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Numerical algorithms for finite element computations on arrays of microprocessorsThe development of a multicolored successive over relaxation (SOR) program for the finite element machine is discussed. The multicolored SOR method uses a generalization of the classical Red/Black grid point ordering for the SOR method. These multicolored orderings have the advantage of allowing the SOR method to be implemented as a Jacobi method, which is ideal for arrays of processors, but still enjoy the greater rate of convergence of the SOR method. The program solves a general second order self adjoint elliptic problem on a square region with Dirichlet boundary conditions, discretized by quadratic elements on triangular regions. For this general problem and discretization, six colors are necessary for the multicolored method to operate efficiently. The specific problem that was solved using the six color program was Poisson's equation; for Poisson's equation, three colors are necessary but six may be used. In general, the number of colors needed is a function of the differential equation, the region and boundary conditions, and the particular finite element used for the discretization.
Document ID
19810011267
Acquisition Source
Legacy CDMS
Document Type
Contractor Report (CR)
Authors
Ortega, J. M. (Virginia Univ. Charlottesville, VA, United States)
Date Acquired
September 4, 2013
Publication Date
March 1, 1981
Subject Category
Computer Programming And Software
Report/Patent Number
NASA-CR-164008
UVA/528190/AMCS81/101
SAR-2
Accession Number
81N19794
Funding Number(s)
CONTRACT_GRANT: NAG1-46
Distribution Limits
Public
Copyright
Work of the US Gov. Public Use Permitted.

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