Perfect Electric Conductor Boundary Conditions Research Articles

Thin Dielectric Sheet Approximation-Based Characteristic Mode Formulations for Lossless Dielectric Coated Conducting Bodies

The thin dielectric sheet (TDS) approximation-based theory of characteristic modes (TCM) is formulated for lossless thin dielectric-coated conducting bodies. The proposed formulations are derived from the TDS-electric, magnetic, and combined field integral operators (TDS-EFIO, TDS-MFIO, and TDS-CFIO). Similar to the cases of perfect electric conductor (PEC) and impedance surface, the TDS-CFIO-based formulation can avoid modes corruption by spurious solutions at the internal resonant frequencies of the PEC cavity filled with the material of the background. Due to the utilization of TDS approximation and PEC boundary conditions, the eigencurrents are expressed only by electric currents on the surface of PEC. Therefore, the proposed formulations are more efficient than the conventional formulations based on the surface integral operator (SIO) or volume-surface integral operator (VSIO). The coating thickness of TDS approximation is recommended to be less than one tenth of a wavelength in the dielectric for accurate analysis of characteristic mode (CM). Several numerical examples are given to validate the proposed formulations.

Higher-order accurate finite-difference simulation for tunnel propagation modeling

PurposeThis paper aims to improve the computational efficiency of higher-order accurate Noye–Hayman [NH (9,9)] implicit finite difference scheme for the solution of electromagnetic scattering problems in tunnel environments.Design/methodology/approachThe proposed method consists of two major steps: First, the higher-order NH (9,9) scheme is numerically discretized using the finite-difference method. The second step is to use an algorithm based on hierarchical interpolative factorization (HIF) to accelerate the solution of this scheme.FindingsIt is observed that the simulation results obtained from the numerical tests illustrate very high accuracy of the NH (9,9) method in typical tunnel environments. HIF algorithm makes the NH (9,9) method computationally efficient for two-dimensional (2D) or three-dimensional (3D) problems. The proposed method could help in reducing the computational cost of the NH (9,9) method very close to O(n) usual O(n3) for a full matrix.Research limitations/implicationsFor simplicity, in this study, perfect electric conductor boundary conditions are considered. Future research may also include the utilization of meteorological techniques, including the effects of backward traveling waves, and make comparisons with the experimental data.Originality/valueThis study is directly applicable to typical problems in the field of tunnel propagation modeling for both national commercial and military applications.

FDTD Schemes for Maxwell’s Equations with Embedded Perfect Electric Conductors Based on the Correction Function Method

In this work, we propose staggered FDTD schemes based on the correction function method (CFM) to discretize Maxwell’s equations with embedded perfect electric conductor boundary conditions. The CFM uses a minimization procedure to compute a correction to a given FD scheme in the vicinity of the embedded boundary to retain its order. The minimization problem associated with CFM approaches is analyzed in the context of Maxwell’s equations with embedded boundaries. In order to obtain a well-posed minimization problem, we propose fictitious interfaces to fulfill the lack of information, namely the surface current and charge density, on the embedded boundary. We introduce CFM-FDTD schemes based on the well-known Yee scheme and a fourth-order staggered FDTD scheme. We investigate the stability of these CFM-FDTD schemes using long time simulations. Convergence studies are performed in 2-D for various geometries of the embedded boundary. CFM-FDTD schemes have shown high-order convergence.

Efficient schemes for Maxwell's equations with PEC boundary condition

High-order compact discretization has been successfully applied to Maxwell's equations with periodic boundary conditions. However, the discretization cannot be applied to Maxwell's equations with perfect electric conductor boundary condition directly since the stencil involves the exterior nodal values of the electric and magnetic fields at/near the boundary. Combining the perfect electric conductor boundary condition with Maxwell's equations, we establish a relationship between the interior and exterior nodal values. The given relationship ensures the stability and accuracy of the high-order compact discretization. Two efficient splitting schemes are developed for Maxwell's equations. Numerical results show the good performance of the proposed schemes.

A Fundamental LOD-FDTD Method in Cylindrical Coordinates

An efficient implicit finite-difference time-domain (FDTD) algorithm in cylindrical coordinates is developed on the basis of a fundamental locally 1-D scheme. The Sherman–Morrison formula is introduced to treat a cyclic matrix and the image theory is utilized to impose the perfect electric conductor boundary condition. The effectiveness of the present method is investigated through the analysis of a metal disc-type terahertz surface wave splitter. The computation time is found to be reduced to less than half that of the explicit FDTD method, while maintaining a comparable accuracy.

Implementation of PEC boundary condition for Laguerre-RPIM meshless method with novel uniform nodal distribution

The implementation of perfect electric conductor (PEC) boundary condition for meshless radial point interpolation method (RPIM) with the weighted decaying Laguerre polynomial (WLP) is investigated. A novel uniform nodal placement is proposed and the number of H-nodes reduces to about a half of that for the conventional scheme. There are only E-nodes scattered on the PEC boundary. The E-node and H-node have the same scale of support domain nodes. The image theory is adopted to update the implicit electric equations on the PEC boundary. This scheme is also suitable for nonuniform node distribution. Numerical results have verified the accuracy of the proposed method.

Equivalent Transmission Conditions for the Time-Harmonic Maxwell Equations in 3D for a Medium with a Highly Conductive Thin Sheet

We propose equivalent transmission conditions of order 1 and 2 for thin and highly conducting sheets for the time-harmonic Maxwell's equation in three dimensions. The transmission conditions are derived asymptotically for vanishing sheet thickness $\varepsilon$ where the skin depth is kept proportional to $\varepsilon$. The condition of order 1 turns out to be the perfect electric conductor boundary condition. The conditions of order 2 appear as generalized Poincareź--Steklov maps between tangential components of the magnetic field and the electric field, and they are of Wentzell type involving second order surface differential operators. Numerical results with finite elements of higher order validate the asymptotic convergence for $\varepsilon\to0$ and the robustness of the equivalent transmission condition of order 2.

A Fourier penalty method for solving the time-dependent Maxwell's equations in domains with curved boundaries

We present a high order, Fourier penalty method for the Maxwell's equations in the vicinity of perfect electric conductor boundary conditions. The approach relies on extending the smooth non-periodic domain of the equations to a periodic domain by removing the exact boundary conditions and introducing an analytic forcing term in the extended domain. The forcing, or penalty term is chosen to systematically enforce the boundary conditions to high order in the penalty parameter, which then allows for higher order numerical methods. We present an efficient numerical method for constructing the penalty term, and discretize the resulting equations using a Fourier spectral method. We demonstrate convergence orders of up to 3.5 for the one-dimensional Maxwell's equations, and show that the numerical method does not suffer from dispersion (or pollution) errors. We also illustrate the approach in two dimensions and demonstrate convergence orders of 2.5 for transverse magnetic modes and 1.5 for the transverse electric modes. We conclude the paper with numerous test cases in dimensions two and three including waves traveling in an irregular waveguide, and scattering off of a windmill-like geometry.

SLAB BAG FERMIONIC CASIMIR EFFECT, CHIRAL BOUNDARIES AND VECTOR BOSON — MAJORANA FERMION PISTONS

In this paper we consider the Casimir energy and force of massless Majorana fermions and vector bosons between parallel plates. The vector bosons satisfy perfect electric conductor boundary conditions, while the Majorana fermions satisfy bag and chiral boundary conditions. We consider various piston configurations containing one vector boson and one fermion. We make use of supersymmetry, broken on the boundaries, to explain the number of fields that appear in all the studied cases. The effect of chiral boundary conditions in a fermion–boson system is investigated. Concerning the supersymmetry issue and the vanishing of the Casimir energy, we study a massive Dirac fermion–scalar boson system with bag and specific Robin type boundary conditions for which the Casimir energy vanishes. Finally, a two-scalar-boson system between parallel plates is presented in which the singularities vanish in the total Casimir energy.

Implementations of PMC and PEC Boundary Conditions for Efficient Fundamental ADI- and LOD-FDTD

This paper presents the implementations of perfect magnetic conductor (PMC) and perfect electric conductor (PEC) boundary conditions for efficient fundamental alternating-direction-implicit (ADI) and locally one-dimensional (LOD) finite-difference time-domain (FDTD). The PMC (or PEC) boundary equations for implicit updating of electric (or magnetic) fields in efficient fundamental ADI- and LOD-FDTD schemes are derived using image theory. Image theory facilitates the implementation of PMC and/or PEC boundary conditions regardless of whether the update equations for electric or magnetic fields are implicit. Comparison between the PMC and PEC boundary equations in conventional and efficient fundamental schemes of ADI- and LOD-FDTD signifies a reduction in the floating-point operations count, thus justifying the higher efficiency and simplicity for the fundamental schemes.

A highly efficient numerical solution for dielectric-coated PEC targets

In this paper, the multi-layer TDS (thin dielectric sheet) integral equation approach is first proposed. This method divides the geometric model into multiple thin layers and assumes the flux density to be constant with respect to the normal direction within each layer. Consequently, the number of unknowns is significantly reduced while the precision of the results could be maintained. Then, the multi-layer TDS integral approach is combined with the PEC (perfect electric conductor) boundary conditions together to handle scattering from dielectric coated PEC objects. This new procedure simplifies the coupled surface (for the conductor)–volume (for dielectric) integral to a surface–surface integral with much fewer unknowns. Furthermore, a remedy approach is also presented in this paper to improve the deteriorated precision for open composed structures due to the significant singular currents near the boundary edges. Compared with traditional PEC-TDS methods, the method presented in this paper can deal with scattering from thick or stratified coatings with arbitrarily lateral or normal inhomogeneity. Its improvement is also capable of handling dielectric coatings on open PEC surfaces. The numerical results at the end show good agreement with the references, showing the accuracy and the validity of these solutions.