Abstract
The numerical solution of partial differential equations leads to large, sparse systems of equations with up a several millions of unknowns. Fast iterative algorithms for the solution of these systems are typically based on the multilevel principle. Unfortunately, some of the commonly used programming techniques lead to a high overhead on many advanced computer architectures. The two main sources of this performance degradation are the effects of non-uniform data access combined with indirect addressing that prohibits the use of instruction-level parallelism. This, however, is essential to exploit many modern CPU designs. The second, and possibly more fundamental problem arises from hierarchical memory architectures with several layers of caches. Their effective use requires programs with data access locality. Unfortunately, iterative solvers are typically implemented by using global sweeps over the whole data set, and thus their performance is essentially limited by the speed of the memory system. These problems are addressed in the patch-adaptive multigrid method, a recently developed experimental software system implementing an adaptive multigrid method based on a locally uniform mesh data structure.
Partly supported by grant RU 422/7-1 of Deutsche Forschungsgemeinschaft
This is written in May 1997
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© 1997 Springer-Verlag Berlin Heidelberg
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Rüde, U. (1997). Iterative algorithms on high performance architectures. In: Lengauer, C., Griebl, M., Gorlatch, S. (eds) Euro-Par'97 Parallel Processing. Euro-Par 1997. Lecture Notes in Computer Science, vol 1300. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0002717
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DOI: https://doi.org/10.1007/BFb0002717
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