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  • 1
    Electronic Resource
    Electronic Resource
    A gradient method for the matrix eigenvalue problemAx=λBx (1974)
    Springer
    Numerische Mathematik 22 (1974), S. 1-16 
    Details
    ISSN: 0945-3245
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract LetA andB ben×m matrices. A gradient method for the minimization of the functionalF(x)=‖Ax−(〈Ax, Bx〉/〈Bx, Bx〉)Bx‖2 is developed. The minima ofF are the eigenvectors of the eigenproblemAx=λBx. The concept of a non-defective eigenvalue for this generalized eigenvalue problem is developed. It is then shown that geometric convergence is attained for non-defective eigenvalues. A convergence rate analysis is given where it is shown that the rapidity of convergence of the gradient method to an eigenvalue λ depends on the degree of non-defectiveness of λ and the singular values ofA−λB.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01436617
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Convergence and comparison analysis of some numerical Schwarz methods (1989)
    Springer
    Numerische Mathematik 56 (1989), S. 123-138 
    Details
    ISSN: 0945-3245
    Keywords: AMS(MOS): 65N99 ; CR: G1.8
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary Domain decomposition methods are a natural means for solving partial differential equations on multi-processors. The spatial domain of the equation is expressed as a collection of overlapping subdomains and the solution of an associated equation is solved on each of these subdomains. The global solution is then obtained by piecing together the subsolutions in some manner. For elliptic equations, the global solution is obtained by iterating on the subdomains in a fashion that resembles the classical Schwarz alternating method. In this paper, we examine the convergence behavior of different subdomain iteration procedures as well as different subdomain approximations. For elliptic equations, it is shown that certain iterative procedures are equivalent to block Gauss-Siedel and Jacobi methods. Using different subdomain approximations, an inner-outer iterative procedure is defined.M-matrix analysis yields a comparison of different inner-outer iterations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01409781
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  • 3
    Electronic Resource
    Electronic Resource
    Improved vector FEM solutions of Maxwell's equations using grid pre-conditioning (1997)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 40 (1997), S. 3815-3837 
    Details
    ISSN: 0029-5981
    Keywords: Maxwell's equations ; wave equation ; finite element ; vector finite element ; Whitney element ; grid relaxation ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The Time Domain Vector Finite Element Method is a promising new approach for solving Maxwell's equations on unstructured triangular grids. This method is sensitive to the quality, or condition, of the grid. In this study grid pre-conditioning techniques, such as edge swapping, Laplacian smoothing, and energy minimization, are shown to improve the accuracy of the solution and also reduce the overall computational effort. © 1997 John Wiley & Sons, Ltd.
    Additional Material: 12 Ill.
    Type of Medium: Electronic Resource
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    Paper (German National Licenses)
  • 4
    Electronic Resource
    Electronic Resource
    Some ideas for decomposing the domain of elliptic partial differential equations in the schwarz process (1986)
    New York, NY [u.a.] : Wiley-Blackwell
    Communications in Applied Numerical Methods 2 (1986), S. 245-249 
    Details
    ISSN: 0748-8025
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1630020304
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    Paper (German National Licenses)
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  • 5
    Electronic Resource
    Electronic Resource
    Expanding stability regions of explicit advective-diffusive finite difference methods by Jacobi preconditioning (1995)
    New York, NY [u.a.] : Wiley-Blackwell
    Numerical Methods for Partial Differential Equations 11 (1995), S. 339-353 
    Details
    ISSN: 0749-159X
    Keywords: Mathematics and Statistics ; Numerical Methods
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics
    Notes: Explicit time differencing methods for solving differential equations are advantageous in that they are easy to implement on a computer and are intrinsically very parallel. The disadvantage of explicit methods is the severe restrictions that are placed on stable time-step intervals. Stability bounds for explicit time differencing methods on advective-diffusive problems are generally determined by the diffusive part of the problem. These bounds are very small and implicit methods are used instead. The linear systems arising from these implicit methods are generally solved by iterative methods. In this article we develop a methodology for increasing the stability bounds of standard explicit finite differencing methods by combining explicit methods, implicit methods, and iterative methods in a novel way to generate new time-difference schemes, called preconditioned time-difference methods. A Jacobi preconditioned time differencing method is defined and analyzed for both diffusion and advection-diffusion equations. Several computational examples of both linear and nonlinear advective-diffusive problems are solved to demonstrate the accuracy and improved stability limits. © 1995 John Wiley & Sons, Inc.
    Additional Material: 7 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/num.1690110404
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  • 6
    Book
    Book
    3rd SIAM conference on parallel processing for scientific computing. Proceedings (1989)
    Philadelphia, PA :SIAM,
    Details
    Title: 3rd SIAM conference on parallel processing for scientific computing. Proceedings
    Contributer: Rodrigue, Garry
    Publisher: Philadelphia, PA :SIAM,
    Year of publication: 1989
    Pages: 428 S.
    Type of Medium: Book
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    Zuse Institute Berlin get availability status
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