A Cascadic Multigrid Method for Eigenvalue Problem

A Cascadic Multigrid Method for Eigenvalue Problem

A cascadic multigrid method is proposed for eigenvalue problems based on the multilevel correction scheme. With this new scheme, an eigenvalue problem on the finest space can be solved by linear smoothing steps on a series of multilevel finite element spaces and nonlinear correcting steps on special coarsest spaces. Once the sequence of finite element spaces and the number of smoothing steps ar...

Classical and Cascadic Multigrid | a Methodical Comparison Classical and Cascadic Multigrid | a Methodical Comparison

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 Deuuhard 2] to be an optimal iteration method with respect to the energy norm. They named this new kind of multigrid iteration the cascadic multigrid method. However, numerical examples with linear nite elements raised serious...

Cascadic Multigrid Methods for Parabolic Problems∗

In this paper, we consider the cascadic multigrid method for a parabolic type equation. Backward Euler approximation in time and linear finite element approximation in space are employed. A stability result is established under some conditions on the smoother. Using new and sharper estimates for the smoothers that reflect the precise dependence on the time step and the spatial mesh parameter, t...

Variable Order Cascadic Multigrid Algorithms

Cascadic multigrid algorithms have been shown by a number of researchers (e.g., Bornemann, Deuflhard, Shaidurov, Shi, and many others) to be useful in a number of application areas. Cascadic multigrid differs from traditional one way multigrid methods by over solving the problem on coarse grids in order to reduce the required work on the finest grids. Since there is a geometric growth in the nu...

7Classical and Cascadic Multigrid| A Methodological Comparison