scholarly journals Unstructured PEEC method with the use of surface impedance boundary condition

2020 ◽  
Vol 39 (5) ◽  
pp. 1017-1030 ◽  
Author(s):  
Gerard Meunier ◽  
Quang-Anh Phan ◽  
Olivier Chadebec ◽  
Jean-Michel Guichon ◽  
Bertrand Bannwarth ◽  
...  
Keyword(s):  
Finite Element ◽  
Surface Impedance ◽  
Computational Effort ◽  
Impedance Boundary Condition ◽  
Surface Mesh ◽  
Impedance Boundary ◽  
Content Type ◽  
Magnetic Effects ◽  
Coupled Circuits ◽  
Simply Connected

Purpose This paper aims to study unstructured-partial element equivalent circuit (PEEC) method for modelling electromagnetic regions with surface impedance condition (SIBC) is proposed. Two coupled circuits representations are used for solving both electric and/or magnetic effects in thin regions discretized by a finite element surface mesh. The formulation is applied in the context of low frequency problems with volumic magnetic media and coils. Non simply connected regions are treated with fundamental branch independent loop matrices coming from the circuit representation. Design/methodology/approach Because of the use of Whitney face elements, two coupled circuits representations are used for solving both electric and/or magnetic effects in thin regions discretized by a finite element surface mesh. The air is not meshed. Findings The new surface impedance formulation enables the modeling of volume conductive regions to efficiently simulate various devices with only a surface mesh. Research limitations/implications The propagation effects are not taken into account in the proposed formulation. Originality/value The formulation is original and is efficient for modeling non simply connected conductive regions with the use of SIBC. The unstructured PEEC SIBC formulation has been validated in presence of volume magnetic nonconductive region and compared with a SIBC FEM approach. The computational effort is considerably reduced in comparison with volume approaches.

scholarly journals FDTD modeling of nonperiodic antenna located above metasurface using surface impedance boundary condition

2019 ◽  
Vol 6 ◽  
pp. 17
Author(s):  
Toru Uno ◽  
Takuji Arima ◽  
Akihide Kurahara
Keyword(s):  
Boundary Condition ◽  
Surface Impedance ◽  
Fdtd Method ◽  
Dipole Antenna ◽  
Point Sources ◽  
Impedance Boundary Condition ◽  
Computational Error ◽  
Impedance Boundary ◽  
Scanning Method ◽  
Computational Resources

This paper investigates an FDTD modeling method for precisely calculating the characteristics of a single, that is, a nonperiodic antenna located above a metasurface that consists of an infinite periodic conducting element on a flat dielectric substrate. The original FDTD method requires enormous computational resources to analyze such structures because an appropriate periodic boundary condition (PBC) is not supported, and a brute force approach has to be used for this reason. Another option is to use the array scanning method in which a single source is synthesized from a superposition of infinite phased array of point sources. In this method, some problems such as a mutual coupling between the single antenna and the metasurface, a computational error contained in a numerical integration over the Brillouin zone and so on have not been resolved yet. In order to resolve these difficulties and to reduce computational resources, a surface impedance boundary condition (SIBC) is incorporated into the FDTD method in this paper. The validity of the method is numerically confirmed by calculating an input impedance and a radiation pattern of a horizontal dipole antenna located above the metasurface.

Nonlinear impedance boundary condition for 2D BEM

2018 ◽  
Vol 37 (2) ◽  
pp. 772-783 ◽  
Author(s):  
Carlo de Falco ◽  
Luca Di Rienzo ◽  
Nathan Ida ◽  
Sergey Yuferev
Keyword(s):  
Magnetic Field ◽  
Perturbation Theory ◽  
Diffusion Equation ◽  
Efficient Implementation ◽  
Impedance Boundary Condition ◽  
Computational Domain ◽  
Impedance Boundary ◽  
Content Type ◽  
The Magnetic Field ◽  
Element Method

PurposeThe purpose of this paper is the derivation and efficient implementation of surface impedance boundary conditions (SIBCs) for nonlinear magnetic conductors. Design/methodology/approachAn approach based on perturbation theory is proposed, which expands to nonlinear problems the methods already developed by the authors for linear problems. Differently from the linear case, for which the analytical solution of the diffusion equation in the semi-infinite space for the magnetic field is available, in the nonlinear case the corresponding nonlinear diffusion equation must be solved numerically. To this aim, a suitable smooth map is defined to reduce the semi-infinite computational domain to a finite one; then the diffusion equation is solved by a Galerkin method relying on basis functions constructed via the push-forward of a Lagrangian polynomial basis whose degrees of freedom are collocated at Gauss–Lobatto nodes. The use of such basis in connection with a suitable under-integration naturally leads to mass-lumping without impacting the order of the method. The solution of the diffusion equation is coupled with a boundary element method formulation for the case of parallel magnetic conductors in terms of E and B fields. FindingsThe results are validated by comparison with full nonlinear finite element method simulations showing very good accordance at a much lower computational cost. Research limitations/implicationsLimitations of the method are those arising from perturbation theory: the introduced small parameter must be much less than one. This implies that the penetration depth of the magnetic field into the magnetic and conductive media must be much smaller than the characteristic size of the conductor. Originality/valueThe efficient implementation of a nonlinear SIBC based on a perturbation approach is proposed for an electric and magnetic field formulation of the two-dimensional problem of current driven parallel solid conductors.

Application of the impedance boundary condition in a finite element environment using the reduced potential formulation

1991 ◽  
Vol 27 (6) ◽  
pp. 5022-5024 ◽  
Author(s):  
J. Sakellaris ◽  
G. Meunier ◽  
X. Brunotte ◽  
C. Guerin ◽  
J.C. Sabonnadiere
Keyword(s):  
Boundary Condition ◽  
Finite Element ◽  
Impedance Boundary Condition ◽  
Impedance Boundary ◽  
Potential Formulation
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