A collocation IGA-BEM for 3D potential problems on unbounded domains

TL;DR

This paper presents a novel isogeometric boundary element method for solving 3D potential problems on unbounded domains, utilizing spline-based cubature formulas and singularity extraction to improve accuracy and efficiency.

Contribution

It introduces a new IGA-BEM approach with specialized spline cubature formulas and a robust singularity extraction method for 3D unbounded potential problems.

Findings

Numerical solutions achieve expected convergence orders

Spline quasi-interpolation enhances integral approximation

The method effectively handles weakly and nearly singular integrals

Abstract

In this paper the numerical solution of potential problems defined on 3D unbounded domains is addressed with Boundary Element Methods (BEMs), since in this way the problem is studied only on the boundary, and thus any finite approximation of the infinite domain can be avoided. The isogeometric analysis (IGA) setting is considered and in particular B-splines and NURBS functions are taken into account. In order to exploit all the possible benefits from using spline spaces, an important point is the development of specific cubature formulas for weakly and nearly singular integrals. Our proposal for this aim is based on spline quasi-interpolation and on the use of a spline product formula. Besides that, a robust singularity extraction procedure is introduced as a preliminary step and an efficient function-by-function assembly phase is adopted. A selection of numerical examples confirms that the numerical solutions reach the expected convergence orders.