Comparison of two algorithms for locating computational nodes in the complex variable boundary element method (CVBEM)

Abstract

In this paper, we introduce a new node positioning algorithm (NPA) for determining suitable locations of the computational nodes that are a typical feature of mesh reduction numerical methods for partial differential equations – specifically, the Complex Variable Boundary Element Method (CVBEM). The novelty of the introduced NPA is a ‘position refinement’ procedure, which facilitates the relocation of nodes that are already being used in the current CVBEM model when such relocation reduces the maximum error of the associated CVBEM model. The results of the new NPA (referred to as NPA2) are compared to the results obtained using the recent NPA described in [1] (referred to as NPA1). We compare NPA1 and NPA2 by modeling two example Dirichlet boundary value problems that have been selected due to having regions of extreme curvature in the analytic flow regime that are difficult to model computationally. Consequently, these problems serve as good benchmark problems for testing the efficacy of the current and future NPAs. Our empirical findings suggest that the use of NPA2 can reduce the maximum error of the associated CVBEM model by several orders of magnitude compared to the corresponding result obtained using NPA1.