A new Half-Sweep Algebraic Multigrid (HSAMG) algorithm for two-point boundary problems

The primary goal of this paper is to propose a new half-sweep algebraic multigrid (HSAMG) algorithm using the finite difference approximation equation for solving two-point boundary problems. The basic idea and formulation of the HSAMG algorithm are inspired by the concept of the half-sweep multigrid method. Some computational experiments have been conducted in order to show that the HSAMG method is superior to the standard algebraic method.

[1]  M. Othman,et al.  A new nine-point multigrid V-cycle algorithm , 2002 .

[2]  Abdul Rahman Abdullah The four point explicit decoupled group (EDG) Method: a fast poisson solver , 1991, Int. J. Comput. Math..

[3]  A. Brandt Multi-level adaptive technique (MLAT) for fast numerical solution to boundary value problems , 1973 .

[4]  David J. Evans,et al.  Explicit De-coupled Group Iterative Methods and their Parallel Implementations , 1995, Parallel Algorithms Appl..

[5]  K. Stüben,et al.  Multigrid methods: Fundamental algorithms, model problem analysis and applications , 1982 .

[6]  Murli M. Gupta,et al.  Comparison of Second- and Fourth-Order Discretizations for Multigrid Poisson Solvers , 1997 .

[7]  P. Wesseling An Introduction to Multigrid Methods , 1992 .

[8]  Mohamed Othman,et al.  The Half-Sweep Iterative Alternating Decomposition Explicit (HSIADE) Method for Diffusion Equation , 2004, CIS.

[9]  A. Brandt Guide to multigrid development , 1982 .

[10]  Wolfgang Hackbusch,et al.  Multi-grid methods and applications , 1985, Springer series in computational mathematics.

[11]  Jumat Sulaiman,et al.  A Parallel Halfsweep Multigrid Algorithm on the Shared Memory Multiprocessors , 2000 .

[12]  Azzam Ibrahim,et al.  Solving the two dimensional diffusion equation by the four point explicit decoupled group (edg) iterative method , 1995, Int. J. Comput. Math..

[13]  G. G. Stokes "J." , 1890, The New Yale Book of Quotations.

[14]  William L. Briggs,et al.  A multigrid tutorial , 1987 .

[15]  A. Brandt Algebraic multigrid theory: The symmetric case , 1986 .

[16]  W. Hackbusch Iterative Solution of Large Sparse Systems of Equations , 1993 .

[17]  Stefan Vandewalle,et al.  Multigrid Waveform Relaxation for Solving Parabolic Partial Differential Equations , 1991 .

[18]  Wolfgang Hackbusch,et al.  Multigrid Methods for FEM and BEM Applications , 2004 .

[19]  Q. Chang,et al.  On the Algebraic Multigrid Method , 1996 .

[20]  Murli M. Gupta,et al.  A Compact Multigrid Solver for Convection-Diffusion Equations , 1997 .

[21]  Mohamed Othman,et al.  The halfsweeps multigrid method as a fast multigrid poisson solver , 1998, Int. J. Comput. Math..