Solving elliptic problems using ELLPACK
Solving elliptic problems using ELLPACK
An iterative method for elliptic problems on regions partitioned into substructures
Mathematics of Computation
The construction of preconditioners for elliptic problems by substructuring. I
Mathematics of Computation
Iterative methods for the solution of elliptic problems on regions partitioned into substructures
SIAM Journal on Numerical Analysis
Analysis of preconditioners for domain decomposition
SIAM Journal on Numerical Analysis
SIAM Journal on Scientific and Statistical Computing
Performance of scientific software
Mathematical aspects of scientific software
Schwarz splitting and template operators
Schwarz splitting and template operators
Schur complement preconditioned conjugate gradient methods for spline collocation equations
ICS '90 Proceedings of the 4th international conference on Supercomputing
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We 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.