An efficient cell-centered multigrid method for problems with discontinuous coefficients on semi-structured triangular grids

This paper is focused on the numerical solution of elliptic equations with discontinuous coefficients. In particular, the design of efficient geometric multigrid methods for cell-centered finite volume schemes for this kind of problems is dealt with. In this work we propose a block-wise multigrid algorithm on semi-structured triangular grids for solving piecewise constant diffusivity problems on relatively complex domains. Appropriate novel smoothers for cell-centered discretizations are considered on each structured patch of the mesh. The difficulties appearing when highly varying coefficients occur are overcome by the use of a modified Galerkin coarse grid approximation. Numerical experiments are presented to illustrate the good behavior of the proposed multigrid method which achieves an h-independent convergence rate.

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