Generalized eigenvalue formulation of the helmholtz equation by the trefftz method

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.

[1]  E. Kita,et al.  Trefftz method: an overview , 1995 .

[2]  P. K. Banerjee,et al.  A new BEM formulation for the acoustic eigenfrequency analysis , 1988 .

[3]  Surendra P. Shah,et al.  Orthotropic model of concrete for triaxial stresses , 1986 .

[4]  N. Kamiya,et al.  Standard eigenvalue analysis by boundary‐element method , 1993 .

[5]  C. Rajakumar,et al.  On the formulation of the acoustic boundary element eigenvalue problems , 1991 .

[6]  Norio Kamiya,et al.  Eigenvalue analysis by the boundary element method: new developments , 1993 .

[7]  N. Kamiya,et al.  Robust Boundary Element Scheme for Helmholtz Eigenvalue Equation , 1991 .

[8]  J. Jiroušek,et al.  T-elements: a finite element approach with advantages of boundary solution methods , 1995 .

[9]  J. Zhou.  Computations of eigenfunctions and eigenfrequencies of two dimensional vibrating structures by the boundary element method , 1989, Proceedings of the 28th IEEE Conference on Decision and Control,.

[10]  G. Bezine,et al.  A mixed boundary integral — Finite element approach to plate vibration problems , 1980 .

[11]  H. E. Salzer,et al.  Table errata: The numerical treatment of differential equations (third edition, Springer, Berlin, 1960) by L. Collatz , 1972 .

[12]  L. Collatz.  The numerical treatment of differential equations , 1961 .

[13]  K. Fyfe,et al.  An improved formulation for acoustic eigenmode extraction from boundary element models , 1990 .

[14]  N. Kamiya,et al.  A note on multiple reciprocity integral formulation for the Helmholtz equation , 1993 .