Analysis of Preconditioners for Domain Decomposition
Copyright policy )Analysis of Preconditioners for Domain Decomposition
This paper presents a simple model problem - Poisson's equation on a rectangle decomposed into two smaller rectangles - for which the capacitance system can be inverted exactly by fast Fourier transform. An exact eigen-decomposition of the capacitance matrix makes it possible to relate and compare the various preconditioners in the literature. Some remarks about an extension on irregular regions and divisions are indicated.
- Yale University United States
- Hong Kong University of Science and Technology (香港科技大學) China (People's Republic of)
- Hong Kong Polytechnic University China (People's Republic of)
Iterative numerical methods for linear systems, fast solvers, Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation, eigen-decomposition, Numerical computation of matrix norms, conditioning, scaling, substructuring, parallel algorithms, Parallel numerical computation, Numerical solution of discretized equations for boundary value problems involving PDEs, fast Fourier transform, capacitance matrix, preconditioners, irregular regions, domain decomposition, Poisson's equation, preconditioned conjugate gradient method
Iterative numerical methods for linear systems, fast solvers, Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation, eigen-decomposition, Numerical computation of matrix norms, conditioning, scaling, substructuring, parallel algorithms, Parallel numerical computation, Numerical solution of discretized equations for boundary value problems involving PDEs, fast Fourier transform, capacitance matrix, preconditioners, irregular regions, domain decomposition, Poisson's equation, preconditioned conjugate gradient method
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