A new complex-valued formulation and eigenvalue analysis of the Helmholtz equation by boundary element method

By considering the close relationship between the multiple reciprocity boundary element formulation and that of the fundamental solution of the Helmholtz differential operator, we present a new complex-valued integral equation formulation for the eigenvalue analysis of the scalar-valued Helmholtz equation. Eigenvalues are determined as local minima of the determinant of the coefficient matrix of the discretized equation iteratively by the Newton scheme. The necessary recurrence formula is derived and computed with high efficiency, due to polynomial representation of the matrix components. Some example computations demonstrate the utility of the proposed formulation and eigenvalue determination scheme, and construction of adaptive boundary elements for the eigenvalue determination is attempted. Copyright (C) 1996 Elsevier Science Limited