Parallel spline collocation-capacitance method for elliptic partial differential equations
Consider the integration of a domain decomposition technique with a new quadratic spline collocation discretization scheme for solving second order elliptic boundary value problems on rectangles. The domain decomposition method is based on the capacitance matrix technique. Due to the limitations of existing methods for solving the corresponding capacitance problem, we develop and analyze iterative methods for its solution. The optimum partitioning and mapping of the underlying computation is studied on hypercube architectures. A numerical realization of this method is presented on NCUBE/7 (128 processors) and its comparative efficiency is measured. The resulting parallel quadratic spline collocation-capacitance method is seen to be efficient in achieving accurate solutions and in using parallel architectures.
- Research Organization:
- Purdue Univ., Lafayette, IN (USA). Dept. of Computer Science
- OSTI ID:
- 6937930
- Report Number(s):
- AD-A-217072/8/XAB
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
990200* -- Mathematics & Computers
BOUNDARY-VALUE PROBLEMS
CALCULATION METHODS
CAPACITANCE
COMPUTER ARCHITECTURE
COMPUTERS
DIFFERENTIAL EQUATIONS
ELECTRICAL PROPERTIES
EQUATIONS
FUNCTIONS
GEOMETRY
HYPERCUBE COMPUTERS
MATHEMATICS
MATRICES
PARALLEL PROCESSING
PARTIAL DIFFERENTIAL EQUATIONS
PHYSICAL PROPERTIES
PROGRAMMING
SPLINE FUNCTIONS