Benchmarking Performance of an MPI-based Solver for 3D Elasticity Problems

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