Fast Iterative Solvers for Large Compressed-Sparse Row Linear Systems on Graphics Processing Unit

Abstract

Engineering problems involve the solution of large sparse linear systems, and require therefore fast and high performance algorithms for algebra operations such as dot product, and matrix-vector multiplication. During the last decade, graphics processing units have been widely used. In this paper, linear algebra operations on graphics processing unit for single and double precision (with real and complex arithmetic) are analyzed in order to make iterative Krylov algorithms efficient compared to central processing units implementation. The performance of the proposed method is evaluated for the Laplace and the Helmholtz equations. Numerical experiments clearly show the robustness and effectiveness of the graphics processing unit tuned algorithms for compressed-sparse row data storage.

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