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Automated Transformations for PDE Systems with Application to Multigrid Solvers

An approach for transforming systems of partial differential equations in order to obtain new formulations which are more accessible to numerical solution is studied. An algorithm is developed for generating such transformations automatically, using symbolic computations employing Grobner bases. The algorithm is implemented using freely available software. This approach, along with planned developments, will potentially provide a powerful set of tools for handling large systems of partial differential equations.