Parallel Iterative Linear Solvers on GPU: A Financial Engineering Case

In many numerical applications resulting from computational science and engineering problems, the solution of sparse linear systems is the most prohibitively compute intensive task. Consequently, the linear solvers need to be carefully chosen and efficiently implemented in order to harness the available computing resources. Krylov subspace based iterative solvers have been widely used for solving large systems of linear equations. In this paper, we focus on the design of such iterative solvers to take advantage of massive parallelism of general purpose Graphics Processing Units (GPU)s. We will consider Stabilized BiConjugate Gradient (BiCGStab) and Conjugate Gradient Squared (CGS) methods for the solutions of sparse linear systems with unsymmetric coefficient matrices. We discuss data structures and efficient implementation of these solvers on the NVIDIA's CUDA platform. We evaluate scalability and performance of our implementations in the context of a financial engineering problem of solving multidimensional option pricing PDEs using sparse grid combination technique.