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  • 1
    Electronic Resource
    Electronic Resource
    A two-level domain decomposition method for the iterative solution of high frequency exterior Helmholtz problems (2000)
    Springer
    Numerische Mathematik 85 (2000), S. 283-308 
    Details
    ISSN: 0945-3245
    Keywords: Mathematics Subject Classification (1991):65N55
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary. We present a Lagrange multiplier based two-level domain decomposition method for solving iteratively large-scale systems of equations arising from the finite element discretization of high-frequency exterior Helmholtz problems. The proposed method is essentially an extension of the regularized FETI (Finite Element Tearing and Interconnecting) method to indefinite problems. Its two key ingredients are the regularization of each subdomain matrix by a complex interface lumped mass matrix, and the preconditioning of the interface problem by an auxiliary coarse problem constructed to enforce at each iteration the orthogonality of the residual to a set of carefully chosen planar waves. We show numerically that the proposed method is scalable with respect to the mesh size, the subdomain size, and the wavenumber. We report performance results for a submarine application that highlight the efficiency of the proposed method for the solution of high frequency acoustic scattering problems discretized by finite elements.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/PL00005389
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  • 2
    Electronic Resource
    Electronic Resource
    Solution of finite element systems on concurrent processing computers (1987)
    Springer
    Engineering with computers 2 (1987), S. 157-165 
    Details
    ISSN: 1435-5663
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics , Technology
    Notes: Abstract A new computer program architecture for the solution of finite element systems using concurrent processing is presented. The basic approach involves the automatic creation of substructures. A host provides control over a set of processors, each of which is assigned initially to one substructure, then dynamically reassigned to the common interface for the solution of the complete system of substructures. Algorithm details are presented fo each phase of the analysis. Results of analysis of large plate bending problems on a hypercube multicomputer are reported. For a system with 2,000 equations, an efficiency of 80 percent of the maximum theoretical value was obtained using 16 processors.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01201263
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Mixed explicit/implicit time integration of coupled aeroelastic problems: Three-field formulation, geometric conservation and distributed solution (1995)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 21 (1995), S. 807-835 
    Details
    ISSN: 0271-2091
    Keywords: CFD ; structures ; aeroelasticity ; parallel processing ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A three-field arbitrary Lagrangian-Eulerian (ALE) finite element/voluem formulation for coupled transient aeroelastic problems is presented. The description includes a rigorous derivation of a geometric conservation law for flow problems with moving boundaries and unstructured deformable meshes. The solution of the coupled governing equations with a mixed explicit (fluid)/implicit (structure) staggered procedure is discussed with particular reference to accuracy, stability, distributed computing, I/O transfers, subcycling and parallel processing. A general and flexible framework for implementing partitioned solution procedures for coupled aeroelastic problems on heterogeneous and/or parallel computational platforms is described. This framework and the explicit/implicit partitioned procedures are demonstrated with the numerical investigation on an iPSC-860 massively parallel processor of the instability of flat panels with infinite aspect ratio in supersonic airstreams.
    Additional Material: 19 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650211004
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  • 4
    Electronic Resource
    Electronic Resource
    Unusual stabilized finite element methods and residual free bubbles (1998)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 27 (1998), S. 159-168 
    Details
    ISSN: 0271-2091
    Keywords: finite element method ; Galerkin method ; residual free bubbles ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: An overview of the unusual stabilized finite element method and of the standard Galerkin method enriched with residual free bubble functions is presented. For the first method a concrete model problem illustrates its application in advective-diffusive-reactive equations and for the second method it is shown how static condensation of residual free bubbles gives rise to mass lumping and selective reduced integration, which are viewed as numerical tricks and can now be derived by the standard Galerkin method without tricks. © 1998 John Wiley & Sons, Ltd.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    A coarse/fine preconditioner for very ill-conditioned finite element problems (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 1715-1723 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: We consider the problem of applying the conjugate gradient method to solve-ill-conditioned large algebraic systems of equations resulting from the finite element discretization of some three-dimensional boundary value problems. We present an effective preconditioner for such systems based on a multigrid technique. We assess its performance with examples borrowed from large flexible aerospace structures.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620280717
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  • 6
    Electronic Resource
    Electronic Resource
    Towards parallel I/O in finite element simulations (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 28 (1989), S. 2541-2553 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: I/O issues in finite element analysis on parallel processors are addressed. Viable solutions for both local and shared memory multiprocessors are presented. The approach is simple but limited by currently available hardware and software systems. Implementation is carried out on a CRAY-2 system. Performance results are reported.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620281105
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    Paper (German National Licenses)
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  • 7
    Electronic Resource
    Electronic Resource
    A method of finite element tearing and interconnecting and its parallel solution algorithm (1991)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 32 (1991), S. 1205-1227 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: A novel domain decomposition approach for the parallel finite element solution of equilibrium equations is presented. The spatial domain is partitioned into a set of totally disconnected subdomains, each assigned to an individual processor. Lagrange multipliers are introduced to enforce compatibility at the interface nodes. In the static case, each floating subdomain induces a local singularity that is resolved in two phases. First, the rigid body modes are eliminated in parallel from each local problem and a direct scheme is applied concurrently to all subdomains in order to recover each partial local solution. Next, the contributions of these modes are related to the Lagrange multipliers through an orthogonality condition. A parallel conjugate projected gradient algorithm is developed for the solution of the coupled system of local rigid modes components and Lagrange multipliers, which completes the solution of the problem. When implemented on local memory multiprocessors, this proposed method of tearing and interconnecting requires less interprocessor communications than the classical method of substructuring. It is also suitable for parallel/vector computers with shared memory. Moreover, unlike parallel direct solvers, it exhibits a degree of parallelism that is not limited by the bandwidth of the finite element system of equations.
    Additional Material: 12 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620320604
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  • 8
    Electronic Resource
    Electronic Resource
    A unified framework for accelerating the convergence of iterative substructuring methods with Lagrange multipliers (1998)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 42 (1998), S. 257-288 
    Details
    ISSN: 0029-5981
    Keywords: parallel computing ; finite elements ; substructures ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The FETI algorithms are a family of numerically scalable substructuring methods with Lagrange multipliers that have been designed for solving iteratively large-scale systems of equations arising from the finite element discretization of structural engineering, solid mechanics, and structural dynamics problems. In this paper, we present a unified framework that simplifies the interpretation of several of the previously presented FETI concepts. This framework has enabled the improvement of the robustness and performance of the transient FETI method, and the design of a new family of coarse operators for iterative substructuring algorithms with Lagrange multipliers. We report on both of these new developments, discuss their impact on the iterative solution of large-scale finite element systems of equations by the FETI method, and illustrate them with a few static and dynamic structural analyses on an IBM SP2 parallel processor. © 1998 John Wiley & Sons, Ltd.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
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    Paper (German National Licenses)
  • 9
    Electronic Resource
    Electronic Resource
    Incorporation of linear multipoint constraints in substructure based iterative solvers. Part 1: a numerically scalable algorithm (1998)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 43 (1998), S. 997-1016 
    Details
    ISSN: 0029-5981
    Keywords: domain decomposition ; multipoint constraints ; numerical scalability ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: We consider the iterative solution by a class of substructuring methods of the large-scale systems of equations arising from the finite element discretization of structural models with an arbitrary set of linear multipoint constraints. We present a methodology for generalizing to such problems numerically scalable substructure based iterative solvers, without interfering with their formulations and their well-established local and global preconditioners. We apply this methodology to the FETI method, and show that the resulting algorithm is numerically scalable with respect to both the substructure and problem sizes. © 1998 John Wiley & Sons, Ltd.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
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    Paper (German National Licenses)
  • 10
    Electronic Resource
    Electronic Resource
    On the general solution by a direct method of a large-scale singular system of linear equations: application to the analysis of floating structures (1998)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 41 (1998), S. 675-696 
    Details
    ISSN: 0029-5981
    Keywords: zero energy modes ; generalized inverse ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: Finding the general solution of a singular system of linear equations requires computing a particular solution and a basis of the null space of the corresponding singular matrix. In this paper, we consider the case where the singular matrix is large and sparse, and the application calls for a direct solution method. We highlight the dependence of straightforward factorization algorithms on an arbitrary constant that can influence the correctness of the computed solution, and describe a family of improved direct solution methods that alleviate this problem. For structural mechanics applications, we propose a hybrid geometric-algebraic method that is more robust than the purely algebraic direct methods that are currently used for solving singular sparse systems of equations. We illustrate the potential of our proposed solution algorithms with examples from structural mechanics and domain-decomposition-based iterative solvers. © 1998 John Wiley & Sons, Ltd.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
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