GPU implementation of iterative solver for linear systems obtained by FEM discretization

Abstract

This work describes the application of modern high-performance computing technologies such as multicore CPUs and GPUs coprocessors to the solution of three-dimensional (3D) problems of geoelectromagnetism with the use of the finite element method. The techniques for speeding up sparse linear system solving via iterative methods are discussed. Programs to solve large sparse complex-valued linear systems with the COCR method, Jacobi preconditioner and residual smoothing technique were developed and implemented for CPU and GPU devices. Jacobi preconditioner was optimized to increase performance with respect to default implementation from cuBLAS and cuSPARSE libraries on GPU. The developed programs were verified on the set of linear systems with large sparse matrices stored in CSR format that were obtained by solving the forward magnetotelluric problem with the finite element method. The comparison of parallelization has been done using both CPU and GPU devices. Our experiments with an NVIDIA Tesla C2075 and Intel i5-2500 show that, using of GPU, we can achieve an acceleration of up to 8 times compared to the single-threaded implementation on the CPU or up to 3.5 times compared to the multithreaded implementation with Intel MKL subroutines.