LANCZOS-ALGORITHM FOR ACOUSTIC BOUNDARY ELEMENT EIGENVALUE PROBLEMS

Acoustic eigenvalue analysis by the boundary element method results in a generalized eigensystem of the form [K{x} = lambda[M]{x}, where [K] and [M] are fully populated unsymmetric matrices. With a brief outline of the boundary element procedure, a Lanczos-two-sided recursion algorithm is presented to solve the unsymmetric eigenproblem. Details on the implementation of the scheme as coded in the ANSYS(R) general purpose computer program are described. Numerical examples on two-dimensional (2-D) acoustic eigenvalue analysis are included to demonstrate the effectiveness of the Lanczos algorithm in extracting the first few eigenfrequencies of large problems. Issues relating to the effectiveness of the boundary element procedure when compared to the acoustic finite element eigenvalue formulation are discussed.