Iterative local minimum search for eigenvalue determination of the Helmholtz equation by boundary element formulation

摘要

A scheme for lcoal minimum search for eigenvalue extraction of the scalar-valued Helmholtz equation is developed in this paper. In place of the zero-point search of the determinant of coefficient matrix by small increments of unknown eigenvalue, known conventionally, the zero-point of the first derivative of the determinant is found out iteratively. For this purpose, the coefficient matrix is represented in polynomial form in terms of the eigenvalue with help of the Multiple Reciprocity Boundary Element (MRM-BEM) formulation. The eigenvalue problem is fully formulated in complex-valued variables, different from the earlier MRM for the eigenvalue determination by the present authros. Two-dimensional formulation and some numerical examples are shown.