| Partial Differential Equations on the Intel Touchstone Delta Supercomputer (2008) | |||||||||||||||
Abstract | |||||||||||||||
| Evolutionary partial differential actuations are usually solved by discretization in time and space, and by applying a marching in time procedure to data and algorithms potentially parallelized in the spatial domain.--2 In a cleparture from such a strictly. sequential temporal paradigm, we have developed the concept of-_.. — tinle~~rgll~l__~~orithms, which allow the marching in time to be fully parallelized. This is achieved by using a transforma-tion based on the eigenvalue-eigenvector decomposition of the matrices resulting from the discretization process. Since these matrices are involved in the time stepping iterations, the resulting diagonalization yields ‘(time parallel ” algorithms, i.e., algorithms that pos-sess a highly decoupled temporal structure, and hence can be efficiently implemented on emerging massively parallel MIMD architectures with a minimum of communication and synchronization overhead. Specifically, our algorithms have been implemented on the Intel Touchstone Delta supercomputer. We have illustrated our approach on a two-dimensional heat equation, and have demonstrated that a linear speedup can be achieved and main-tained, even for a very large number of processor nodes. 1. | |||||||||||||||
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