No Arabic abstract
Higher-order accurate solution to electromagnetic scattering problems are obtained at reduced computational cost in a {it p}-variable finite volume time domain method. Spatial operators of lower, including first-order accuracy, are employed locally in substantial parts of the computational domain during the solution process. The use of computationally cheaper lower order spatial operators does not affect the overall higher-order accuracy of the solution. The order of the spatial operator at a candidate cell during numerical simulation can vary in space and time and is dynamically chosen based on an order of magnitude comparison of scattered and incident fields at the cell center. Numerical results are presented for electromagnetic scattering from perfectly conducting two-dimensional scatterers subject to transverse magnetic and transverse electric illumination.
In this paper, a perfectly matched layer (PML) method is proposed to solve the time-domain electromagnetic scattering problems in 3D effectively. The PML problem is defined in a spherical layer and derived by using the Laplace transform and real coordinate stretching in the frequency domain. The well-posedness and the stability estimate of the PML problem are first proved based on the Laplace transform and the energy method. The exponential convergence of the PML method is then established in terms of the thickness of the layer and the PML absorbing parameter. As far as we know, this is the first convergence result for the time-domain PML method for the three-dimensional Maxwell equations. Our proof is mainly based on the stability estimates of solutions of the truncated PML problem and the exponential decay estimates of the stretched dyadic Greens function for the Maxwell equations in the free space.
In this paper, we propose and study the uniaxial perfectly matched layer (PML) method for three-dimensional time-domain electromagnetic scattering problems, which has a great advantage over the spherical one in dealing with problems involving anisotropic scatterers. The truncated uniaxial PML problem is proved to be well-posed and stable, based on the Laplace transform technique and the energy method. Moreover, the $L^2$-norm and $L^{infty}$-norm error estimates in time are given between the solutions of the original scattering problem and the truncated PML problem, leading to the exponential convergence of the time-domain uniaxial PML method in terms of the thickness and absorbing parameters of the PML layer. The proof depends on the error analysis between the EtM operators for the original scattering problem and the truncated PML problem, which is different from our previous work (SIAM J. Numer. Anal. 58(3) (2020), 1918-1940).
A radial-dependent dispersive finite-difference time-domain (FDTD) method is proposed to simulate electromagnetic cloaking devices. The Drude dispersion model is applied to model the electromagnetic characteristics of the cloaking medium. Both lossless and lossy cloaking materials are examined and their operating bandwidth is also investigated. It is demonstrated that the perfect invisibility from electromagnetic cloaks is only available for lossless metamaterials and within an extremely narrow frequency band.
We introduce a new method for the numerical approximation of time-harmonic acoustic scattering problems stemming from material inhomogeneities. The method works for any frequency $omega$, but is especially efficient for high-frequency problems. It is based on a time-domain approach and consists of three steps: emph{i)} computation of a suitable incoming plane wavelet with compact support in the propagation direction; emph{ii)} solving a scattering problem in the time domain for the incoming plane wavelet; emph{iii)} reconstruction of the time-harmonic solution from the time-domain solution via a Fourier transform in time. An essential ingredient of the new method is a front-tracking mesh adaptation algorithm for solving the problem in emph{ii)}. By exploiting the limited support of the wave front, this allows us to make the number of the required degrees of freedom to reach a given accuracy significantly less dependent on the frequency $omega$, as shown in the numerical experiments. We also present a new algorithm for computing the Fourier transform in emph{iii)} that exploits the reduced number of degrees of freedom corresponding to the adapted meshes.
The scattering of electromagnetic pulses is described using a non-singular boundary integral method to solve directly for the field components in the frequency domain, and Fourier transform is then used to obtain the complete space-time behavior. This approach is stable for wavelengths both small and large relative to characteristic length scales. Amplitudes and phases of field values can be obtained accurately on or near material boundaries. Local field enhancement effects due to multiple scattering of interest to applications in microphotonics are demonstrated.