Generalized eigenvalue formulation of the helmholtz equation by the trefftz method

Abstract

A new‐type eigenvalue formulation of the two‐dimensional Helmholtz equation is presented in this paper. A boundary integral equation is derived using the T‐complete functions relevant to the Trefftz method, which is further transformed to the generalized eigenvalue problem. Boundary discretization and a standard eigenvalue computation routine, offered as a black box, are sufficient for the determination of the eigenvalues. The proposed method can reduce the users’ task in preprocessing and initial rough estimation when compared with the existing domain‐type solvers.

Citation

Kamiya, N. and Wu, S.T. (1994), "Generalized eigenvalue formulation of the helmholtz equation by the trefftz method", Engineering Computations, Vol. 11 No. 2, pp. 177-186. https://doi.org/10.1108/02644409410799218