IJPAM: Volume 10, No. 4 (2004)

IMPROVING ALGEBRAIC MULTIGRID EFFICIENCY
FOR IMMERSED INTERFACE PROBLEMS

Miranda J. Antonelli$^1$, Timothy P. Chartier$^2$
$^1$Applied and Computational Mathematical Sciences Program
University of Washington
Seattle, Washington 98195, USA
e-mail: mjanto@hotmail.com
Department of Mathematics
University of Washington
Seattle, Washington 98195, USA
e-mail: chartier@math.washington.edu


Abstract.Computational complexity versus accuracy play a fundamental role in the efficiency of an iterative algorithm. In [#!Adams-Chartier2!#], the robustness of algebraic multigrid (AMG) for interface problems that have been discretized using the methods described in [#!Adams-Li!#] and in [#!Li-Ito!#] for elliptic interface problems using the maximum principle preserving schemes was demonstrated. This paper conducts a parameter study on the strength threshold parameter that is a cornerstone to the AMG algorithm as defined in [#!AMG-RS!#]. The value of the strength threshold in the AMG algorithm directly relates to the speed of the method. This paper analyzes the performance of AMG on various interface problems and improves on the efficiency of AMG as compared to the results in [#!Adams-Chartier2!#].

Received: August 12, 2003

AMS Subject Classification: 65N55, 65F10, 65N20

Key Words and Phrases: multiscale algorithms, multigrid, algebraic multigrid, AMG, iterative methods, immersed interface, elliptic interface problems

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2004
Volume: 10
Issue: 4