Non-symmetric isogeometric FEM-BEM couplings

TL;DR

This paper introduces a non-symmetric coupling of FEM and BEM within an isogeometric framework for efficient and accurate simulation of interface problems involving bounded and unbounded domains, with theoretical analysis and numerical validation.

Contribution

It develops a novel non-symmetric FEM-BEM coupling method using NURBS-based isogeometric analysis, providing well-posedness, error estimates, and improved convergence insights.

Findings

The coupled method is well-posed under monotonicity and Lipschitz conditions.

Error estimates are derived for the coupled system.

Numerical examples confirm theoretical convergence rates.

Abstract

We present a coupling of the Finite Element and the Boundary Element Method in an isogeometric framework to approximate either two-dimensional Laplace interface problems or boundary value problems consisting in two disjoint domains. We consider the Finite Element Method in the bounded domains to simulate possibly non-linear materials. The Boundary Element Method is applied in unbounded or thin domains where the material behavior is linear. The isogeometric framework allows to combine different design and analysis tools: first, we consider the same type of NURBS parameterizations for an exact geometry representation and second, we use the numerical analysis for the Galerkin approximation. Moreover, it facilitates to perform h- and p-refinements. For the sake of analysis, we consider the framework of strongly monotone and Lipschitz continuous operators to ensure well-posedness of the coupled system. Furthermore, we provide an a priori error estimate. We additionally show an improved convergence behavior for the errors in functionals of the solution that may double the rate under certain assumptions. Numerical examples conclude the work which illustrate the theoretical results.