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Stencil-Aware GPU Optimization of Iterative Solvers

Chekuri Choudary, Jeswin Godwin, Justin Holewinski, Deepan Karthik, Daniel Lowell, Azamat Mametjanov, Boyana Norris, Gerald Sabin, P. Sadayappan
Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, IL 60439
Preprint ANL/MCS-P3008-0712, 2012

@article{choudary2012stencil,

   title={STENCIL-AWARE GPU OPTIMIZATION OF ITERATIVE SOLVERS},

   author={CHOUDARY, C. and GODWIN, J. and HOLEWINSKI, J. and KARTHIK, D. and LOWELL, D. and MAMETJANOV, A. and NORRIS, B. and SABIN, G. and SADAYAPPAN, P.},

   year={2012}

}

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Numerical solutions of nonlinear partial differential equations frequently rely on iterative Newton-Krylov methods, which linearize a finite-difference 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.
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