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Using domain decomposition in the JacobiDavidson method
, 2000
"... The JacobiDavidson method is suitable for computing solutions of large ndimensional eigenvalue problems. It needs (approximate) solutions of specific ndimensional linear systems. Here we propose a strategy based on a nonoverlapping domain decomposition technique in order to reduce the wall clock ..."
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The JacobiDavidson method is suitable for computing solutions of large ndimensional eigenvalue problems. It needs (approximate) solutions of specific ndimensional linear systems. Here we propose a strategy based on a nonoverlapping domain decomposition technique in order to reduce the wall clock time and local memory requirements. For a model eigenvalue problem we derive optimal coupling parameters. Numerical experiments show the effect of this approach on the overall JacobiDavidson process. The implementation of the eventual process on a parallel computer is beyond the scope of this paper. 2000 Mathematics Subject Classification: 65F15, 65N25, 65N55. Keywords and Phrases: Eigenvalue problems, domain decomposition, JacobiDavidson, Schwarz method, nonoverlapping, iterative methods. Note: The first author's contribution was carried out partly under project MAS2, and sponsored by the Netherlands Organization for Scientific Research (NWO) under Grant No. 611302100. Note: This wo...
Onelevel KrylovSchwarz Domain Decomposition for Finite Volume Advectiondiffusion
 In Bjrstad P., Espedal M., and Keyes D. (eds) Domain Decomposition Methods 9
, 1998
"... Introduction We consider the twodimensional advectiondiffusion equation discretized with cellcentered finite volumes and the trapezoidal time integration scheme. Several aspects of KrylovSchwarz domain decomposition will be discussed. The name KrylovSchwarz refers to methods in which Schwarz d ..."
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Introduction We consider the twodimensional advectiondiffusion equation discretized with cellcentered finite volumes and the trapezoidal time integration scheme. Several aspects of KrylovSchwarz domain decomposition will be discussed. The name KrylovSchwarz refers to methods in which Schwarz domain decomposition is used as a preconditioner for a Krylov subspace method, see the preface of [KX95]. Our interests in domain decomposition are more practical than theoretical. Our goals are towards solving largescale 'reallife' problems. As such, it is important to work with a method that is not too difficult to implement. Onelevel Schwarz methods belong to this class. Our attention is drawn by nonoverlapping Schwarz methods (sometimes called Schwarz with minimal overlap), because the use of nonoverlapping subdomains facilitates the implementation. Of course, there is a price to be paid; the number of ddmiterations will grow if the number of subdomains increases. With a two
Proceedings of the Federated Conference on Computer Science and Information Systems pp. 459–464
"... The influence of a matrix condition number on iterative methods ’ convergence ..."
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The influence of a matrix condition number on iterative methods ’ convergence
Geological Storage
, 2011
"... pour obtenir le grade de Docteur de l’Université Paris XIII ..."
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Scalability and Load Imbalance for Domain Decomposition Based Transport
, 54
"... this paper only tracer flows are considered. The coefficients '; v and D are assumed to be timeindependent and f(c) = c. Our interests are on the advectiondominated case, i.e. the diffusion tensor D depends on small parameters. For the spatial discretization we employ cellcentered triangular ..."
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this paper only tracer flows are considered. The coefficients '; v and D are assumed to be timeindependent and f(c) = c. Our interests are on the advectiondominated case, i.e. the diffusion tensor D depends on small parameters. For the spatial discretization we employ cellcentered triangular finite volumes, based upon a 10point molecule [WF97]. This results in the semidiscrete system