MPI solver for 3D elasticity problems

Authors:
Ivan Lirkov
Affiliations:
Central Laboratory for Parallel Processing, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Bl. 25A, 1113 Sofia, Bulgaria
Venue:
Mathematics and Computers in Simulation - MODELLING 2001 - Second IMACS conference on mathematical modelling and computational methods in mechanics, physics, biomechanics and geodynamics
Year:
2003

Citing 3
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Parallel Performance of an MPI Solver for 3D Elasticity Problems

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Abstract

The numerical solution of 3D linear elasticity equations is considered. The problem is described by a coupled system of second-order elliptic partial differential equations. This system is discretized by trilinear parallelepipedal finite elements.The preconditioned conjugate gradient iterative method is used for solving of the large-scale linear algebraic systems arising after the finite element method (FEM) discretization of the problem. Displacement decomposition technique is applied at the first step to construct a preconditioner using the decoupled block-diagonal part of the original matrix. Then circulant block-factorization is used for preconditioning of the obtained block-diagonal matrix. Both techniques, displacement decomposition and circulant block-factorization, are highly parallelizable.A parallel algorithm is invented for the proposed preconditioner. The theoretical analysis of the execution time shows that the algorithm is highly efficient for coarse-grain parallel computer systems.A portable MPI parallel FEM code is developed. Numerical tests for real-life engineering problems of the geomechanics in geosciences on a number of modern parallel computers are presented. The reported speed-up and parallel efficiency well illustrate the parallel features of the proposed method and its implementation.