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An efficient algorithm for the parallel solution of high-dimensional differential equations
Stefan Klus, Tuhin Sahai, Cong Liu, Michael Dellnitz · 2010-03-27 · via cs.DC updates on arXiv.org

The study of high-dimensional differential equations is challenging and difficult due to the analytical and computational intractability. Here, we improve the speed of waveform relaxation (WR), a method to simulate high-dimensional differential-algebraic equations. This new method termed adaptive waveform relaxation (AWR) is tested on a communication network example. Further we propose different heuristics for computing graph partitions tailored to adaptive waveform relaxation. We find that AWR coupled with appropriate graph partitioning methods provides a speedup by a factor between 3 and 16.

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