Abstract
We propose asynchronous parallel algorithms for numerically solving systems of hyperbolic partial differential equations. The algorithms are based on the solutions along the characteristic directions. We show that the characteristic directions can be computed in parallel without the need for sharing information or synchronizing on a common time step. This permits the development of efficient asynchronous parallel algorithms. Our solutions cover the cases when the characteristic lines are intersected to form shock waves. We discuss the time performance of our algorithms as well as their implementation on a parallel computer.
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