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  • 1
    Electronic Resource
    Electronic Resource
    On the preconditioning of matrices with skew-symmetric splittings (2000)
    Springer
    Numerical algorithms 25 (2000), S. 223-239 
    Details
    ISSN: 1572-9265
    Keywords: preconditioning ; skew-symmetry ; incomplete orthogonal ; factorization
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract The rates of convergence of iterative methods with standard preconditioning techniques usually degrade when the skew-symmetric part S of the matrix is relatively large. In this paper, we address the issue of preconditioning matrices with such large skew-symmetric parts. The main idea of the preconditioner is to split the matrix into its symmetric and skew-symmetric parts and to “invert” the (shifted) skew-symmetric matrix. Successful use of the method requires the solution of a linear system with matrix I+S. An efficient method is developed using the normal equations, preconditioned by an incomplete orthogonal factorization. Numerical experiments on various systems arising in physics show that the reduction in terms of iteration count compensates for the additional work per iteration when compared to standard preconditioners.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1016637813615
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    A parallel solver based on the dual Schur decomposition of general finite element matrices (1998)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 28 (1998), S. 23-46 
    Details
    ISSN: 0271-2091
    Keywords: domain decomposition ; parallel algorithms ; finite element ; Lagrange multipliers ; projected GMRES ; 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: A parallel solver based on domain decomposition is presented for the solution of large algebraic systems arising in the finite element discretization of mechanical problems. It is hybrid in the sense that it combines a direct factorization of the local subdomain problems with an iterative treatment of the interface system by a parallel GMRES algorithm. An important feature of the proposed solver is the use of a set of Lagrange multipliers to enforce continuity of the finite element unknowns at the interface. A projection step and a preconditioner are proposed to control the conditioning of the interface matrix.The decomposition of the finite element mesh is formulated as a graph partitioning problem. A two-step approach is used where an initial decomposition is optimized by non-deterministic heuristics to increase the quality of the decomposition.Parallel simulations of a Navier-Stokes flow problem carried out on a Convex Exemplar SPP system with 16 processors show that the use of optimized decompositions and the preconditioning step are keys to obtaining high parallel efficiencies. Typical parallel efficiencies range above 80%. © 1998 John Wiley & Sons, Ltd.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
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    Paper (German National Licenses)
  • 3
    Electronic Resource
    Electronic Resource
    Optimized partitioning of unstructured finite element meshes (1995)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 38 (1995), S. 433-450 
    Details
    ISSN: 0029-5981
    Keywords: mesh partitioning ; finite elements ; parallel computing ; optimization ; heuristics ; frontal method ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: We address the problem of automatic partitioning of unstructured finite element meshes in the context of parallel numerical algorithms based on domain decomposition. A two-step approach is proposed, which combines a direct partitioning scheme with a non-deterministic procedure of combinatorial optimization. In contrast with previously published experiments with non-deterministic heuristics, the optimization step is shown to produce high-quality decompositions at a reasonable compute cost. We also show that the optimization approach can accommodate complex topological constraints and minimization objectives. This is illustrated by considering the particular case of topologically one-dimensional partitions, as well as load balancing of frontal subdomain solvers. Finally, the optimization procedure produces, in most cases, decompositions endowed with geometrically smooth interfaces. This contrasts with available partitioning schemes, and is crucial to some modern numerical techniques based on domain decomposition and a Lagrange multiplier treatment of the interface conditions.
    Additional Material: 12 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620380306
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    Paper (German National Licenses)
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