@MISC{Allgower96exploitingsymmetry, author = {Eugene L. Allgower and Kurt Georg}, title = {Exploiting Symmetry in BEM}, year = {1996} }

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Abstract

: Classical integral operators usually display invariance with respect to orthogonal transformations. If the domain of an operator equation is symmetric with respect to some orthogonal transformations, then appropriate discretizations of the operator equation lead to system matrices which are equivariant with respect to a group of permutations. This property can be exploited to design efficient methods for solving the discrete problem. A generalization of the finite Fourier transform for arbitrary finite groups is used for this purpose. Some nodes of the discretization may be left invariant under some actions. This leads to complications in the numerical treatment which have recently been overcome. Often an operator equation is considered over a domain which is only nearly symmetric with respect to certain orthogonal transformations. Then the Fourier transform techniques on a related symmetrized problem can be used to obtain efficient preconditioners. This is especially important for i...