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Finite-difference methods are widely used in solving partial differentialequations. In a large problem set, approximations can take days or weeks toevaluate, yet the bulk of computation may occur within a single loop nest. Themodelling process for researchers is not straightforward either, requiringmodels with differential equations to be translated into stencil kernels, thenoptimised separately. One tool that seeks to speed up and eliminate mistakesfrom this tedious procedure is Devito, used to efficiently employfinite-difference methods.  In this work, we implement time-tiling, a loop nest optimisation, in Devitoyielding a decrease in runtime of up to 45%, and at least 20% across stencilsfrom the acoustic wave equation family, widely used in Devito's target domainof seismic imaging. We present an estimator for arithmetic intensity undertime-tiling and a model to predict runtime improvements in stencilcomputations. We also consider generalisation of time-tiling to imperfect loopnests, a less widely studied problem.

Optimising finite-difference methods for PDEs through parameterised time-tiling in Devito