Enhancing the performance of the FETI method with preconditioning ¶techniques implemented on clusters of networked computers |
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Authors: | D C Charmpis M Papadrakakis |
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Affiliation: | (1) Institute of Structural Analysis & Seismic Research, National Technical University of Athens, 9, Iroon Polytechniou Str., Zografou Campus, GR-15780 Athens, Greece e-mail: mpapadra@central.ntua.gr, GR |
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Abstract: | The FETI domain decomposition method for solving large-scale problems in computational structural mechanics involves the
solution of an interface problem, which is handled by a Preconditioned Conjugate Projected Gradient (PCPG) algorithm. Two
preconditioners are widely used to accelerate the convergence of the iterative PCPG algorithm: the optimal Dirichlet preconditioner
and the economical lumped preconditioner. The Dirichlet preconditioner is computationally more efficient than the lumped preconditioner
for ill-conditioned problems, but needs additional storage for the stiffness matrices of the subdomains' internal degrees
of freedom (d.o.f.). In this study a new set of PCPG preconditioners is presented by providing approximate expressions to
the inverse iteration matrix of the PCPG algorithm. The resulting approximate Dirichlet preconditioners are obtained by using
instead of the whole stiffness matrix of the internal d.o.f. in each subdomain the following alternatives: a diagonal scaling
matrix, a SSOR type matrix or an incomplete Cholesky factorization matrix. The computational behavior and performance of the
proposed PCPG preconditioners is evaluated using an implementation of the FETI method on a cluster of ethernet-networked PCs
running the message passing software PVM. It is demonstrated that the FETI method equipped with the approximate Dirichlet
preconditioners leads for a number of large-scale problems to faster and less storage demanding overall solutions than with
either Dirichlet or lumped preconditioner.
Received: 28 December 2001 / Accepted: 22 August 2002 |
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Keywords: | Parallel Distributed Domain decomposition FETI Preconditioning PC cluster |
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