GPU-Accelerated Sparse Matrix Solvers for Large-Scale Simulations

At the heart of scientific computing and numerical analysis are linear algebra solvers. In scientific computing, the focus is on the partial differential equations (PDEs) that arise from computational fluid dynamics (CFD), climate modeling, astrophysics, and structural and heat analysis that cannot be solved analytically. Certain problem formulations lead to sparse matrices, in which the majority of matrix elements are zero. Special attention is required when computing on sparse matrices in order to avoid using unrealistic amounts of memory or produce ill-performing software. Such topics have been the subject of considerable research and the limits of CPU-based performance have been reached.Recently, the graphics processing unit (GPU) has emerged as an attractive platform for high performance computing. The modern GPU boasts over 1 TFLOPS performance and as much as 6 GB onboard memory, but harnessing the power can be challenging. A library-based approach is common for HPC, with most applications using several libraries to offload well-known tasks. EM Photonics maintains a library of GPU-accelerated dense linear algebra solvers that has over 5000 users. In this project we will extend this library to include a wide range of sparse solvers, including many that have direct relevance to NASA projects.