The Multigrid Iteration Applied to the Collocation Method
Copyright policy )The Multigrid Iteration Applied to the Collocation Method
We describe an application of the multigrid iteration to the collocation approximation for elliptic equations using a bicubic Hermite basis. A block relaxation and a projection operator specific to the collocation approximation were required to obtain convergence. We illustrate the method with the two-point boundary problem: Results are also given for an elliptic problem in two dimensions. Comments on computational efficiency are given along with operational counts. Results for a block SOR algorithm are also given. Comparison with a multigrid finite difference method indicates that the collocation method is less efficient.
Numerical solution of boundary value problems involving ordinary differential equations, Iterative numerical methods for linear systems, collocation, Boundary value problems for second-order elliptic equations, block Gauss- Seidel relaxation, Linear boundary value problems for ordinary differential equations, multigrid methods, Numerical solution of discretized equations for boundary value problems involving PDEs, numerical experiments, bicubic Hermite splines
Numerical solution of boundary value problems involving ordinary differential equations, Iterative numerical methods for linear systems, collocation, Boundary value problems for second-order elliptic equations, block Gauss- Seidel relaxation, Linear boundary value problems for ordinary differential equations, multigrid methods, Numerical solution of discretized equations for boundary value problems involving PDEs, numerical experiments, bicubic Hermite splines
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