Pii: S0378-4754(02)00104-0

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. © 2002 IMACS. Published by Elsevier Science B.V. All rights reserved. MSC: 65F10; 68W10; 74B05; 74B20; 74S05