches Material: 2 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/cnm.1640110103
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  • 39
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    Digitale Medien
    Inflow and outflow boundary conditions in the finite element solution of the streamfunction-vorticity equations (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 33-40 
    Details
    ISSN: 1069-8299
    Schlagwort(e): boundary conditions ; streamfunction-vorticity equations ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik , Technik allgemein
    Notizen: The appropriate specification of boundary conditions is the main difficulty in the finite element solution of the streamfunction-vorticity equations for two-dimensional incompressible laminar flows. In this context, we show that the appropriate specification of both the outflow and the inflow boundary conditions is required for the successful modelling of two well known test problems.
    Zusätzliches Material: 3 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/cnm.1640110106
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  • 40
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    Analytical solutions of mass transport problems for error estimation of finite/infinite element methods (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 13-23 
    Details
    ISSN: 1069-8299
    Schlagwort(e): mass transport problems ; error estimation ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik , Technik allgemein
    Notizen: In order to make an exact estimation of discretization error for finite/infinite element methods, it is necessary to develop analytical solutions for some transient mass transport problems in infinite media. These transient mass transport problems may be viewed as the benchmark problems for the discretization error estimation of a new numerical method so that they generally have the following characteristics: (1) their initial and boundary conditions can be exactly modelled by the finite/infinite element method; (2) their solutions can be rigorously expressed in a closed form. In this paper, several of the aforementioned problems have been constructed and solved mathematically for transient mass transport problems in both 1D and 2D infinite media.
    Zusätzliches Material: 7 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/cnm.1640110104
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  • 41
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    Solution of the differential Riccati equation using the transmission line modelling (TLM) technique (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 25-32 
    Details
    ISSN: 1069-8299
    Schlagwort(e): Riccati equation ; transmission line modelling ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik , Technik allgemein
    Notizen: In this communication, the application of the transmission line modelling (TLM) technique to the solution of the differential Riccati equation is described. A comparison is made between the TLM, fourth-order Runge-Kutta and the first-order Gear methods, for the case where one is applying the Kalman filter to the estimation of a voltage in a passive analogue circuit. In the particular example studied, the state equation is second-order. It is found that, when the system is underdamped, the fourth-order Runge-Kutta method has the best performance, followed by the TLM method. When the system is overdamped and stiff, the TLM method yields results that are closest to the analytical solution. Finally, a discussion is presented of the effects of errors in the TLM solution of the Riccati equation on the accuracy of the solution to the continuous Kalman filter estimation equation.
    Zusätzliches Material: 4 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/cnm.1640110105
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  • 42
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    Digitale Medien
    Influence of contact area on service life of gears with crack in tooth root (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 49-58 
    Details
    ISSN: 1069-8299
    Schlagwort(e): gears ; fracture mechanics ; service life ; fatigue process ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik , Technik allgemein
    Notizen: The paper describes the influence of contact area on the service life of dynamically loaded gears with a crack in a tooth root. Numerical results obtained with the finite element method using the program package BERSAFE are compared with the experimental results obtained on the universal testing machine INSTRON 1255. Numerical and experimental results are in good agreement. The analysis shows that the contact area directly influences the speed and direction of the crack propagation and the service life of the gear with a crack in a tooth root.
    Zusätzliches Material: 11 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/cnm.1640110108
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  • 43
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    Digitale Medien
    Transverse shear correction factors for laminates in cylindrical bending (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 41-47 
    Details
    ISSN: 1069-8299
    Schlagwort(e): shear correction ; laminates ; cylindrical bending hypothesis ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik , Technik allgemein
    Notizen: Mindlin-type plate and shell finite elements are the most widely used ones in the analysis of laminated composite structures. In the commercially available finite element programs, the transverse shear correction factors for these elements are usually the same as for structures made of isotropic materials. In the paper the shear correction factors are determined using energy principles for general laminates in cylindrical bending. Results for various materials and laminates are presented.
    Zusätzliches Material: 5 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/cnm.1640110107
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  • 44
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    A B-spline finite element method for the regularized long wave equation (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 59-68 
    Details
    ISSN: 1069-8299
    Schlagwort(e): RLW equation ; finite elements ; splines ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik , Technik allgemein
    Notizen: A B-spline finite element method is used to solve the regularized long wave equation numerically. This approach involves a Galerkin method with quadratic B-spline finite elements so that there is continuity of the dependent variable and its first derivative throughout the solution range. Time integration of the resulting system of ordinary differential equations is effected using a Crank-Nicolson approximation. Standard problems are used to validate the algorithm, which is then used to model the smooth development of an undular bore.
    Zusätzliches Material: 5 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/cnm.1640110109
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  • 45
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    Modified calculation of the dissipation term in thermoplastic finite element equations (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 69-72 
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    ISSN: 1069-8299
    Schlagwort(e): finite element method ; thermoplasticity ; internal dissipation ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik , Technik allgemein
    Notizen: In the paper, a simple modification of the internal dissipation term in coupled thermoplastic finite element equations is presented. A modified form of the heat capacity and the thermomechanical coupling matrices are derived. These modifications are based on a decomposition of the internal dissipation term into two parts, which depend on the total strain rate and the rate of temperature change, respectively.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/cnm.1640110110
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  • 46
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    Digitale Medien
    Conference diary (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 91-92 
    Details
    ISSN: 1069-8299
    Schlagwort(e): Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik , Technik allgemein
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/cnm.1640110112
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  • 47
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    Digitale Medien
    Announcements (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 93-94 
    Details
    ISSN: 1069-8299
    Schlagwort(e): Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik , Technik allgemein
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/cnm.1640110113
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  • 48
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    Digitale Medien
    Books received (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 95-95 
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    ISSN: 1069-8299
    Schlagwort(e): Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik , Technik allgemein
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/cnm.1640110114
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  • 49
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    Investigation of equilibrium states of viscoelastic circular plates by the deformation map technique (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 73-90 
    Details
    ISSN: 1069-8299
    Schlagwort(e): circular plate ; viscoelasticity ; equilibrium states ; deformation map ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik , Technik allgemein
    Notizen: The geometrically non-linear response of a circular plate is investigated by means of a ‘deformation map’. The plate is subjected to static radial forces and bending moments, both uniformly distributed along the supported edges, in addition to a transverse load. The deformation map gives the complete picture for the investigated structure. The classical formulation of large deformation for the above-mentioned problem goes back to Timoshenko (1940). To create a deformation map, it is necessary to convert the boundary value problem into an initial value problem (Cauchy's problem). The Runge-Kutta (RK) method can then be used to solve numerically the equilibrium equations for the above-mentioned circular plate. In the paper several kinds of transverse loading are considered and their influence on the plate response is examined. It is shown that in some cases the plate's behaviour is chaotic-like (unpredictable), in the sense that various equilibrium states are possible for a certain given set of loads. Yet, it is shown that the viscoelasticity reduces the range of the possible equilibrium states, and thus stabilizes the system.
    Zusätzliches Material: 6 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/cnm.1640110111
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  • 50
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    Masthead (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995) 
    Details
    ISSN: 1069-8299
    Schlagwort(e): Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik , Technik allgemein
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/cnm.1640110201
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  • 51
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    Announcement (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. iii 
    Details
    ISSN: 1069-8299
    Schlagwort(e): Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik , Technik allgemein
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/cnm.1640110202
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  • 52
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    On understanding and teaching of the finite element method (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 105-115 
    Details
    ISSN: 1069-8299
    Schlagwort(e): finite element method ; conceptual diagrams ; error estimation ; postprocessing ; teaching ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik , Technik allgemein
    Notizen: The success of the finite element method depends on the highly systematic way the analysis is built up, which means that the structure of the theoretical description and the code is transferable between different applications. It is advisable to teach the subject in such a way that this fact is fully exploited. It is a fact that most FE calculations today do not contain a check of the accuracy/quality of the solution. In the teaching of the FE method nothing is more important than the basic knowledge and understanding of the properties and behaviour of the obtained FE solution. The paper deals with the methodology in presenting the method, by use of conceptual diagrams. It also discusses the interpretation of the results from a classical FE analysis and the extraction of high quality information. Finally, error estimation and postprocessing are discussed. The detailed description of the boundary conditions is lost in the FE solution. In the postprocessing stage they should be taken into account once more.
    Zusätzliches Material: 9 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/cnm.1640110204
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  • 53
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    Dispersion properties of simple 3D finite elements (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 97-103 
    Details
    ISSN: 1069-8299
    Schlagwort(e): dispersion relation ; isotropy ; numerical dispersion ; stiffness integration ; zero wave speed ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik , Technik allgemein
    Notizen: The dispersion properties of plane waves, propagating in an infinite uniform mesh with linear cubic 3D finite elements, are investigated. Time discretization is performed with the central-difference time-stepping scheme in combination with lumped mass matrices. The stiffness matrices are integrated analytically with different integration schemes, and dispersion relations are derived. The results show that the stiffness integration scheme can be chosen to reduce dispersion and improve the isotropy of wave propagation. It is also observed that the numerical wave speed becomes zero along certain wave propagation directions for specific wave numbers.
    Zusätzliches Material: 3 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/cnm.1640110203
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  • 54
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    Some conformal map constructs for numerical grids (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 127-135 
    Details
    ISSN: 1069-8299
    Schlagwort(e): conformal mapping ; numerical grids ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik , Technik allgemein
    Notizen: We develop some special conformal maps and related strategies for grid generation in certain ‘difficult’ domains. Of particular interest are non-convex domains, and domains with corners and cusps.
    Zusätzliches Material: 12 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/cnm.1640110206
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  • 55
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    Easy adaptation of a commercial FEM code for self-similarity (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 117-125 
    Details
    ISSN: 1069-8299
    Schlagwort(e): self similarity ; FEM ; plasticity ; crack growth ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik , Technik allgemein
    Notizen: Self-similar situations are idealized states often referred to in continuum mechanics. Such a situation is generally expected when the formulated problem only involves one significant length parameter. The state at a stationary or at a steadily moving concentrated load may be self-similar. In heat conductivity, the progressive phase transformation near a point-shaped heat source results in a self-similar situation. The problem may be non-linear and history-dependent. Thus, an incremental theory is needed, generally implying that the load has to be applied in small increments. However, at self-similarity the solutions for different loads are similar. The final solution therefore includes its own history, which may be exploited.This short communication demonstrates how an available FEM code (including many commercial codes) may be conveniently used for investigations of self-similar situations in solid mechanics. Quasistatic elastic-plastic problems are considered. The theory covers a general material behaviour including large strains and large deformations. The FEM code must allow for a user-defined material. The technique is demonstrated on a problem for an edge crack growing while the scale of yielding is large. The result is compared with calculations using a node relaxation technique.
    Zusätzliches Material: 4 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/cnm.1640110205
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  • 56
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    On the pseudomaterial approach for the analysis of transient forming processes (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 137-148 
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    ISSN: 1069-8299
    Schlagwort(e): pseudomaterial ; forming processes ; porous wall ; moving surfaces ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik , Technik allgemein
    Notizen: A fixed-mesh method for the analysis of transient forming processes is presented. The mesh covers material regions and zones through which the material may flow. These last zones are identified by a pseudomaterial with relatively small physical parameters. During time processing, the interface between both materials is followed by an arbitrary Lagrangian mesh. This technique appears to be suitable for the treatment of moving surfaces with sharp corners. A particular boundary condition for the Navier-Stokes equations is also introduced in order to model a porous wall.
    Zusätzliches Material: 6 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/cnm.1640110207
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  • 57
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    A note on FEM buckling analysisThis paper is dedicated to R. L. Taylor on the occasion of his 60th birthday. (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 149-158 
    Details
    ISSN: 1069-8299
    Schlagwort(e): FEM ; stability analysis ; algorithms ; shell structures ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik , Technik allgemein
    Notizen: The investigation of the non-linear response of shell-like structures requires insight into stability behaviour. In the paper we compare two strategies to compute singular points based on different eigenvalue problems. We show a simple algorithm to calculate critical load factors A used in engineering buckling analysis from the eigenvalues of the standard eigenvalue problem (KT - ω1) ϕ = 0. Some numerical examples illustrate the derived results and algorithms.
    Zusätzliches Material: 3 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/cnm.1640110208
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  • 58
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    On the assumed displacement fields of a shallow curved shell finite element (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 159-166 
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    ISSN: 1069-8299
    Schlagwort(e): assumed displacement fields ; shallow curved shell ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik , Technik allgemein
    Notizen: An essential requirement for a satisfactory curved shell finite element is a capability for exact representation of rigid body movements: otherwise serious difficulties can occur, as is well known from early developments in shell finite element analysis. It is shown in this paper that appropriate assumed displacement fields for a particular shallow curved shell finite element with 18 degrees of freedom can be obtained in a very simple, yet apparently novel, way which permits the exact recovery of all rigid body movements. The shallow curved shell finite element considered here is constructed on a triangular flat facet approximation to a general thin elastic shell; it has quadratic middle surface geometry to allow for accurate modelling of arbitrary curvatures.
    Zusätzliches Material: 2 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/cnm.1640110209
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  • 59
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    An automatic procedure for mixed-mode crack growth analysis (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 167-177 
    Details
    ISSN: 1069-8299
    Schlagwort(e): boundary element method ; crack growth ; fracture mechanics ; stress intensity factors ; hypersingular ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik , Technik allgemein
    Notizen: In the paper the application of the dual boundary element method to three-dimensional crack growth problems is presented. A procedure for remeshing of the free surfaces is presented to allow the simulation of surface breaking crack growth.
    Zusätzliches Material: 11 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/cnm.1640110210
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  • 60
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    On boundary conditions for unbounded flows (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 179-185 
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    ISSN: 1069-8299
    Schlagwort(e): finite elements ; fluid flow ; open boundaries ; Sommerfield boundary conditions ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik , Technik allgemein
    Notizen: We examine a method to impose boundary conditions on arbitrary boundaries, introduced to make domains of infinite extent finite for the purpose of numerical calculations, when a finite element discretization based on linear, bilinear or trilinear elements is used, in one, two or three dimensions, respectively. In particular, we look at the so-called ‘free’ boundary condition, which consists in retaining the boundary integrals generated by the weighted-residuals formulation along the open boundaries and adding them to the stiffness matrix. We show that this procedure is exactly equivalent to imposing on the boundary nodes a Sommerfeld radiation condition in one dimension, and a slightly modified form of the Sommerfeld boundary condition in two and three dimensions. We also show that the procedure is not applicable to the purely elliptic case.
    Zusätzliches Material: 3 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/cnm.1640110211
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  • 61
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    Announcements (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 189-190 
    Details
    ISSN: 1069-8299
    Schlagwort(e): Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik , Technik allgemein
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/cnm.1640110213
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  • 62
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    Digitale Medien
    Conference diary (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 187-188 
    Details
    ISSN: 1069-8299
    Schlagwort(e): Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik , Technik allgemein
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/cnm.1640110212
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  • 63
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    Digitale Medien
    Masthead (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995) 
    Details
    ISSN: 1069-8299
    Schlagwort(e): Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik , Technik allgemein
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/cnm.1640110301
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  • 64
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    Structural improvement of planar triangulations: Some constraints and practical issues (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 191-198 
    Details
    ISSN: 1069-8299
    Schlagwort(e): triangulations ; mesh relaxation ; computational geometry ; planar mesh generation ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik , Technik allgemein
    Notizen: Recent advances in planar mesh generation of arbitrary domains incorporate methods for placing points as well as connecting them into a triangulation. Postprocessing techniques such as Laplacian smoothing and mesh relaxation enhance the shape of triangles in these meshes but do not address the construction of meshes near boundaries or provide a criterion to determine the number of interior points of the initial triangulation. The paper addresses these issues by investigating the construction of degree-6 triangulations, the primary goal of the mesh relaxation method.
    Zusätzliches Material: 7 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/cnm.1640110302
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  • 65
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    Distributed finite element structural analysis using the client-server model (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 227-233 
    Details
    ISSN: 1069-8299
    Schlagwort(e): finite element analysis ; distributed computing ; structures ; client-server model ; remote procedure calls ; structural mechanics ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik , Technik allgemein
    Notizen: The paper presents a distributed computing approach for concurrent finite element analysis of truss structures. The client-server model of distributed computation is applied to the plane frame finite element algorithm and implemented on SUN workstations. The remote procedure call combined with the ability to create threads of computation allows one to efficiently implement distributed and concurrent programs. The present approach is demonstrated through a typical truss structure to illustrate the details of the implementation. This approach can be used for very large finite element systems.
    Zusätzliches Material: 4 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/cnm.1640110305
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  • 66
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    Fluid flows around turbomachinery using an explicit pseudo-temporal Euler FEM (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 199-211 
    Details
    ISSN: 1069-8299
    Schlagwort(e): SUPG ; Petrov-Galerkin methods ; finite elements ; explicit scheme ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik , Technik allgemein
    Notizen: This work is devoted to the simulation by finite elements of nearly incompressible inviscid flows in real 3D geometries, by means of an Euler code based on the SUPG (streamline upwind Petrov-Galerkin) method, explicit forward Euler pseudo-temporal time integration and periodic and absorbing boundary conditions, among other features. The main goal is the application to flow around turbomachinery, with special emphasis on the performance analysis of a given machine, that involves several numerical computations at different operation points. Finally, these results are summarized in the form of characteristic curves.
    Zusätzliches Material: 14 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/cnm.1640110303
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  • 67
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    A posteriori finite element method error estimates for fourth-order problems (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 213-226 
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    ISSN: 1069-8299
    Schlagwort(e): a posteriori error estimates ; asymptotic exactness ; finite elements ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik , Technik allgemein
    Notizen: A posteriori error estimation for typical Euler-Bernoulli beam bending problems is developed using a recovery operator based on a smoothing technique that is applied in the context of one-dimensional fourth-order problems. The development exploits a discrete superconvergence property of the ‘bending moments’ of the trial space interpolant of a polynomial solution of sufficiently low degree at certain Gauss points, and the superconvegence property of the energy norm difference of the trial space interpolant (of the weak solution) and the finite element approximation. An asymptotically exact error estimator is developed.
    Zusätzliches Material: 1 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/cnm.1640110304
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  • 68
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    A superposition method for the solution of crack problems (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 243-254 
    Details
    ISSN: 1069-8299
    Schlagwort(e): fracture ; boundary elements ; superposition ; stress intensity factor ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik , Technik allgemein
    Notizen: We discuss a two-step superposition method for calculating linear elastic stress intensity factors. The procedure requires the solution to the full cracked problem and the solution to a problem on the same mesh assuming the singularity due to a crack tip in an infinite region. We show that this is equivalent to the well known subtraction of singularity method if the two solutions are characterized by crack tip stress. The advantages of our procedure are that no modifications need to be made to a standard computer program and that once one singular solution is available on a given cracked mesh, solutions with different boundary conditions on the same mesh may be obtained in one step without including any singular crack effects. The mesh required to represent the singular crack tip field may also be studied independently of the complete problem. The additional computational cost of a two-step procedure is minimal since the solution matrix from step one may be reused with a new right-hand side. Numerical experiments using the boundary element method demonstrate the high accuracy and simplicity of the superposition approach.
    Zusätzliches Material: 5 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/cnm.1640110307
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  • 69
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    Selecting upwind parameters for improved iterative performance (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 235-242 
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    ISSN: 1069-8299
    Schlagwort(e): upwinding ; iterative methods ; convection-diffusion ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik , Technik allgemein
    Notizen: The effect of upwinding on iterative performance of convection-diffusion problems is investigated. An analysis of the iterative method considered here leads to a criterion for selecting the optimal upwinding parameter to improve iterative performance for a class of two-dimensional convection-diffusion problems. Supporting numerical experiments are presented.
    Zusätzliches Material: 2 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/cnm.1640110306
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  • 70
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    Digitale Medien
    A numerical solution for dynamic interaction between rigid wheel and flexible beam (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 267-279 
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    ISSN: 1069-8299
    Schlagwort(e): dynamic interaction ; rigid wheel ; flexible beam ; contact force ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik , Technik allgemein
    Notizen: A numerical method is presented for the analysis of dynamic interaction between rigid wheel and flexible beam. In contrast to traditional approaches, the wheel nominal motion as well as the contact force are considered here as unknowns. The correct contact force between the wheel and the beam is computed by iteratively reducing the constraint error towards zero, and a simple time integration is employed for the solution of equations of motion. Convergence of the iterative scheme is analysed, and numerical simulations are conducted to demonstrate the accuracy of the solution.
    Zusätzliches Material: 10 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/cnm.1640110309
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  • 71
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    The h-, p- and hp-versions of the BEM in elasticity: Numerical results (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 255-265 
    Details
    ISSN: 1069-8299
    Schlagwort(e): boundary element method ; error estimation ; hp-version ; Galerkin BEM ; numerical results ; elasticity ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik , Technik allgemein
    Notizen: The paper investigates the convergence of the h-, p- and hp-versions of a variational symmetric boundary element method (BEM) in plane elasticity by numerical experiments. The study discusses mixed boundary value problems on polygonal domains, i.e. problems for which the exact solution is analytic except in a finite number of points. The convergence of the error in energy norm is displayed for all versions of the BEM. All results are also compared with those obtained by the corresponding finite element methods. The theoretically predicted asymptotic convergence rates for all versions of the method can be observed in the numerical experiments. A comparison of computer times is given as well.
    Zusätzliches Material: 7 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/cnm.1640110308
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    Background to bench marks, edited by G. E. O. Davies, R. T. Fenner and R. W. Lewis, NAFEMS, Birniehill, East Kilbride, Glasgow. ISBN 1 874376 10 7 (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 281-282 
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    ISSN: 1069-8299
    Schlagwort(e): Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik , Technik allgemein
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/cnm.1640110310
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  • 73
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    Conference diary (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 283-284 
    Details
    ISSN: 1069-8299
    Schlagwort(e): Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik , Technik allgemein
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/cnm.1640110311
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  • 74
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    Announcements (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 285-286 
    Details
    ISSN: 1069-8299
    Schlagwort(e): Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik , Technik allgemein
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/cnm.1640110312
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  • 75
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    Masthead (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995) 
    Details
    ISSN: 1069-8299
    Schlagwort(e): Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik , Technik allgemein
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/cnm.1640110401
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  • 76
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    On the eigenvalues basic to the analytical solution of convective heat transfer with axial diffusion effects (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 287-296 
    Details
    ISSN: 1069-8299
    Schlagwort(e): eigenvalues ; integral transforms ; analytical methods ; convection ; Sturm-Liouville system ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik , Technik allgemein
    Notizen: The integral transform method is employed in the analytical solution of the non-classical eigenvalue problem that appears in connection with the analysis of forced convection in ducts, including the effect of fluid heat diffusion in the axial direction. The related eigenfunctions are expanded in terms of eigenfunctions from a simpler auxiliary eigenvalue problem, and the original eigenvalues are determined from the associated matrix eigensystem analysis. Convergence rates of the proposed solutions are illustrated and reference results established for different values of the governing parameters.
    Zusätzliches Material: 4 Tab.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/cnm.1640110402
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    On the evaluation of nearly singular kernel integrals in boundary element analysis (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 331-337 
    Details
    ISSN: 1069-8299
    Schlagwort(e): nearly singular kernel integrals ; curved boundary elements ; numerical integration ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik , Technik allgemein
    Notizen: The paper concentrates on the numerical evaluation of nearly singular kernel integrals commonly encountered in boundary element analysis. Limitations of the method developed recently by Huang and Cruse (1993) for the direct evaluation of nearly singular kernel integrals are analysed and pointed out. A general method is developed that extends the idea for all practical cases. Example results are presented, demonstrating the effectiveness of the method.
    Zusätzliches Material: 3 Tab.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/cnm.1640110406
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  • 78
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    Pseudoconsistent load vector and mass matrix for the discrete Kirchhoff triangle and the discrete shear triangle elements (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 317-330 
    Details
    ISSN: 1069-8299
    Schlagwort(e): DKT and DST elements ; pseudo consistent load vector ; pseudo consistent mass matrix ; plate bending elements ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik , Technik allgemein
    Notizen: Many finite elements based on Reissner-Mindlin plate bending theory with discrete constraints have been developed in the past few years. This approach avoids the C1 continuity required by the classical Kirchhoff plate theory. However, in those elements the shape functions for deflections (or their derivatives) are not integrated. Particularly in DKT (discrete Kirchhoff triangle) and in DST (discrete shear triangle) elements, the lateral deflections are defined only on the boundaries. In the paper we briefly discuss the definition of the transverse displacement for these elements, and present a simple approach to define a pseudoconsistent load vector and mass matrix.
    Zusätzliches Material: 4 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/cnm.1640110405
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  • 79
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    Comparison of symbolic and numerical integration methods for an assumed-stress hybrid shell element (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 307-316 
    Details
    ISSN: 1069-8299
    Schlagwort(e): hybrid shell finite element ; symbolic integration ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik , Technik allgemein
    Notizen: Hybrid shell elements have long been regarded with reserve by the commercial finite element developers despite the high degree of reliability and accuracy associated with such formulations. The fundamental reason is the inherent higher computational cost of the hybrid approach as compared to the displacement-based formulations. However, a noteworthy factor in favour of hybrid elements is that numerical integration to generate element matrices can entirely be avoided by the use of symbolic integration. In this paper, the use of the symbolic computational approach is presented for an assumed-stress hybrid shell element with drilling degrees of freedom, and the significant time saving achieved is demonstrated through an example.
    Zusätzliches Material: 2 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/cnm.1640110404
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  • 80
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    A semi-analytic method for dynamic response analysis based on Gurtin's variational principle (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 297-306 
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    ISSN: 1069-8299
    Schlagwort(e): semi-analytic method ; dynamic response ; convolution ; variational principle ; series ; finite element method ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik , Technik allgemein
    Notizen: In the paper a semi-analytic approach for solving dynamic response problems is developed which is based on Gurtin's convolution-type variational principle. A finite element discretization in the space domain and a series representation in the time domain are considered. This approach overcomes the shortcomings of existing methods yet utilizes their advantages for solving dynamic response problems. The example of a beam shows that this new approach is a very effective method in obtaining solutions for dynamic response problems. The paper also concentrates on utilizing time domain series for various boundary conditions, so that solutions calculated by this approach have a very high accuracy and efficiency.
    Zusätzliches Material: 1 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/cnm.1640110403
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  • 81
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    Digitale Medien
    Pressure-dependent plasticity models: Loading-unloading criteria and the consistent linearization of an integration algorithm (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 339-345 
    Details
    ISSN: 1069-8299
    Schlagwort(e): numerical integration ; plasticity ; pressure-dependent plasticity ; porous metals ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik , Technik allgemein
    Notizen: A general methodology for the numerical integration of pressure-dependent plasticity models is developed, and the corresponding ‘linearization moduli’ are derived.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/cnm.1640110407
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  • 82
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    Digitale Medien
    New stress recovery formula for B-bar methods (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 347-353 
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    ISSN: 1069-8299
    Schlagwort(e): assumed strain methods ; Hu-Washizu principle ; stress recovery ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik , Technik allgemein
    Notizen: An alternative justification of the B-bar procedure using the Hu-Washizu variational principle is presented. In contrast to previous work, the derivation starts from the three groups of algebraic equations (strain-displacement equations, stress-strain equations and equations of equilibrium) obtained by discretization of the Hu-Washizu functional. Based on an appropriate assumption, these equations can be manipulated to yield the element stiffness matrix in the form typical of the B-bar procedure. This approach directly leads to a stress-recovery formula different from the one suggested before. The theory is illustrated by application to a family of quadrilateral plane elements.
    Zusätzliches Material: 1 Tab.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/cnm.1640110408
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  • 83
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    Digitale Medien
    Permanent heavy waves in circular-shaped channels (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 355-362 
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    ISSN: 1069-8299
    Schlagwort(e): permanent heavy waves ; circular shaped channels ; conformal mapping ; Fatou's method ; Levi-Civita's decomposition ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik , Technik allgemein
    Notizen: Because of the earth's curvature, all existing channels have a curvature. E. Zeidler gave an existence and uniqueness proof for permanent heavy and capillar-heavy waves in such circular shaped channels. Based on this proof and on a general computational method for constructing the solutions numerically, the case of permanent heavy waves in circular-shaped channels is considered in this work.
    Zusätzliches Material: 2 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/cnm.1640110409
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  • 84
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    Digitale Medien
    Introduction to finite and boundary element methods for engineers, by G. Beer and J. O. Watson, John Wiley and Sons, Chichester, U.K. ISBN 0-471-92813-5. £29.95/$49.95, Program disk £19.95 (extra) (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 373-374 
    Details
    ISSN: 1069-8299
    Schlagwort(e): Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik , Technik allgemein
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/cnm.1640110411
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  • 85
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    Digitale Medien
    Conference diary (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 375-377 
    Details
    ISSN: 1069-8299
    Schlagwort(e): Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik , Technik allgemein
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/cnm.1640110412
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  • 86
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    Digitale Medien
    Masthead (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995) 
    Details
    ISSN: 1069-8299
    Schlagwort(e): Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik , Technik allgemein
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/cnm.1640110501
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  • 87
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    Digitale Medien
    Announcements (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 379-381 
    Details
    ISSN: 1069-8299
    Schlagwort(e): Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik , Technik allgemein
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/cnm.1640110413
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  • 88
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    On the convergence of the generalized matrix multisplitting relaxed methods (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 363-371 
    Details
    ISSN: 1069-8299
    Schlagwort(e): matrix multisplitting ; relaxed method ; convergence ; divergence ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik , Technik allgemein
    Notizen: In this paper, I discuss the convergence and divergence rates for a class of generalized matrix multisplitting relaxation methods in a detailed manner. In particular, when the coefficient matrix is an L-matrix, I obtain several sufficient and necessary conditions ensuring the convergence of these methods.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/cnm.1640110410
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  • 89
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    Digitale Medien
    An independent refinement and integration procedure in multiregion finite element analysis (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 383-390 
    Details
    ISSN: 1069-8299
    Schlagwort(e): finite elements analyses ; global and local analyses ; multiregion ; interfaces ; interpolation functions ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik , Technik allgemein
    Notizen: An independent refinement and integration procedure is developed to couple together independently modelled (global and local) regions in a single analysis. The finite element models can have different levels of refinement and the nodes along the interface between them need not coincide with one another. A spline interpolation function that satisfies the linear isotropic plate-bending differential equation is used to relate the local model interface nodal displacements to the global model interface displacements. The proposed independent refinement and integration procedure is validated by applying it to problems involving in-plane and out-of-plane deformations.
    Zusätzliches Material: 2 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/cnm.1640110502
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  • 90
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    A quadratic boundary element for potential problems in 2D with no numerical integration (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 391-401 
    Details
    ISSN: 1069-8299
    Schlagwort(e): boundary element method ; two-dimensional potential problems ; logarithmic kernel ; derivative kernal ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik , Technik allgemein
    Notizen: Both the logarithmic and derivative kernel integrations for potential problems, solved with quadratic isoparametric boundary elements, contain quartic functions of the integration parameter. It is shown that such functions can be written as the product of two quadratic functions with real coefficients. The derivative kernel integration is then represented as the sum of two integrals, which can be evaluated analytically. The logarithmic kernel integration can be similarly split but needs a Taylor series expansion of the Jacobian of the integration to enable analytical integration. The use of this Taylor series expansion means that the method presented is limited to problems involving weakly curved elements.
    Zusätzliches Material: 1 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/cnm.1640110503
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  • 91
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    Digitale Medien
    The variationally correct rate of convergence for a two-noded beam element, or why residual bending flexibility correction is an extravariational trick (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 403-407 
    Details
    ISSN: 1069-8299
    Schlagwort(e): finite element method ; residual bending flexibility ; convergence ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik , Technik allgemein
    Notizen: In this paper I re-examine the mechanics of the residual bending flexibility correction and show that it is an extravariational trick.
    Zusätzliches Material: 2 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/cnm.1640110504
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  • 92
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    Digitale Medien
    Discrete element dynamic response of elastoplastic shells subjected to impulsive loading (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 417-426 
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    ISSN: 1069-8299
    Schlagwort(e): discrete elements ; dynamic analysis ; impact ; impulsive loads ; elastoplastic response ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik , Technik allgemein
    Notizen: The determination of the dynamic response of plate and shell structures is carried out employing a discrete representation of the continuum, associated with an explicit integration scheme in the time domain. Comparisons with experimental results certify the accuracy and reliability of the proposed method.
    Zusätzliches Material: 10 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/cnm.1640110506
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  • 93
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    A robust implementation of Zienkiewicz and Zhu's local patch recovery method (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 427-434 
    Details
    ISSN: 1069-8299
    Schlagwort(e): finite element solver ; local system ; ill-conditioning ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik , Technik allgemein
    Notizen: While implementing Zienkiewicz and Zhu's superconvergent patch recovery method in our finite element solver, we came across two difficulties: rank deficiency of the local system to be solved, and ill-conditioning. The first problem was solved by increasing the number of sampling points and the second by using LU decomposition with partial pivoting.
    Zusätzliches Material: 9 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/cnm.1640110507
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  • 94
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    On the solution of second-order post-buckling fields (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 443-453 
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    ISSN: 1069-8299
    Schlagwort(e): initial post-buckling ; second-order fields ; iteration ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik , Technik allgemein
    Notizen: Second-order post-buckling fields emanate from the solutions of a constrained minimization problem. Two iterative solution algorithms for this specific type of constrained problem are described. A classical augmented Lagrangian algorithm is compared with a simpler one utilizing the specific feature of the initial post-buckling analysis. Numerical examples of prismatic plate-type structures are presented.
    Zusätzliches Material: 7 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/cnm.1640110509
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  • 95
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    Digitale Medien
    Generalized Laplacian smoothing of unstructured grids (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 455-464 
    Details
    ISSN: 1069-8299
    Schlagwort(e): Laplacian smoothing ; grid smoothing ; surface grids ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik , Technik allgemein
    Notizen: In this note we point out the natural choice of smoothing by use of a metric tensor to maintain control of the local element stretch. The extension to grids on surfaces in 3D is straightforward. Numerical examples are given.
    Zusätzliches Material: 9 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/cnm.1640110510
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  • 96
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    Digitale Medien
    2D or 3D frictional contact algorithms and applications in a large deformation context (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 409-416 
    Details
    ISSN: 1069-8299
    Schlagwort(e): contact ; friction ; finite element method ; large deformation ; augmented Lagrangian method ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik , Technik allgemein
    Notizen: The paper is devoted to the analysis of two- or three-dimensional contact problems with Coulomb friction and large deformation. The classical approach is based on two minimum principles or two variational inequalities: the first for unilateral contact and the second for friction. A coupled approach using only one principle or one inequality is presented. This new approach allows us to extend the notion of normality law to dissipative behaviours with a non-associated flow rule, such as surface friction. Non-differentiable contact potentials are regularized by means of the augmented Lagrangian method. Using the C++ language, an object-oriented finite element database is created, which allows us to implement the contact and friction in an existing code in a very simple and neat way. Numerical examples are carried out in many difficult cases such as shock absorber and three-dimensional contact. The numerical results prove that this approach is robust and efficient concerning numerical stability.
    Zusätzliches Material: 7 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/cnm.1640110505
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  • 97
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    On a novel mesh for the regular boundary layers arising in advection-dominated transport in two dimensions (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 435-441 
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    ISSN: 1069-8299
    Schlagwort(e): regular boundary layers ; ∊-uniform numerical method ; advection-dominated transport ; piecewise uniform mesh ; singular perturbations ; numerical experiments ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik , Technik allgemein
    Notizen: Upwind finite difference operators on uniform meshes are well known to be unsuitable for the numerical solution of singularly perturbed partial differential equations, in the sense that, in the neighbourhood of the boundary layers, the error in the numerical approximation may increase as the mesh is refined. Recently, on the other hand, it has been predicted theoretically that the use of upwind finite difference operators on specially designed piecewise uniform meshes guarantees the decrease of the nodal error to zero as the number of mesh elements increases. In the paper the general theorem is quoted and its prediction is validated by numerical experiment for a specific linear advection-dominated transport equation in two dimensions. Experimental values of the convergence rate are obtained, which also agree with the theoretical estimates.
    Zusätzliches Material: 3 Ill.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/cnm.1640110508
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  • 98
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    Digitale Medien
    Conference diary (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 475-476 
    Details
    ISSN: 1069-8299
    Schlagwort(e): Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik , Technik allgemein
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/cnm.1640110512
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  • 99
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    Masthead (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995) 
    Details
    ISSN: 1069-8299
    Schlagwort(e): Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik , Technik allgemein
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/cnm.1640110601
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  • 100
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    Announcements (1995)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 11 (1995), S. 477-478 
    Details
    ISSN: 1069-8299
    Schlagwort(e): Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik , Technik allgemein
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1002/cnm.1640110513
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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