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Multigrid method and fourth-order compact difference discretization scheme with unequal meshsizes for 3D Poisson equation. (English) Zbl 1197.65169
Summary: A fourth-order compact difference discretization scheme with unequal meshsizes in different coordinate directions is employed to solve a three-dimensional (3D) Poisson equation on a cubic domain. Two multgrid methods are developed to solve the resulting sparse linear systems. One is to use the full-coarsening multigrid method with plane Gauss-Seidel relaxation, which uses line Gauss-Seidel relaxation to compute each planewise solution. The other is to construct a partial semi-coarsening multigrid method with the traditional point or plane Gauss-Seidel relaxations. Numerical experiments are conducted to test the computed accuracy of the fourth-order compact difference scheme and the computational efficiency of the multigrid methods with the fourth-order compact difference scheme.
MSC:
65N06Finite difference methods (BVP of PDE)
35J05Laplacian operator, reduced wave equation (Helmholtz equation), Poisson equation
65F10Iterative methods for linear systems
65F50Sparse matrices (numerical linear algebra)
65N50Mesh generation and refinement (BVP of PDE)
65N55Multigrid methods; domain decomposition (BVP of PDE)
65Y20Complexity and performance of numerical algorithms
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