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We consider the numerical discretization of the time-domain Maxwell'sequations with an energy-conserving discontinuous Galerkin finite elementformulation. This particular formulation allows for higher order approximationsof the electric and magnetic field. Special emphasis is placed on an efficientimplementation which is achieved by taking advantage of recurrence propertiesand the tensor-product structure of the chosen shape functions. Theserecurrences have been derived symbolically with computer algebra methodsreminiscent of the holonomic systems approach.

Computer Algebra meets Finite Elements: an Efficient Implementation for Maxwell's Equations