Performance of Parallel Sparse Matrix-Vector Multiplications in Linear Solves on Multiple GPUs

Modern numerical simulations often require solving extremely large sparse linear systems. Solving these linear systems using Krylov iterative methods requires repeated sparse matrix-vector multiplications which can be the most computationally expensive part of the simulation. Since Graphics Processing Units (GPUs) provide a significant increase in floating point operations per second and memory bandwidth over conventional Central Processing Units (CPUs), performing sparse matrix-vector multiplications with these co-processors can decrease the amount of time required to solve a given linear system. In this paper, we investigate the performance of sparse matrix-vector multiplications across multiple GPUs. This is performed in the context of the solution of symmetric positive-definite linear systems using a conjugate-gradient iteration preconditioned with a least-squares polynomial preconditioner using the PETSc library.