An efficient algorithm for the parallel solution of high-dimensional differential equations

Authors:
Stefan Klus;Tuhin Sahai;Cong Liu;Michael Dellnitz
Affiliations:
Institute for Industrial Mathematics, University of Paderborn, 33095 Paderborn, Germany;United Technologies Research Center, East Hartford, CT 06108, USA;United Technologies Research Center, East Hartford, CT 06108, USA;Institute for Industrial Mathematics, University of Paderborn, 33095 Paderborn, Germany
Venue:
Journal of Computational and Applied Mathematics
Year:
2011

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Abstract

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.