Related papers: Computing Maxwell eigenmodes with Bloch boundary c…
We study the inverse boundary value problem for the Helmholtz equation using the Dirichlet-to-Neumann map at selected frequency as the data. We develop an explicit reconstruction of the wavespeed using a multi-level nonlinear projected…
This work concerns inverse boundary value problems for the time-harmonic Maxwell's equations on differential $1-$forms. We formulate the boundary value problem on a $3-$dimensional compact and simply connected Riemannian manifold $M$ with…
The construction of fast iterative solvers for the indefinite time-harmonic Maxwell's system at mid- to high-frequency is a problem of great current interest. Some of the difficulties that arise are similar to those encountered in the case…
We introduce an efficient method for computing the Stekloff eigenvalues associated with the Helmholtz equation. In general, this eigenvalue problem requires solving the Helmholtz equation with Dirichlet and/or Neumann boundary condition…
A uniqueness result for the recovery of the electric and magnetic coefficients in the time-harmonic Maxwell equations from local boundary measurements is proven. No special geometrical condition is imposed on the inaccessible part of the…
This thesis presents a physics-informed machine learning framework for solving the Floquet-Bloch eigenvalue problem associated with particles in two-dimensional periodic potentials, with a focus on honeycomb lattice geometry, due to its…
The Poisson-Boltzmann equation offers an efficient way to study electrostatics in molecular settings. Its numerical solution with the boundary element method is widely used, as the complicated molecular surface is accurately represented by…
This research explores refined boundary conditions for a traction-free surface in a non-local micropolar half-space, combining non-local and micropolar elasticity effects to study Rayleigh wave propagation in an isotropic, homogeneous…
This paper investigates an adaptive wavelet collocation time domain method for the numerical solution of Maxwell's equations. In this method a computational grid is dynamically adapted at each time step by using the wavelet decomposition of…
We consider the problem of homogenizing the Maxwell equations for periodic composites. The analysis is based on Bloch-Floquet theory. We calculate explicitly the reflection coefficient for a half-space, and derive and implement a…
Nonlinear ultrasound imaging leverages harmonic wave generation to enhance contrast and spatial resolution beyond the capabilities of conventional linear techniques. This behavior is commonly modeled by the Westervelt equation, which…
Computing more than one eigenvalue for (large sparse) one-parameter polynomial and general nonlinear eigenproblems, as well as for multiparameter linear and nonlinear eigenproblems, is a much harder task than for standard eigenvalue…
We propose an efficient algorithm for density fitting of Bloch waves for Hamiltonian operators with periodic potential. The algorithm is based on column selection and random Fourier projection of the orbital functions. The computational…
We provide two new methods for computing lower bounds of eigenvalues of symmetric elliptic second-order differential operators with mixed boundary conditions of Dirichlet, Neumann, and Robin type. The methods generalize ideas of Weinstein's…
We study photonic band structure of two- and three-dimensional magnetophotonic crystals and the polarization properties of their eigenmodes using a plane wave expansion method. The alteration of the photonic band structure and eigenmodes by…
We present a finite element algorithm that computes eigenvalues and eigenfunctions of the Laplace operator for two-dimensional problems with homogeneous Neumann or Dirichlet boundary conditions or combinations of either for different parts…
Inspired by recent developments in the theory of stability results in the context of certain wave type phenomena, we discuss abstract damped hyperbolic type equations given in a block operator matrix form with regards to asymptotic…
Recently, the extrapolation theory has become a mainsteam method to investigate some integral type operators, since it does not depend on the density of spaces. The purpose of this paper is threefold. The first is to establish product…
We study the Pauli operator in a two-dimensional, connected domain with Neumann or Robin boundary condition. We prove a sharp lower bound on the number of negative eigenvalues reminiscent of the Aharonov-Casher formula. We apply this lower…
We extend classical time-frequency limiting analysis, historically applied to one-dimensional finite signals, to the multidimensional discrete setting. This extension is relevant for images, videos, and other multidimensional signals, as it…