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Compilers for Regular and Irregular Stencils: Some Shared Problems and Solutions

Solving partial differential equations results in a continuum of regular and irregular stencil computation implementations. In this paper, we use heat diffusion on a bar to show how regular and irregular stencil computations are related, and then illustrate five complicating issues that occur in implementing the continuum of regular and irregular stencil computations in full applications. These complicating issues make it difficult for compilers to discover stencil computations and to represent and generate code for the combination of regular and irregular transformations that are relevant. We overview projects at Colorado State University and elsewhere that are developing solutions to the complicating issues surrounding stencil computations in partial differential equation (PDE) solver applications. Keywords-regular and irregular stencils, sparse matrix vector multiplication (SpMV), sparse tiling, sparse polyhedral framework, heat diffusion problem, PDE solvers