A least squares approach for determining the coefficients of the CVBEM approximation function

Abstract

Two approaches for formulating a computational Complex Variable Boundary Element Method (CVBEM) model are examined. In particular, this paper considers a collocation approach as well as a least squares approach. Both techniques are used to fit the CVBEM approximation function to given boundary conditions of benchmark boundary value problems (BVPs). Both modeling techniques provide satisfactory computational results, when applied to the demonstration problems, but differ in specific outcomes depending on the number of nodes used and the type of BVP being examined. Historically, the CVBEM has been implemented using the collocation approach. Therefore, the novelty of this work is in formulating the least squares approach and applying the least squares formulation to a Dirichlet BVP as well as a mixed BVP. This work does not claim that one technique should always be used over the other, but rather it seeks to demonstrate the viability of the least squares approach and assert that both techniques for determining the coefficients of the CVBEM approximation function should be considered during the modeling process.