Average source boundary node method for potential problems

Abstract

A new boundary meshfree method, named the average source boundary node method (ASBNM), is presented in this paper for potential problems. The method is based on coupling a ‘completely’ regularized boundary integral equation (CRBIE) with direct unknowns developed in this paper, removing the singularity computation, and an average source technique (AST). In this approach there are two critical developments. One is the presentation of a new removal singularity technique that results in the CRBIE, and therefore all diagonal coefficients of influence matrices can be determined analytically by the off-diagonal ones, unlike some existing boundary meshless approaches that determine diagonal coefficients from the fundamental solution by applying a known solution inside the domain, which amounts to solve the problem twice. The other is the introduction of an AST, by which the distributed source on a segment/cell can be reduced to a concentrated point source and therefore the boundary integrals in the CRBIE are not necessary. Hence, in the ASBNM only boundary nodes are required for computation without using any element or integration concept. Several test examples are presented to demonstrate the effectiveness and robustness of the proposed ASBNM.