A Semicoarsening Multigrid Method for Elliptic Partial Differential Equations with Highly Discontinuous and Anisotropic Coefficients

The purpose of this paper is to present a semicoarsening multigrid algorithm for solving the finite difference discretization of symmetric and nonsymmetric, two- and three-dimensional elliptic partial differential equations with highly discontinuous and anisotropic coefficients. The discrete equations are assumed to be defined on a logically rectangular grid, obtained possibly through grid generation for a problem defined on an irregular domain. The basic algorithm is described along with some modifications which are designed to improve its efficiency and robustness for certain types of problem cases. FORTRAN codes that implement the two- and three-dimensional semicoarsening multigrid algorithms are described briefly, and numerical results are presented.

[1]  Stephen F. McCormick,et al.  Multigrid Methods for Three-Dimensional Petroleum Reservoir Simulation , 1989 .

[2]  Stanly Steinberg,et al.  Finite difference methods for modeling porous media flows , 1994 .

[3]  Tony F. Chan,et al.  A Note on the Efficiency of Domain Decomposed Incomplete Factorizations , 1990, SIAM J. Sci. Comput..

[4]  Wolfgang Hackbusch.  The frequency decomposition multi-grid method , 1989 .

[5]  J. Dendy.  Black box multigrid , 1982 .

[6]  D. Brandt,et al.  Multi-level adaptive solutions to boundary-value problems math comptr , 1977 .

[7]  Alan Weiser,et al.  Semicoarsening Multigrid on a Hypercube , 1992, SIAM J. Sci. Comput..

[8]  M. P. Ida,et al.  A Semicoarsening Multigrid Algorithm for SIMD Machines , 1992, SIAM J. Sci. Comput..

[9]  G. Wittum.  On the Robustness of ILU Smoothing , 1989 .

[10]  Paul N. author-Swarztrauber.  Approximate Cyclic Reduction for Solving Poisson's Equation , 1987 .

[11]  StübenKlaus.  Algebraic multigrid (AMG) , 1983 .

[12]  P. J. Roache.  The SECO suite of codes for site Performance Assessment , 1993 .

[13]  J. E. Dendy.  Black box multigrid for nonsymmetric problems , 1983 .

[14]  S. F. McCormick.  An Algebraic Interpretation of Multigrid Methods , 1982 .

[15]  J. E. Dendy.  Two multigrid methods for three-dimensional problems with discontinuous and anisotropic coefficients , 1987 .

[16]  P. M. De Zeeuw,et al.  Matrix-dependent prolongations and restrictions in a blackbox multigrid solver , 1990 .

[17]  Peter A. Forsyth,et al.  Multi-grid solution of three-dimensional problems with discontinuous coefficients , 1983 .

[18]  Patrick M. Knupp,et al.  Fundamentals of Grid Generation , 2020 .

[19]  J. E. Dendy,et al.  Black box multigrid for systems , 1986 .

[20]  Tony F. Chan,et al.  The Interface Probing Technique in Domain Decomposition , 1992, SIAM J. Matrix Anal. Appl..