Argonne National Laboratory

Stencil-Aware GPU Optimization of Iterative Solvers*

TitleStencil-Aware GPU Optimization of Iterative Solvers*
Publication TypeJournal Article
Year of Publication2012
AuthorsChoudary, C, Godwin, J, Holewinski, J, Karthik, D, Lowell, D, Mametjanov, A, Norris, B, Sabin, G, Sadayappan, P
Date Published07/2012
Other NumbersANL/MCS-P3008-0712

Numerical solutions of nonlinear partial differential equations frequently rely on iterative Newton-Krylov methods, which linearize a finite-diff erence stencil-based discretization of a problem, producing a sparse matrix with regular structure. Knowledge of this structure can be used to exploit parallelism and locality of reference on modern cache-based multi and many-core architectures, achieving high performance for computations underlying commonly used iterative linear solvers. In this paper we describe our approach to sparse matrix data structure design and our implementation of the kernels underlying iterative linear solvers in PETSc. We also describe autotuning of CUDA implementations based on high-level descriptions of the stencil-based matrix and vector operations.