Parallel finite element solver for multi-core computers with shared memory

Abstract

A direct finite element solver is considered for symmetric sparse matrices arising from the application of the finite element method to problems of structural mechanics and solid mechanics. The solver is based on the block Cholesky method generalized to indefinite matrices. A distinctive feature of the proposed method from other known approaches is the original algorithm for parallelizing the factorization procedure, as well as assembling the matrix of a system of linear and linearized algebraic equations, based on the analysis of the adjacency graph for the finite elements of the design model. All the proposed parallelization algorithms use dynamic mapping of computational tasks to threads and are based on a general idea that uses a dependency vector that controls the execution of computational tasks in a parallel region. This approach is relatively simple and at the same time demonstrates high efficiency. It was developed for solving nonlinear static and dynamic problems of structural mechanics, requiring multiple assembly and factorization of a sparse matrix, but can be successfully applied in other areas of computational mathematics.