Dimensional Electromagnetic Problems Research Articles

Global energy‐tracking identities and global energy‐tracking splitting FDTD schemes for the Drude Models of Maxwell's equations in three‐dimensional metamaterials

In this article, we study the Drude models of Maxwell's equations in three‐dimensional metamaterials. We derive new global energy‐tracking identities for the three dimensional electromagnetic problems in the Drude metamaterials, which describe the invariance of global electromagnetic energy in variation forms. We propose the time second‐order global energy‐tracking splitting FDTD schemes for the Drude model in three dimensions. The significant feature is that the developed schemes are global energy‐preserving, unconditionally stable, second‐order accurate both in time and space, and computationally efficient. We rigorously prove that the new schemes satisfy these energy‐tracking identities in the discrete form and the discrete variation form and are unconditionally stable. We prove that the schemes in metamaterials are second order both in time and space. The superconvergence of the schemes in the discrete H1 norm is further obtained to be second order both in time and space. Their approximations of divergence‐free are also analyzed to have second‐order accuracy both in time and space. Numerical experiments confirm our theoretical analysis results. © 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 763–785, 2017

HYBRID FINITE DIFFERENCE/FINITE VOLUME METHOD FOR 3-D CONDUCTING MEDIA PROBLEMS

A hybrid time-domain method combing flnite-difierence and cell-centered flnite-volume method is presented in this paper. This method is applied to solve three dimensional electromagnetic problems which involve media having flnite conductivity. The fractional-step technique (FST) for FVTD scheme is applied to solve these problems. Local time-step scheme is used to enhance the e-ciency of this method. Numerical results are given and compared with a reliable numerical method, which is used to show the validation of this method.

The closed-form solution of vector finite element integral equations for three dimensional electromagnetic analysis

In this paper, a set of closed-form formulas for vector Finite Element Method (FEM) to analyze three dimensional electromagnetic problems is presented on the basis of Gaussian quadrature integration scheme. By analyzing the open region problems, the first-order Absorbing Boundary Condition (ABC) is considered as the truncation boundary condition and the equation is carried out in a closed-form. Based on the formulas, the hybrid Expanded Cholesky Method (ECM) and MultiFrontal algorithm (MF) is applied to solve finite element equations. Using the closed-form solution, the electromagnetic field of three dimensional targets can be studied sententiously and accurately. Simulation results show that the presented formulas are successfully and concise, which can be easily used to analyze three dimensional electromagnetic problems.

ANALYSIS OF 3-DIMENSIONAL ELECTROMAGNETIC FIELDS IN DISPERSIVE MEDIA USING CUDA

This research presents the implementation of the Finite- Difierence Time-Domain (FDTD) method for the solution of 3- dimensional electromagnetic problems in dispersive media using Graphics Processor Units (GPUs). By using the newly introduced CUDA technology, we illustrate the e-cacy of GPUs in accelerating the FDTD computations by achieving appreciable speedup factors with great ease and at no extra hardware/software cost. We validate our approach by comparing the results with their corresponding simulated results obtained from Remcom's XFDTD software.

A Low-Dispersion 3-D Second-Order in Time Fourth-Order in Space FDTD Scheme (<tex>$ M3d_24 $</tex>)

A second-order in time fourth-order in space modified finite-difference time-domain (FDTD) scheme for three dimensional electromagnetic problems M3d/sub 24/ is presented. The algorithm enables the numerical phase error to be minimized, so that it leads to high accuracy with low resolution grids. The advantage of this method is demonstrated by considering the long distance propagation of the wave radiated from a time harmonic elementary dipole using a low resolution grid, and comparing the results with other FDTD schemes.