New Geometric Immersed Interface Multigrid Solvers

Authors:
Loyce Adams;Timothy P. Chartier
Affiliations:
-;-
Venue:
SIAM Journal on Scientific Computing
Year:
2004

Citing 0
Cited 8

High order matched interface and boundary method for elliptic equations with discontinuous coefficients and singular sources

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A new high-order immersed interface method for solving elliptic equations with imbedded interface of discontinuity

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A coupling interface method for elliptic interface problems

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A kernel-free boundary integral method for elliptic boundary value problems

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Piecewise-polynomial discretization and Krylov-accelerated multigrid for elliptic interface problems

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Constructing spectral schemes of the immersed interface method via a global description of discontinuous functions

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A high-order cut-cell method for numerical simulation of hypersonic boundary-layer instability with surface roughness

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A second order virtual node method for elliptic problems with interfaces and irregular domains in three dimensions

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Abstract

In [L. Adams and Z. Li, SIAM J. Sci. Comput., 24 (2002), pp. 463--479], a multigrid method was designed specifically for interface problems that have been discretized using the methods described therein, and in [Z. Li and K. Ito, SIAM J. Sci. Comput., 23 (2001), pp. 339--361] for elliptic interface problems using the maximum principle preserving schemes. In this paper, we improve on this method by giving a new interpolator for grid points near the immersed interface and a new restrictor that guarantees the coarse-grid matrices are M-matrices. We compare this new restrictor to injection and the transpose of interpolation. We show that the number of V-cycles is constant as the mesh size decreases and increases only slightly as the ratio of the discontinuous problem coefficient grows at the interface only when this new restrictor is used.