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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.

74S05 Finite element methods applied to problems in solid mechanics
74K99 Thin bodies, structures
Full Text: DOI
[1] Farhat, C.; Wilson, E., A parallel active column equation solver, Comput. & struct., 28, 289-304, (1988)
[2] Rothberg, E.; Goopta, A., An efficient block-oriented approach to parallel sparse Cholesky factorization, (1993), private communication
[3] Simon, H.; Vu, P.; Yang, C., Performance of a supernodal general sparse solver on the CRAY Y-MP:1.68 GFLOPS with autotasking, Applied mathematics technical report, boeing computer services, SCA-TR-117, (March 1989)
[4] ()
[5] Bjordstad, P.E.; Widlund, O.B., Iterative methods for solving elliptic problems on regions partitioned into substructures, SIAM J. numer. anal., 23, 1097-1120, (1986) · Zbl 0615.65113
[6] Farhat, C.; Roux, F.X., A method of finite element tearing and interconnecting and its parallel solution algorithm, Internat. J. numer. methods engrg., 32, 1205-1227, (1991) · Zbl 0758.65075
[7] Farhat, C.; Lesoinne, M., Automatic partitioning of unstructured meshes for the parallel solution of problems in computational mechanics, Internat. J. numer. methods engrg., 36, 745-764, (1993) · Zbl 0825.73997
[8] Farhat, C., A saddle-point principle domain decomposition method for the solution of solid mechanics problems, (), 271-292 · Zbl 0778.73067
[9] Farhat, C.; Roux, F.X., An unconventional domain decomposition method for an efficient parallel solution of large-scale finite element systems, SIAM J. sci. stat. comput., 13, 379-396, (1992) · Zbl 0746.65086
[10] Farhat, C.; Geradin, M., Using a reduced number of Lagrange multipliers for assembling parallel incomplete field finite element approximations, Comput. methods appl. mech. engrg., 97, 333-354, (1992) · Zbl 0826.73056
[11] Roux, F.X., Acceleration of the outer conjugate gradient iteration by reorthogonalization for a domain decomposition method with Lagrange multipliers, (), 314-321
[12] C. Farhat, L. Crivelli and F.X. Roux, A transient FETI methodology for large-scale parallel implicit computations in structural mechanics, Internat. J. Numer. Methods Engrg. (to appear). · Zbl 0824.73067
[13] Davis, D.D.; Krishnamurthy, T.; Stroud, W.J.; McCleary, S.L., An accurate nonlinear finite element analysis and test correlation of a stiffened composite wing panel, ()
[14] Farhat, C.; Mandel, J.; Roux, F.X., Optimal convergence properties of the FETI domain decomposition method, Comput. methods appl. mech. engrg., 115, 365-385, (1994)
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