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Mathematics
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The BEM and FEM/BEM Methods in Computational Electromagnetics
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The BEM and FEM/BEM Methods in Computational Electromagnetics

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Difference and Differential Equations".

Deadline for manuscript submissions: closed (30 April 2022) | Viewed by 7451

Special Issue Editor

Prof. Dr. Jacques Lobry

E-Mail Website
Guest Editor
General Physics Department, Faculty of Engineering, University of Mons, 7000 Mons, Belgium
Interests: computational electromagnetics; high voltage engineering

Special Issue Information

Dear Colleagues,

It is well known that many boundary-value problems can efficiently be solved numerically by means of the finite element method (FEM) and the boundary element method (BEM). The finite element method is very general and flexible. It can be applied to nonlinear problems, and the system of algebraic equations obtained is sparse and often symmetric and positive definite. However, it requires a bounded domain. By contrast, the boundary element method can elegantly deal with unbounded regions. It is more efficient in meshing due to the reduction of dimensions, and the resulting stiffness matrix is smaller but is fully populated, which is an often mentioned drawback. BEM is also restricted to linear problems. Clearly, FEM and BEM are complementary. This is the reason why hybrid FEM/BEM schemes have been developed for many years in order “to get the best of both worlds”. Several FEM/BEM coupling implementations are found in the literature. A distinguishing feature is the BEM procedure employed. Collocation and symmetric Galerkin are the most common approaches.

The aim of this Special Issue is to update the related techniques in the context of computational electromagnetics. Topics of interest include (but are not limited to) numerical methods as well as DC to high-frequency applications. Contributions that involve a review of the state-of-the-art in this area will be welcome.

Prof. Dr. Jacques Lobry
Guest Editor

Manuscript Submission Information

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Keywords

  • FEM/BEM coupling
  • Computational electromagnetics
  • Finite element analysis
  • Boundary integral equations
  • Collocation BEM
  • Symmetric Galerkin boundary element method

Published Papers (4 papers)

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Research

18 pages, 3668 KiB  
Article
The Hybrid FEM-DBCI for the Solution of Open-Boundary Low-Frequency Problems
by Giovanni Aiello, Salvatore Alfonzetti, Santi Agatino Rizzo and Nunzio Salerno
Mathematics 2021, 9(16), 1968; https://0-doi-org.brum.beds.ac.uk/10.3390/math9161968 - 17 Aug 2021
Viewed by 1189
Abstract
This paper describes a particular use of the hybrid FEM-DBCI, for the computation of low-frequency electromagnetic fields in open-boundary domains. Once the unbounded free space enclosing the system has been truncated, the FEM is applied to the bounded domain thus obtained, assuming an [...] Read more.
This paper describes a particular use of the hybrid FEM-DBCI, for the computation of low-frequency electromagnetic fields in open-boundary domains. Once the unbounded free space enclosing the system has been truncated, the FEM is applied to the bounded domain thus obtained, assuming an unknown Dirichlet condition on the truncation boundary. An integral equation is used to express this boundary condition in which the integration surface is selected in the middle of the most external layer of finite elements, very close to the truncation boundary, so that the integral equation becomes quasi-singular. The method is described for the computation of electrostatic fields in 3D and of eddy currents in 2D, but it is also applicable to the solution of other kinds of electromagnetic problems. Comparisons are made with other methods, concluding that FEM-DBCI is competitive with the well-known FEM-BEM and coordinate transformations for what concerns accuracy and computing time. Full article
(This article belongs to the Special Issue The BEM and FEM/BEM Methods in Computational Electromagnetics)
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18 pages, 3041 KiB  
Article
Electromagnetic Devices with Moving Parts—Simulation with FEM/BEM Coupling
by Thomas Rüberg, Lars Kielhorn and Jürgen Zechner
Mathematics 2021, 9(15), 1804; https://0-doi-org.brum.beds.ac.uk/10.3390/math9151804 - 30 Jul 2021
Cited by 2 | Viewed by 1919
Abstract
The numerical analysis of electromagnetic devices by means of finite element methods (FEM) is often hindered by the need to incorporate the surrounding domain. The discretisation of the air may become complex and has to be truncated by artificial boundaries incurring a modelling [...] Read more.
The numerical analysis of electromagnetic devices by means of finite element methods (FEM) is often hindered by the need to incorporate the surrounding domain. The discretisation of the air may become complex and has to be truncated by artificial boundaries incurring a modelling error. Even more problematic are moving parts that require tedious re-meshing and mapping techniques. In this work, we tackle these problems by using the boundary element method (BEM) in conjunction with FEM. Whereas the solid parts of the electrical device are discretised by FEM, which can easily account for material non-linearities, the surrounding domain is represented by BEM, which requires only a surface discretisation. This approach completely avoids an air mesh and its re-meshing during the simulation with moving or deforming parts. Our approach is robust, shows optimal complexity, and provides an accurate calculation of electromagnetic forces that are required to study the mechanical behaviour of the device. Full article
(This article belongs to the Special Issue The BEM and FEM/BEM Methods in Computational Electromagnetics)
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11 pages, 4295 KiB  
Article
A FEM-Green Approach for Magnetic Field Problems with Open Boundaries
by Jacques Lobry
Mathematics 2021, 9(14), 1662; https://0-doi-org.brum.beds.ac.uk/10.3390/math9141662 - 15 Jul 2021
Cited by 4 | Viewed by 1782
Abstract
A new finite element method/boundary element method (FEM/BEM) scheme is proposed for the solution of the 2D magnetic static and quasi-static problems with unbounded domains. The novelty is an original approach in the treatment of the outer region. The related domain integral is [...] Read more.
A new finite element method/boundary element method (FEM/BEM) scheme is proposed for the solution of the 2D magnetic static and quasi-static problems with unbounded domains. The novelty is an original approach in the treatment of the outer region. The related domain integral is eliminated at the discrete level by using the finite element approximation of the fundamental solutions (Green’s functions) at every node of the related mesh. This “FEM-Green” approach replaces the standard boundary element method. It is simpler to implement because no integration on the boundary of the domain is required. Then, the method leads to a substantially reduced computational burden. Moreover, the coupling with finite elements is more natural since it is based on the same Galerkin approximation. Some examples with open boundary and nonlinear materials are presented and compared with the standard finite element method. Full article
(This article belongs to the Special Issue The BEM and FEM/BEM Methods in Computational Electromagnetics)
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30 pages, 3148 KiB  
Article
Coupling the Cell Method with the Boundary Element Method in Static and Quasi–Static Electromagnetic Problems
by Federico Moro and Lorenzo Codecasa
Mathematics 2021, 9(12), 1426; https://0-doi-org.brum.beds.ac.uk/10.3390/math9121426 - 19 Jun 2021
Cited by 6 | Viewed by 1616
Abstract
A unified discretization framework, based on the concept of augmented dual grids, is proposed for devising hybrid formulations which combine the Cell Method and the Boundary Element Method for static and quasi-static electromagnetic field problems. It is shown that hybrid approaches, already proposed [...] Read more.
A unified discretization framework, based on the concept of augmented dual grids, is proposed for devising hybrid formulations which combine the Cell Method and the Boundary Element Method for static and quasi-static electromagnetic field problems. It is shown that hybrid approaches, already proposed in literature, can be rigorously formulated within this framework. As a main outcome, a novel direct hybrid approach amenable to iterative solution is derived. Both direct and indirect hybrid approaches, applied to an axisymmetric model, are compared with a reference third-order 2D FEM solution. The effectiveness of the indirect approach, equivalent to the direct approach, is finally tested on a fully 3D benchmark with more complex topology. Full article
(This article belongs to the Special Issue The BEM and FEM/BEM Methods in Computational Electromagnetics)
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