Collection of abstracts 13th GAMM-Seminar Kiel on Numerical Treatment of Multi-Scale Problems January 24th to 26th, 1997.

Friday, January 24th, 1997

Classical and Cascadic Multigrid - A Methodical Comparison

Rolf Krause
Universität Stuttgart, Mathematisches Institut A
Pfaffenwaldring 57, 70569 Stuttgart

Using the full multigrid method without any coarse grid correction steps but with an a posteriori control of the number of smoothing iterations was shown by Bornemann and Deuflhard to be an optimal iteration method with respect to the energy norm. They named this kind of multigrid iteration the cascadic multigrid method. However, numerical examples with linear finite elements raised serious doubts, wether the cascadic multigrid method can be made optimal with respect to the L^2 - norm. It will be shown that the cascadic multigrid method cannot be optimal for linear finite elements. The cascadic multigrid method does not work well on problems with highly jumping coefficents. A careful analysis of the twogrid method of the cascadic multigrid method provides a setting where one can understand the difference between the cascadic multigrid method and the classical V-cycle.