John Vincent Atanasoff Modern Computing, International Symposium on (2006)
Oct. 3, 2006 to Oct. 6, 2006
DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/JVA.2006.9
Ivan Lirkov , Bulgarian Academy of Sciences
Svetozar Magenov , Bulgarian Academy of Sciences
Marcin Paprzycki , Computer Science, SWPS, Poland
Numerical solution of 3D linear elasticity equations is considered. Problem is described by a coupled system of second order elliptic partial differential equations. This system is discretized by trilinear parallelepipedal finite elements. Preconditioned Conjugate Gradient iterative method is used for solving large-scale linear algebraic systems arising after the Finite Element Method (FEM) discretization of the problem. The 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 to precondition thus obtained block- diagonal matrix. Since both preconditioning techniques, displacement decomposition and circulant block- factorization, are highly parallelizable, a portable parallel FEM code based on MPI is developed. Results of numerical tests performed on a number of modern parallel computers using real-life engineering problems from the geomechanics in geosciences are reported and discussed.
I. Lirkov, M. Paprzycki and S. Magenov, "Benchmarking Performance of an MPI-based Solver for 3D Elasticity Problems," 2006 John Vincent Atanasoff International Symposium on Modern Computing(JVA), Sofia, 2006, pp. 260-265.