EXPLOITING SYMMETRY IN BOUNDARY ELEMENT METHODS

Linear operator equations Lf = g are considered in the context of boun dary element methods, where the operator L is equivariant, i.e., commu tes with the actions of a given finite symmetry group. By introducing a generalization of Reynolds projectors, a decomposition of the identi ty operator is constructed, which in turn allows the decomposition of the problem Lf = g into a finite number of symmetric subproblems. The data function g does not need to possess any symmetry properties. It i s shown that analogous reductions are possible for discretizations. An explicit construction of the corresponding reduced system matrices is given. This effects a considerable reduction in the computational com plexity. For example, in the case of the isometry group of the 3-cube, the computational complexity of a direct linear equation solver for f ull matrices is reduced by 99.65 percent. Specific decompositions of t he identity are given for most of the significant finite isometry grou ps acting on R2 and R3.