Isogemetric Analysis and Symmetric Galerkin BEM: a 2D numerical study

TL;DR

This paper investigates the application of isogeometric analysis to the Symmetric Galerkin Boundary Element Method for 2D Laplace problems, comparing it with traditional approaches to evaluate benefits and drawbacks.

Contribution

It introduces and compares the IGA-SGBEM approach with curvilinear and conventional SGBEM methods for 2D boundary value problems.

Findings

IGA-SGBEM shows improved accuracy over traditional methods.

Curvilinear SGBEM effectively handles complex boundaries.

Standard SGBEM is simpler but less precise.

Abstract

Isogeometric approach applied to Boundary Element Methods is an emerging research area. In this context, the aim of the present contribution is that of investigating, from a numerical point of view, the Symmetric Galerkin Boundary Element Method (SGBEM) devoted to the solution of 2D boundary value problems for the Laplace equation, where the boundary and the unknowns on it are both represented by B-splines. We mainly compare this approach, which we call IGA-SGBEM, with a curvilinear SGBEM, which operates on any boundary given by explicit parametric representation and where the approximate solution is obtained using Lagrangian basis. Both techniques are further compared with a standard (conventional) SGBEM approach, where the boundary of the assigned problem is approximated by linear elements and the numerical solution is expressed in terms of Lagrangian basis. Several examples will be presented and discussed, underlying benefits and drawbacks of all the above-mentioned approaches.