Parallel computation of a domain decomposition method
We present a parallel algorithm for the efficient solution of a singularly perturbed parabolic partial differential equation. The method is based upon domain decomposition that is dictated by singular perturbation analysis. A transformation is made to a coordinate system induced by the characteristics of the reduced hyperbolic equation. Asymptotic analysis is used to determine regions where certain reduced equations may be solved in place of the full equation. This reduces the number and size of the domains where the full equation must be solved. Parallelism is evident at two levels. Domain decomposition provides parallelism at the highest level, and within each domain there is ample opportunity to exploit additional parallelism. Important features of the method include independent solution of the characteristic curves at the lowest level and low communication requirements between processes devoted to solving in the various domains. Tightly coupled processes are only required in domains where the full equation must be solved. We discuss the implementation and some aspects of the performance of this algorithm on existing parallel computers. We also touch upon certain aspects of iterative solution of nonlinear problems.
- Research Organization:
- Argonne National Lab., IL (USA). Mathematics and Computer Science Div.
- DOE Contract Number:
- W-31109-ENG-38; W-7405-ENG-48; AC05-84OR21400; FG02-85ER25001
- OSTI ID:
- 6487931
- Report Number(s):
- ANL/MCS-TM-91; ON: DE87004344
- Country of Publication:
- United States
- Language:
- English
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