Semicoarsening Multgrid for Systems

Multigrid Method and Fourth-Order CompactScheme for 2D Poisson Equation withUnequal Mesh-Size Discretization

A fourth-order compact difference scheme with unequal mesh sizes in different coordinate directions is employed to discretize a two-dimensional Poisson equation in a rectangular domain. Multigrid methods using a partial semicoarsening strategy and line Gauss–Seidel relaxation are designed to solve the resulting sparse linear systems. Numerical experiments are conducted to test the accuracy of t...

Flexible Multiple Semicoarsening for Three-Dimensional Singularly Perturbed Problems

We present robust parallel multigrid-based solvers for 3D scalar partial differential equations. The robustness is obtained by combining multiple semicoarsening strategies, matrixdependent transfer operators, and a Krylov subspace acceleration. The basis for the 3D preconditioner is a 2D method with multiple semicoarsened grids based on the MG-S method from [C. W. Oosterlee, Appl. Numer. Math.,...

Revenge of the Semicoarsening Frequency Decomposition Multigrid Method

SUMMARY The frequency decomposition multigrid method was previously considered and modiied so as to obtain robustness for problems with discontinuous coeecients while retaining robustness for problems with anisotropic coeecients. The application of this modiied method to a problem arising in global ocean modeling was also considered. For this problem it was shown that the discretization employe...

Semicoarsening Multigrid on Distributed Memory Machines

Electronic Transactions on Numerical Analysis

Previously we examined the black box multigrid approach to systems of equations. The approach was a direct extension of the methodology used for scalar equations; that is, interpolation and residual weighting were operator induced, and coarsening employed a Galerkin strategy. The application was to standard coarsening of the unknowns. In this paper we consider a semicoarsening approach and find...