@**incollection**{RISC4252,author = {Christoph Koutschan and Christoph Lehrenfeld and Joachim Schoeberl},

title = {{Computer Algebra meets Finite Elements: an Efficient Implementation for Maxwell's Equations}},

booktitle = {{Numerical and Symbolic Scientific Computing: Progress and Prospects}},

language = {english},

abstract = {We consider the numerical discretization of the time-domain Maxwell's
equations with an energy-conserving discontinuous Galerkin finite
element formulation. This particular formulation allows for higher
order approximations of the electric and magnetic field. Special
emphasis is placed on an efficient implementation which is achieved by
taking advantage of recurrence properties and the tensor-product
structure of the chosen shape functions. These recurrences have been
derived symbolically with computer algebra methods reminiscent of the
holonomic systems approach.},

series = {Texts and Monographs in Symbolic Computation},

volume = {1},

pages = {105--121},

publisher = {Springer},

address = {Wien},

isbn_issn = {ISBN 978-3-7091-0793-5},

year = {2012},

editor = {Ulrich Langer and Peter Paule},

refereed = {yes},

length = {18}

}