Q F. Stout,
D.L. De Zeeuw, T.I. Gombosi, C.P.T. Groth, H.G. Marshall,
University of Michigan
Abstract: We have created a data structure which combines flexible adaptivity with high performance for both serial and parallel computers. Using it, we were able to sustain 17Gflops on a simulation of the magneto-hydrodynamic (MHD) properties of the solar wind emanating from the sun, using a 512-processor Cray T3D at NASA Goddard. This simulation included 5 levels of resolution adaptivity, and on-going work of our NASA Grand Challenge Team will exploit the adaptivity over vastly greater ranges.
The data structure is an adaptive grid which partitions a given region into regular cells. Its closest relative is the oct-tree, but there are several important differences. Adaptive blocks can be thought of as being similar to the leaves of an oct-tree, where each leaf is a block which partitions its region of space into an regular a×b×c array of cells. If a block needs to be refined, it is replaced by 8 children, each with a×b×c cells, where each cell's extent in each dimension is 1/2 the extent of its parent's cells. If the 8 children need to be coarsened, they are replaced by their parent. In our application, each block points to the blocks it shares a face with, though in other applications one may also need pointers to blocks sharing an edge or corner.
The primary advantages of adaptive blocks over oct-trees are:
This paper appears in Proceedings Supercomputing 1997 (SC'97). Complete paper (PDF) (html)
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