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

• Main Authors: Jamroz, B., Mullowney, P.
• Format: Conference Proceeding
• Language: English
• Subjects: Approximation methods; Graphics processing unit; graphics processing units; linear algebra; Linear systems; Performance evaluation; Polynomials; preconditioner; Sparse matrices; Vectors
• ISSN: 2166-5133; 2166-515X
• DOI: 10.1109/SAAHPC.2012.27

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.