Variable Order Cascadic Multigrid Algorithms
نویسندگان
چکیده
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 number of unknowns as the grids get finer and finer, useful work done on the coarse grids has a significant impact on the work estimate for the entire process. We take the approach that solving a higher order problem on some of the coarse grids will be even better than over solving the problem with a standard order discretization. We combine our approach with higher order, operator based interpolation to get an inexpensive, high order cascadic multigrid algorithm.
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