Collection of abstracts 14th GAMM-Seminar Kiel on Concepts of Numerical Software January 23rd to 25th, 1998.

Saturday, January 24th, 1998

Cache Based Multigrid on Structured/Unstructured Grids in 2D/3D

Computers today rely heavily on good utilization of their cache memory subsystems. Compilers are optimized for business applications, not scientific computing ones, however. Automatic tiling of basic numerical algorithms is simply not provided by any compiler. Thus, absolutely terrible cache performance is normal for scientific computing applications.

Multigrid algorithms combine several numerical algorithms into a more complicated algorithm. An algorithm is derived that allows for data to pass through cache exactly once per multigrid level during a V cycle before the level changes. This is optimal cache usage for large problems that do not fit entirely in cache.

The new algorithm would appear to be quite complicated to implement, leading to spaghetti coding. Actually, an efficient implementation of the algorithm requires a rigid, highly structured coding style. A coding example is given that is suitable for almost all common discretization methods.

Numerical experiments are provided that show that the new algorithm is up to an integer factor faster than the traditional implementation method for common multigrid parameter choices.