Coupling of finite element method and integral formulation for vector Helmholtz equation

Abstract

PurposeConsidering the vector Helmholtz equation in three dimensions, this paper aims to present a novel approach for coupling the finite element method and a boundary integral formulation. It is demonstrated that the method is well-suited for many realistic three-dimensional problems in high-frequency engineering.Design/methodology/approachThe formulation is based on partial solutions fulfilling the global boundary conditions and the iterative interaction between them. In comparison to other coupling formulation, this approach avoids the typical singularity in the integral kernels. The approach applies ideas from domain decomposition techniques and is implemented for a parallel calculation.FindingsUsing confirming elements for the trace space and default techniques to realize the infinite domain, no additional loss in accuracy is introduced compared to a monolithic finite element method approach. Furthermore, the degree of coupling between the finite element method and the integral formulation is reduced. The accuracy and convergence rate are demonstrated on a three-dimensional antenna model.Research limitations/implicationsThis approach introduces additional degrees of freedom compared to the classical coupling approach. The benefit is a noticeable reduction in the number of iterations when the arising linear equation systems are solved separately.Practical implicationsThis paper focuses on multiple heterogeneous objects surrounded by a homogeneous medium. Hence, the method is suited for a wide range of applications.Originality/valueThe novelty of the paper is the proposed formulation for the coupling of both methods.