Competitive numerical algorithms for solving partial differential equations have to work with the most efficient numerical methods like multigrid and adaptive grid refinement and thus with hierarchical data structures. Unfortunately, in most implementations, hierarchical datatypically stored in trees-cause a nonnegligible overhead in data access. To overcome this quandarynumerical efficiency versus efficient implementation-our algorithm uses space-filling curves to build up data structures which are processed linearly. In fact, the only kind of data structure used in our implementation is stacks. Thus, data access becomes very fast-even faster than the common access to nonhierarchical data stored in matrices-and, in particular, cache misses are reduced considerably. Furthermore, the implementation of multigrid cycles and/or higher order discretizations as well as the parallelization of the whole algorithm become very easy and straightforward on these data structures.
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