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Extending substructure based iterative solvers to multiple load and repeated analyses. (English) Zbl 0851.73059
We present a methodology for extending the range of applications of domain decomposition methods to problems with multiple or repeated right hand sides. Basically, we formulate the overall problem as a series of minimization problems over \(K\)-orthogonal and supplementary subspaces, and tailor the preconditioned conjugate gradient algorithm to solve them efficiently. The resulting solution method is scalable, whereas direct factorization schemes and forward and backward substitution algorithms are not. We illustrate the proposed methodology with the solution of a linear structural dynamics problem with 11640 degrees of freedom, every time-step beyond time-step 15 is solved in a single iteration and consumes 1.0 second on a 32 processor iPSC-860 system; for the same problem and the same parallel processor, a pair of forward/backward substitutions at each step consumes 15.0 seconds.

MSC:
74S05 Finite element methods applied to problems in solid mechanics
74K99 Thin bodies, structures
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