Related papers: Higher-Order Spectral Element Methods for Electrom…
The $h$-version of the finite-element method ($h$-FEM) applied to the high-frequency Helmholtz equation has been a classic topic in numerical analysis since the 1990s. It is now rigorously understood that (using piecewise polynomials of…
Solving the electroencephalography (EEG) forward problem is a fundamental step in a wide range of applications including biomedical imaging techniques based on inverse source localization. State-of-the-art electromagnetic solvers resort to…
The Maximum Eccentricity Method (MEM) is a standard tool for the analysis of planetary systems and their stability. The method amounts to estimating the maximal stretch of orbits over sampled domains of initial conditions. The present paper…
In this paper we focus on high order finite element approximations of the electric field combined with suitable preconditioners, to solve the time-harmonic Maxwell's equations in waveguide configurations.The implementation of high order…
Over the past decades, high-harmonic spectroscopy (HHS) has emerged as a powerful tool for all-optical probing of topological properties of solids. There are outstanding questions regarding universal nature of the spectral features of…
In this paper we present a mode-matching technique to study the transmission coefficient of mesoscopic devices such as electron waveguides in the presence of high magnetic fields for different situations. A detailed study of the…
We develop a fast solver for the spectral element method (SEM) applied to the two-sided fractional diffusion equation on uniform, geometric and graded meshes. By approximating the singular kernel with a degenerate kernel, we construct a…
This work presents a Boundary Element Method (BEM) formulation for contactless electromagnetic field assessments. The new scheme is based on a regularized BEM approach that requires the use of electric measurements only. The regularization…
Topologically ordered systems in the presence of symmetries can exhibit new structures which are referred to as symmetry enriched topological (SET) phases. We introduce simple methods to detect the SET order directly from a complete set of…
We consider the scattering of elastic waves by highly oscillating anisotropic periodic media with bounded support. Applying the two-scale homogenization, we first obtain a constant coefficient second-order partial differential elliptic…
The oversampling multiscale finite element method (MsFEM) is one of the most popular methods for simulating composite materials and flows in porous media which may have many scales. But the method may be inapplicable or inefficient in some…
This work presents a mathematical theory for electromagnetic scattering resonances in a subwavelength annular hole embedded in a metallic slab, with the annulus width $h\ll1$. The model is representative among many 3D subwavelength hole…
Extraordinary dispersion features of a circular waveguide filled by a longitudinally magnetized composite gyroelectromagnetic medium are studied. The composite medium is considered to be constructed by juxtaposition together of magnetic and…
The Helmholtz equation with variable wavenumbers is challenging to solve numerically due to the pollution effect, which often results in a huge ill-conditioned linear system. In this paper, we present a high-order wavelet Galerkin method to…
At Argonne National Laboratory, we are developing hard X-ray (2 to 20 keV) Transition Edge Sensor (TES) arrays for beamline science. The significantly improved energy resolution provided by superconducting detectors compared to…
It is important to develop fast yet accurate numerical methods for seismic wave propagation to characterize complex geological structures and oil and gas reservoirs. However, the computational cost of conventional numerical modeling…
Analyses in high energy physics aim to put the Standard Model---the commonly accepted theory---to test. For convincing conclusions, analysis methods are needed which offer an unambiguous comparison between data and theory while allowing…
Swift electrons passing near or through metallic structures have proven to be an excellent tool for studying plasmons and other types of confined optical modes involving collective charge oscillations in the materials hybridized with…
In the present work, we consider multi-scale computation and convergence for nonlinear time-dependent thermo-mechanical equations of inhomogeneous shells possessing temperature-dependent material properties and orthogonal periodic…
The concentration of electromagnetic waves (EM) is of utmost importance in many engineering applications such as solar-cells. According to the transformation optics (TO) methodology, a feasible approach for obtaining arbitrary shape…