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Using domain decomposition to solve symmetric, positive‐definite systems on the hypercube computer
Author(s) -
Hennigan Gary L.,
Castillo Steven,
Hensel Edward
Publication year - 1992
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620330911
Subject(s) - domain decomposition methods , hypercube , discretization , finite element method , domain (mathematical analysis) , laplace transform , decomposition method (queueing theory) , computer science , system of linear equations , mathematics , factorization , algorithm , mathematical optimization , parallel computing , mathematical analysis , discrete mathematics , physics , thermodynamics
A distributed method of solving sparse, positive‐definite systems of equations, like those arising from many finite‐element problems, on a hypercube computer is studied. A domain‐decomposition method is introduced wherein the domain of the problem to be solved is physically split into several subdomains. Each of these subdomains is then distributed to a separate processor on the hypercube where the fill, factorization and solution of the system of equations proceeds. This physical split is based on a nodal ordering known as one‐way dissection. 4 The method is applied to two‐dimensional electrostatic problems which are governed by Laplace's equation. Since the finite‐element method is used to discretize the problem, the algorithm is developed to take full advantage of the inherent sparsity in the system of equations by using an envelope storage scheme. The method is applied to several geometries, and results as well as performance data for the algorithm will be given.