Cellular Computing and Least Squares for Partial Differential Problems Parallel Solving

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.