NDLI: A Comparison of Algebraic Multigrid and Geometric Immersed Interface Multigrid Methods for Interface Problems

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Chartier, Timothy P. Adams, Loyce
Copyright Year	2005
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 in [L. Adams and Z. Li, SIAM J. Sci. Comput., 24 (2002), pp. 463--479] 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 [L. Adams and T. P. Chartier, SIAM J. Sci. Comput., 25 (2002), pp. 1516--1533], a new method was introduced that utilizes a new interpolator for grid points near the immersed interface and a new restrictor that guarantees the coarse-grid matrices are M-matrices. This paper compares the immersed interface multigrid methods introduced in [L. Adams and Z. Li, SIAM J. Sci. Comput., 24 (2002), pp. 463--479] and [L. Adams and T. P. Chartier, SIAM J. Sci. Comput., 25 (2002), pp. 1516--1533] with algebraic multigrid, which uses no geometric information to set up the multigrid components for coarse-grid correction. We show that algebraic multigrid is a robust solver for our test problems. It outperforms the method in [L. Adams and Z. Li, SIAM J. Sci. Comput., 24 (2002), pp. 463--479] and performs nearly as well as the method in [L. Adams and T. P. Chartier, SIAM J. Sci. Comput., 25 (2002), pp. 1516--1533] which is shown to be the most efficient for all problem parameters and sizes.
Starting Page	762
Ending Page	784
Page Count	23
File Format	PDF
ISSN	10648275
DOI	10.1137/S1064827503425262
e-ISSN	10957197
Issue Number	3
Volume Number	26
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2006-07-25
Access Restriction	Subscribed
Subject Keyword	Solution of discretized equations discontinuous coefficients maximum principle preserving schemes immersed interface problems algebraic multigrid geometric multigrid Multigrid methods; domain decomposition M-matrices
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Computational Mathematics

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