Out of the three main ingredients of numerical simulations - numerical algorithms, physics models, and computers -it is the hardware whose evolution far outpaces that of the other two, and which tends to dominate the overall turn-around time. As computational platforms are becoming increasingly more complicated and heterogeneous, numerical algorithms that can efficiently use such hardware must evolve or be replaced. This symposium session intends to raise awareness of this issue among applied mathematicians, and to facilitate a dialog between mathematicians, physicists and computer scientists. The papers here present recent ideas and solutions, as well as work in progress and outstanding problems in developing algorithms and computational environments that fit well on a particular platform for a given area of computational physics.
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