English

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

Distributed, Parallel, and Cluster Computing 2019-08-14 v3 Numerical Analysis

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.

Keywords

Cite

@article{arxiv.1003.5238,
  title  = {An efficient algorithm for the parallel solution of high-dimensional differential equations},
  author = {Stefan Klus and Tuhin Sahai and Cong Liu and Michael Dellnitz},
  journal= {arXiv preprint arXiv:1003.5238},
  year   = {2019}
}
R2 v1 2026-06-21T15:03:16.819Z