Review of the Dual BEM and Recent Development of Null-Field Integral Equation Approach by NTOU/MSV

Abstract

In this lecture, the development of dual BEM is reviewed since its appearance in 1986 by Hong and Chen. The academic activity of BEM community in Taiwan is also reported. Methods to deal with hypersigularity are also examined. A novel method using the singular value decomposition (SVD) for problems with degenerate boundaries is proposed to distinguish the rank deficiency due to the rigid body mode and the degenerate boundary. Applications of the dual BEM to civil engineering and military problems are reviewed. To avoid singularities, a null-field integral equation approach in companion with an addition theorem (or so called degenerate kernel or separable kernel) is proposed. Several gains, exponential convergence, free of singularity and boundary layer effect, are achieved. Applications to circular, elliptical (2D), spherical and spheriroidal boundaries (3D) with emphasis on harbor resonance and SH wave scattering of hill and canyon are done. Focusing effect in harbor engineering and earthquake engineering are addressed.