Revist of the dual BEM for crack problems using SVD updating technique

Abstract

The boundary element method (BEM) is easier than the finite element method (FEM) on the viewpoint of the discretization of one dimension reduction rather than the domain discretization of the finite element method. The disadvantage of BEM is the rank deficiency in the influence matrix, which do not occur in the FEM. The dual BEM is used to ensure a unique solution for the problem containing a degenerate boundary by combining the singular and hypersingular equations. Following the successful experience on the retrieval of information using singular value decomposition (SVD) updating term and updating document, this technique is also used to extract out the informations in the dual BEM. Finally, a cracked bar under torsion was demonstrated to see the mathematical SVD structure of four influence matrices in the dual BEM.