Optimized overdetermination for interior Helmholtz problem coupled solvers.

Abstract

The use of points of overdetermination, so-called CHIEF points, in numerical solutions to exterior Helmholtz problems for the elimination of spurious modes is well established. Further, the number and relative position of such points in two-dimensional radially symmetric geometries has been demonstrated theoretically. Since CHIEF points require lower computational overhead than collocation nodes, strategic use represents an opportunity for the improvement of predictions with maximal efficiency. Given the differing uniqueness properties of solutions to the interior and exterior problems, the former allows for development of optimization in the absence of competing priorities. Theory for two- and three-dimensional analytical cases is developed and subsequently extended to general geometries. Localization with respect to subdomains of spatial decomposition is investigated as well.