Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

Date and Time: Thursday, September 15, 2011, 12:15 pm

Duration: 30 minutes

Location: ML J37.1

Speaker: Philipp Hupp (TU München)

On the I/O Complexity of Stencil Computations on 2 Dimensional Grids

Over the past years computer architecture has changed and the gap between floating point performance and memory bandwidth has expanded. Furthermore the size of datasets increases continuously. Therefore the bottleneck limiting the performance of many computations seems to be more and more given by the memory subsystem. Important kernels in scientific computing are stencil computations. They can be used to model the evaluation of an interpolation function or solving a partial differential equation. While memory efficient algorithms to evaluate stencils are usually known, they have not been studied from an theoretical I/O point of view and the lower bounds are missing. Here we derive the first two terms of the I/O complexity of the 5-point stencil which arises when differential quotients are approximated in two dimensions. The research prepares future analysis of stencil computations in higher dimensions and on sparse grids, a variation of grids that reduce the number of grid points to tackle high dimensional problems.

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