相关论文: Well-conditioned boundary integral equation formul…
The boundary element method (BEM) enables solving three-dimensional electromagnetic problems using a two-dimensional surface mesh, making it appealing for applications ranging from electrical interconnect analysis to the design of…
The accuracy of the electric field integral equation (EFIE) can be substantially improved using high-order discretizations. However, this equation suffers from ill-conditioning and deleterious numerical effects in the low-frequency regime,…
The problem of the fictitious frequency spectrum resulting from numerical implementations of the boundary element method for the exterior Helmholtz problem is revisited. When the ordinary 3D free space Green's function is replaced by a…
A general principle says that the matrix of a Fourier integral operator with respect to wave packets is concentrated near the curve of propagation. We prove a precise version of this principle for Fourier integral operators with a smooth…
In this paper, we perform a numerical analysis in frequency domain for various electromagnetic problems based on discrete exterior calculus (DEC) with an arbitrary 2-D triangular or 3-D tetrahedral mesh. We formulate the governing equations…
The domain integral equation method with its FFT-based matrix-vector products is a viable alternative to local methods in free-space scattering problems. However, it often suffers from the extremely slow convergence of iterative methods,…
Realistic physical phenomena exhibit random fluctuations across many scales in the input and output processes. Models of these phenomena require stochastic PDEs. For three-dimensional coupled (vector-valued) stochastic PDEs (SPDEs), for…
We study the classical first-kind boundary integral equation reformulations of time-harmonic acoustic scattering by planar sound-soft (Dirichlet) and sound-hard (Neumann) screens. We prove continuity and coercivity of the relevant boundary…
This paper introduces a boundary integral equation for time-harmonic electromagnetic scattering by composite dielectric objects. The formulation extends the classical M\"uller equation to composite structures through the global multi-trace…
We show that the standard boundary integral operators, defined on the unit sphere, for the Stokes equations diagonalize on a specific set of vector spherical harmonics and provide formulas for their spectra. We also derive analytical…
Conventional classical solvers are commonly used for solving matrix equation systems resulting from the discretization of SIEs in computational electromagnetics (CEM). However, the memory requirement would become a bottleneck for classical…
We consider the numerical solution of high-frequency scattering problems modeled by the Helmholtz equation with a bounded obstacle. Although the analysis of this problem dates back at least 50 years, over the past decade or so, tools and…
Volume integral equations have been used as a theoretical tool in scattering theory for a long time. A classical application is an existence proof for the scattering problem based on the theory of Fredholm integral equations. This approach…
We obtain wavenumber-robust error bounds for the deep neural network (DNN) emulation of the solution to the time-harmonic, sound-soft acoustic scattering problem in the exterior of a smooth, convex obstacle in two physical dimensions. The…
Integral-equation-based fast direct solvers for electromagnetic scattering can substantially reduce computational costs, especially in the presence of multiple excitations. We recently proposed a new high-frequency fast direct solver…
An electron in quantum confinement takes on a discrete energy spectrum which is defined based on the solution to the Schrodinger Equation for a given potential. Well defined closed-form energy spectra are known for the particle in a box,…
In this paper, we present a finite-element-extended boundary condition (FE-EBC) method for an efficient calculation of the electromagnetic wave scattering from inhomogeneous magneto-dielectric objects. To this end, we apply the hierarchical…
We introduce and validate a theoretical framework for coherent control of multichannel scattering of linear waves to route waves through complex geometries with multiple scattering. We show that steady-state perfect routing solutions are…
The accurate electromagnetic modeling of both low- and high-frequency physics is crucial in the signal and power integrity analysis of electrical interconnects. The boundary element method (BEM) is appealing for lossy conductor modeling…
In his monograph Chebyshev and Fourier Spectral Methods, John Boyd claimed that, regarding Fourier spectral methods for solving differential equations, ``[t]he virtues of the Fast Fourier Transform will continue to improve as the relentless…