Fast sparse matrix-vector multiplication on graphics processing unit for finite element analysis

Finite element analysis involves the solution of linear systems described by large size sparse matrices. Iterative Krylov methods are well suited for such type of problems. These methods require linear algebra operations, including sparse matrix-vector multiplication which can be computationally expensive for large size matrices. In this paper, we present the best way to perform these operations, in double precision, on Graphics Processing Unit (GPU). Several linear algebra libraries are considered and compared to our proper implementation. These libraries and our proper implementation are then integrated within an iterative Krylov method on the GPU. Numerical experiments done on a set of finite element matrices are presented and illustrate the performance, robustness and accuracy of our proper implementation compared to the existing libraries and its suitability for finite element analysis. Dynamic tuning of the gridification, upon the GPU architecture and the finite element matrix characteristics, is finally applied to faster the sparse matrix-vector multiplication operation.