A collocation CVBEM using program Mathematica

The well-known complex variable boundary element method (CVBEM) is extended for using collocation points not located at the usual boundary nodal point locations. In this work, several advancements to the implementation of the CVBEM are presented. The first advancement is enabling the CVBEM nodes to vary in location, impacting the modeling accuracy depending on chosen node locations. A second advancement is determining values of the CVBEM basis function complex coefficients by collocation at evaluation points defined on the problem boundary but separate and distinct from nodal point locations (if some or all nodes are located on the problem boundary). A third advancement is the implementation of these CVBEM modeling features on computer program Mathematica, in order to reduce programming requirements and to take advantage of Mathematica’s library of mathematical capabilities and graphics features.