Eigenvalue analysis by the boundary element method: new developments

Abstract Recent developments in boundary element eigenvalue analysis are reviewed, focusing on the Helmholtz equation in terms of a scalar-valued function. The problem is of fundamental importance in the framework of the sophisticated boundary element scheme, in general devised for the non-homogeneous differential equation. The most popular approach using domain cells for domain integration and some transformation methods, such as the dual reciprocity method (DRM) and the multiple reciprocity method (MRM), are discussed. Two key issues are the solution without domain integration and the standard routine eigenvalue search in contrast to the conventional domain cell discretization and the direct eigenvalue search using distribution of the magnitude of the determinant, which are the marked item of the boundary element method for numerical efficiency and are preffered over other methods.

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