Using HYB Sparse Matrix Storage Format for Solving Linear Systems Obtained by FEM Discretization on GPU

In this paper we consider the use of the CSR and the HYB sparse matrix storage formats in application to matrix vector multiplication to solve three dimensional (3D) problems of geoelectromagnetism on a graphics processing unit (GPU). The subroutines for both complex- and real- valued sparse matrix-vector multiplication in the CSR and the HYB formats were implemented and parallelized on a graphics processing unit. The programs developed were verified on linear systems with large sparse matrices that were obtained by solving a forward magnetotelluric problem with the finite element method. We present the investigation results on how bandwidth affects the matrix-vector multiplication time for matrices in the HYB format. We compare computational time of matrix-vector multiplication for large sparse matrices stored in the HYB format with the same operations on matrices in the CSR format. It was done for both complex- and real-valued matrices. Experiments showed that acceleration by 20-25 percent can be achieved using the HYB format for real-valued matrices in comparison to the CSR with the parallelization on graphics processing unit NVIDIA Tesla C2075.