Application of an accelerated boundary-based mesh-free method to two-dimensional problems in potential theory

Abstract

The boundary node method (BNM) is a boundary-only meshfree method based on boundary integral equations (BIE). One drawback of the usual BNM, however, is that it typically requires much more computer time than the usual boundary element method (BEM). The multipole method (MM) has been demonstrated, in the context of the n body problem, and the BEM, to greatly accelerate these methods while still maintaining sufficient accuracy. The present paper explores, for the first time, a coupling of the BNM with the MM (called the BNMM) in the context of 2-D potential theory. Numerical results (for selected problems) from the BNM are compared with those from the BNMM with regard to accuracy and computational efficiency.