Above:
Several compressed fluid subspace re-simulations of varying quality. Visual quality is preserved for up to an order of magnitude compression and degrades gracefully as the compression level increases.

Abstract

Subspace fluid simulations, also known as reduced-order simulations, can be extremely fast, but also require basis matrices that consume an enormous amount of memory. Motivated by the extreme sparsity of Laplacian eigenfunctions in the frequency domain, we design a frequency-space codec that is capable of compressing basis matrices by up to an order of magnitude. However,
if computed naively, decompression can be highly inefficient and dominate the running time, effectively negating the advantage of the subspace approach. We show how to significantly accelerate the decompressor by performing the key matrix-vector product in the sparse frequency domain. Subsequently, our codec only adds a factor of three or four to the overall runtime. The compression preserves the overall quality of the simulation, which we show in a variety of examples.

This material is based upon work supported by a National Science Foundation CAREER award (IIS-1253948). We acknowledge rendering support from the Center for Scientific Computing from the CNSI, MRL: an NSF MRSEC (DMR-1121053), Hewlett-Packard, and NSF CNS-0960316. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.