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CivilComp Proceedings
ISSN 17593433 CCP: 94
PROCEEDINGS OF THE SEVENTH INTERNATIONAL CONFERENCE ON ENGINEERING COMPUTATIONAL TECHNOLOGY Edited by:
Paper 33
Parallel Mixed Constraint Preconditioners for the Iterative Solution of Coupled Consolidation Problems L. Bergamaschi, A. Martinez and G. Pini
Department of Mathematical Methods and Models for Scientific Applications, University of Padua, Italy L. Bergamaschi, A. Martinez, G. Pini, "Parallel Mixed Constraint Preconditioners for the Iterative Solution of Coupled Consolidation Problems", in , (Editors), "Proceedings of the Seventh International Conference on Engineering Computational Technology", CivilComp Press, Stirlingshire, UK, Paper 33, 2010. doi:10.4203/ccp.94.33
Keywords: parallel computing, preconditioning, Krylov subspace methods, coupled consolidation.
Summary
Large and sparse linear systems of saddle point type arise in many engineering
applications such as mixed finite element discretizations of PDEs, constrained
optimization and coupled consolidation problems. Iterative
solution is recommended as opposed to direct factorization methods because of
the extremely large size of these systems. However, well established iterative
methods such as Krylov subspace methods are very slow or even fail to converge if
not conveniently preconditioned.
In this paper we propose and describe a parallel implementation of a block preconditioner in the solution of saddle point linear systems arising from finite element (FE) discretization of threedimensional coupled consolidation problems. The constraint preconditioners for Krylov solvers in the solution of saddle point problems have been studied by a number of authors. Bergamaschi et al. [1,2] have developed a mixed constraint preconditioner (MCP) which couples two explicitimplicit approximations of the inverse of the (1,1) block (K in the sequel) provided by an approximate inverse preconditioner such as AINV, and the IC preconditioner, respectively. In this paper we propose a parallel preconditioner (FSAIMPC) which uses two factorized sparse approximate inverse (FSAI) [3] approximations, G1 and G2, of the inverse of K. The FSAI preconditioner has been successfully implemented in parallel and tested on large geomechanical models [4]. The sparser approximation G2 is used to explicitly construct the Schur complement matrix which in its turn is preconditioned by another FSAI approximation. We have developed a fully parallel code which implements the BiCGSTAB solver accelerated with the parallel MCP preconditioner described above. The code is written in Fortran 90 and uses the MPI standard to perform interprocessor communication. We present numerical results of several run solving a number of threedimensional test cases of large size arising from threedimensional finite element discretization of coupled consolidation problems. The resulting preconditioner proves effective in the acceleration of the BiCGSTAB iterative solver. The numerical results of a number of test cases of size up to 2 million unknowns and 120 million nonzeros show the perfect scalability of the overall code up to 256 processors. The proposed iterative method is shown to outperform the wellestablished pARMS multilevel solver on the largest problem. References
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