One of the ways that the Sun interacts with the Earth is through the solar wind, which is an ionized multi-component fluid that emanates from the Sun and travels radially outward at hundreds of kilometers per second. Solar-wind transients, such as Coronal Mass Ejections (CME's), can be particularly important. In rare cases, CME's have affected the lower atmosphere of the Earth, causing regional power-grid failures. More regularly, CME's pose threats to satellites and spacecraft. Due to the extreme range of temporal and spatial scales involved in solar-wind phenomena, it had previously been impossible to predict CME propagation to Earth with faster-than-real-time, well-resolved calculations. Our team has now developed a highly scalable solution-adaptive scheme for predicting CME propagation. The solution-adaptive technique is an adaptive mesh refinement (AMR) scheme for magneto- hydrodynamic (MHD) calculations. The physical domain is decomposed into three- dimensional blocks, where each block forms a regular grid. In regions of relatively high gradients, blocks are successively refined. Blocks are distributed to processors, with communication between neighboring blocks is handled by asynchronous message passing. The benchmark calculation achieved 212 Gflops on a 1024-processor Cray T3E-1200, with the grid adapting over the course of the calculation from 2048 blocks to 11,729 blocks, where each block was composed of 10x10x10 cells. On a 512-processor Cray T3E-600, our benchmark simulations were performed 16 times faster than real time.

We examine a data structure which uses flexible "adaptivity" to obtain high performance for both serial and parallel computers. The data structure is an adaptive grid which partitions a given region into regular cells. Its closest relatives are cell-based tree decompositions, but there are several important differences which lead to significant performance advantages. Using this block data structure to support adaptive mesh refinement (AMR), we were able to sustain 17 GFLOPS in ideal magnetohydrodynamic (MHD) simulations of the solar wind emanating from the base of the solar corona, using a 512 processor Cray T3D at NASA Goddard.