Search

When solving open-region electromagnetic scattering problems using the standard finite element method, the infinite region exterior to the scatterer must be truncated with an artificial outer boundary. In the interior or finite part of the domain, finite elements can be used, but a boundary condition must be introduced at this artificial boundary to obtain a unique finite element solution. One class of boundary conditions designed for this purpose is called absorbing boundary conditions (ABCs). Several ABCs have been reported in the literature. These can be broadly classified into two categories: local and non-local. In this paper, we present new closed-form expressions for Nth-order local ABCs, equivalent to the well-known sequences of the Bayliss, Gunzburger, and Turkel boundary operators. To the best of our knowledge, these expressions have not yet been reported in the literature. Two- and three-dimensional problems are considered in this study. We also discuss the problem of incorporating custom ABCs into commercial finite element method programs, which are usually closed-source software packages. Two 2D electromagnetic scattering and radiation problems with known analytical solutions are analyzed. [ABSTRACT FROM AUTHOR]

When solving open-region electromagnetic scattering problems using the standard finite element method, the infinite region exterior to the scatterer must be truncated with an artificial outer boundary. In the interior or finite part of the domain, finite elements can be used, but a boundary condition must be introduced at this artificial boundary to obtain a unique finite element solution. One class of boundary conditions designed for this purpose is called absorbing boundary conditions (ABCs). Several ABCs have been reported in the literature. These can be broadly classified into two categories: local and non-local. In this paper, we present new closed-form expressions for Nth-order local ABCs, equivalent to the well-known sequences of the Bayliss, Gunzburger, and Turkel boundary operators. To the best of our knowledge, these expressions have not yet been reported in the literature. Two- and three-dimensional problems are considered in this study. We also discuss the problem of incorporating custom ABCs into commercial finite element method programs, which are usually closed-source software packages. Two 2D electromagnetic scattering and radiation problems with known analytical solutions are analyzed.

This article describes a novel and accurate implementation of finite element method-boundary element method (FEM-BEM) coupling based on Argyris element (AE), for the $C^{1}$ solution of axi-symmetric magnetostatic problems in open boundary domains. The aim of the work is twofold: 1) to provide novel, easy, and accurate way to compute the basis functions that is strongly not affected by accuracy errors and 2) to give a clear mathematical and numerical description of the FEM-BEM coupling based on AE. The first goal is achieved by shifting to the origin the physical triangular elements and computing the basis function in the shifted coordinate system. Second, AE-based FEM-BEM coupling relies on the boundary integral equations (BIEs) for poloidal flux and its partial derivatives of both first and second order, accurately computed by combining the analytical formula based on elliptic integrals together with high degree Gaussian cubature. The application of the proposed method to an advanced plasma equilibrium magnetic configuration, typical of magnetic confinement fusion (MCF) (i.e., snowflake configuration), highlights that, even in case of coarse triangulation, satisfactory results can be achieved, and the error on the boundary conditions (BCs) is well below machine working precision. [ABSTRACT FROM AUTHOR]

In this paper an improved placement of the integration surface for the integral equation in the hybrid finite element method--Dirichlet boundary condition iteration (FEM-DBCI) method is achieved by selecting it as lying in the middle of the tetrahedral or hexahedral finite elements. A better accuracy is obtained with respect to the case in which the integration surface lies along the element faces. Some numerical examples are provided. [ABSTRACT FROM AUTHOR]