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Marcus Sarkis - One of the best experts on this subject based on the ideXlab platform.

  • restricted overlapping balancing Domain Decomposition Methods and restricted coarse problems for the helmholtz problem
    Computer Methods in Applied Mechanics and Engineering, 2007
    Co-Authors: Junghan Kimn, Marcus Sarkis
    Abstract:

    Overlapping balancing Domain Decomposition Methods and their combination with restricted additive Schwarz Methods are proposed for the Helmholtz equation. These new Methods also extend previous work on non-overlapping balancing Domain Decomposition Methods toward simplifying their coarse problems and local solvers. They also extend restricted Schwarz Methods, originally designed to overlapping Domain Decomposition and Dirichlet local solvers, to the case of non-overlapping Domain Decomposition and/or Neumann and Sommerfeld local solvers. Finally, we introduce coarse spaces based on partitions of unity and planes waves, and show how oblique projection coarse problems can be designed from restricted additive Schwarz Methods. Numerical tests are presented.

  • obdd overlapping balancing Domain Decomposition Methods and generalizations to the helmholtz equation
    2007
    Co-Authors: Junghan Kimn, Marcus Sarkis
    Abstract:

    Jung-Han Kimn and Marcus Sarkis 1 Department of Mathematics and the Center for Computation and Technology, Louisiana State University, Baton Rouge, LA, 70803, USA. kimn@math.lsu.edu 2 Instituto Nacional de Matematica Pura e Aplicada, Rio de Janeiro, Brazil, and Worcester Polytechnic Institute, Worcester, MA 01609, USA. msarkis@fluid.impa.br. Research supported in part by CNPQ (Brazil) under grant 305539/2003-8 and by the U.S. NSF under grant CGR 9984404.

Jongho Park - One of the best experts on this subject based on the ideXlab platform.

Chang-ock Lee - One of the best experts on this subject based on the ideXlab platform.

Danping Yang - One of the best experts on this subject based on the ideXlab platform.

  • convergence rate of overlapping Domain Decomposition Methods for the rudin osher fatemi model based on a dual formulation
    Siam Journal on Imaging Sciences, 2015
    Co-Authors: Huibin Chang, Lilian Wang, Danping Yang
    Abstract:

    This paper is concerned with overlapping Domain Decomposition Methods (DDMs), based on succes- sive subspace correction (SSC) and parallel subspace correction (PSC), for the Rudin-Osher-Fatemi (ROF) model in image restoration. In contrast to recent attempts, we work with a dual formulation of the ROF model, where one significant difficulty resides in the Decomposition of the global con- straint of the dual variable. We introduce a stable "unity Decomposition" using a set of "partition of unity functions," which naturally leads to overlapping DDMs based on the dual formulation. The main objective of this paper is to rigorously analyze the convergence of the SSC and PSC algorithms and derive the rate of convergence O(n −1/2 ), where n is the number of iterations. Moreover, we characterize the explicit dependence of the convergence rate on the subDomain overlapping size and other important parameters. To the best of our knowledge, such a convergence rate has not yet been claimed for Domain Decomposition related algorithms for the ROF model.

Charbel Farhat - One of the best experts on this subject based on the ideXlab platform.

  • the feti family of Domain Decomposition Methods for inequality constrained quadratic programming application to contact problems with conforming and nonconforming interfaces
    Computer Methods in Applied Mechanics and Engineering, 2009
    Co-Authors: Philip Avery, Charbel Farhat
    Abstract:

    Two Domain Decomposition Methods with Lagrange multipliers for solving iteratively quadratic programming problems with inequality constraints are presented. These Methods are based on the FETI and FETI-DP substructuring algorithms. In the case of linear constraints, they do not perform any Newton-like iteration. Instead, they solve a constrained problem by an active set strategy and a generalized conjugate gradient based descent method equipped with controls to guarantee convergence monotonicity. Both Methods possess the desirable feature of minimizing numerical oscillations during the iterative solution process. Performance results and comparisons are reported for several numerical simulations that suggest that both Methods are numerically scalable with respect to both the problem size and the number of subDomains. Their parallel scalability is also illustrated on a Linux cluster for a complex 1.4 million degree of freedom multibody problem with frictionless contact and nonconforming discrete interfaces.

  • Two-level Domain Decomposition Methods with Lagrange multipliers for the fast iterative solution of acoustic scattering problems
    Computer Methods in Applied Mechanics and Engineering, 2000
    Co-Authors: Charbel Farhat, M. Lesoinne, Antonini Macedo, François-xavier Roux, Frederic Magoules, Armel De La Bourdonnaie
    Abstract:

    We present two different but related Lagrange multiplier based Domain Decomposition (DD) Methods for solving iteratively large-scale systems of equations arising from the finite element discretization of high-frequency exterior Helmholtz problems. The proposed Methods are essentially two distinct extensions of the regularized finite element tearing and interconnecting (FETI) method to indefinite or complex problems. The first method employs a single Lagrange multiplier field to glue the local solutions at the subDomain interface boundaries. The second method employs two Lagrange multiplier fields for that purpose. The key ingredients of both of these FETI Methods are the regularization of each subDomain matrix by a complex lumped mass matrix defined on the subDomain interface boundary, and the preconditioning of the global interface problem by a coarse second-level problem constructed with planar waves. We show numerically that both Methods are scalable with respect to the mesh size, the subDomain size, and the wavenumber, but that the FETI method with a single Lagrange multiplier field – labeled FETI-H (H for Helmholtz) in this paper – delivers superior computational performances. We apply the FETI-H method to the parallel solution on a 24-processor Origin 2000 of an acoustic scattering problem with a submarine shaped obstacle, and report performance results that highlight the unique efficiency of this DD method for the solution of high frequency acoustic scattering problems.

  • A New Coarsening Operator for the Optimal Preconditioning of the Dual and Primal Domain Decomposition Methods: Application to Problems with Severe Coefficient Jumps
    Proceedings of the Seventh Copper Mountain Conference on Multigrid Methods, 1995
    Co-Authors: Charbel Farhat, Daniel Rixen
    Abstract:

    We present an optimal preconditioning algorithm that is equally applicable to the dual (FETI) and primal (Balancing) Schur complement Domain Decomposition Methods, and which successfully addresses the problems of subDomain heterogeneities including the effects of large jumps of coefficients. The proposed preconditioner is derived from energy principles and embeds a new coarsening operator that propagates the error globally and accelerates convergence. The resulting iterative solver is illustrated with the solution of highly heterogeneous elasticity problems.