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Cellular Computing and Least Squares for Partial Differential Problems Parallel Solving
Nicolas Fressengeas and Hevre Frezza-Buet

This paper shows how partial differential problems can be numerically solved on a parallel cellular architecture through a completely automated procedure. This procedure leads from a discrete differential problem to a Cellular Algorithm that efficiently runs on parallel distributed memory architectures.

This completely automated procedure is based on a adaptation of the Least Square Finite Elements Method that allows local only computations in a discrete mesh. These local computations are automatically derived from the discrete differential problem through formal computing and lead automatically to a Cellular Algorithm which is efficiently coded for parallel execution on a dedicated distributed interactive platform.

Keywords: Partial differential equations, cellular automata, distributed memory, parallel architectures, LSFEM, finite elements

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