A Monte Carlo boundary propagation method for the solution of Poisson's equation
To often the parallelism of a computational algorithm is used (or advertised) as a desirable measure of its performance. That is, the higher the computational parallelism the better the expected performance. With the current interest and emphasis on massively parallel computer systems, the notion of highly parallel algorithms is the subject of many conferences and funding proposals. Unfortunately, the revolution'' that this vision promises has served to further complicate the measure of parallel performance by the introduction of such notions as scaled speedup and scalable systems. As a counter example to the merits of highly parallel algorithms whose parallelism scales linearly with increasing problem size, we introduce a slight modification to a highly parallel Monte Carlo technique that is used to estimate the solution of Poisson's equation. This simple modification is shown to yield a much better estimate to the solution by incorporating a more efficient use of boundary data (Dirichlet boundary conditions). A by product of this new algorithm is a much more efficient sequential algorithm but at the expense of sacrificing parallelism. 3 refs.
- Research Organization:
- Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
- Sponsoring Organization:
- DOE/MA
- DOE Contract Number:
- W-7405-ENG-36
- OSTI ID:
- 6856563
- Report Number(s):
- LA-UR-90-2577; CONF-901101-22; ON: DE90015060
- Resource Relation:
- Conference: American Nuclear Society winter meeting, Washington, DC (USA), 11-15 Nov 1990
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
POISSON EQUATION
MONTE CARLO METHOD
ALGORITHMS
DIRICHLET PROBLEM
PARALLEL PROCESSING
PERFORMANCE
DIFFERENTIAL EQUATIONS
EQUATIONS
MATHEMATICAL LOGIC
PARTIAL DIFFERENTIAL EQUATIONS
PROGRAMMING
990200* - Mathematics & Computers