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The time-harmonic Maxwell equations are used to study the effect of electric and magnetic fields on each other. Although the linear systems resulting from solving this system using FEMs are sparse, direct solvers cannot reach the linear…

Numerical Analysis · Mathematics 2023-04-28 Maryam Parvizi , Amirreza Khodadadian , Sven Beuchler , Thomas Wick

We study a transmission problem for the time harmonic Maxwell's equations between a classical positive material and a so-called negative index material in which both the permittivity $\varepsilon$ and the permeability $\mu$ take negative…

Analysis of PDEs · Mathematics 2025-02-26 Anne-Sophie Bonnet-Ben Dhia , Lucas Chesnel , Mahran Rihani

In this article, we present a new preconditioner, MatExPre, for the high-frequency Helmholtz equation by leveraging the properties of matrix exponentials. Our approach begins by reformulating the Helmholtz equation into a…

Numerical Analysis · Mathematics 2025-06-05 Shubin Fu , Qing Huo Liu , Qiwei Zhan , Eric T. Chung , Changqing Ye

This paper is concerned with the Klein-Gordon-Maxwell system in a bounded spatial domain. We discuss the existence of standing waves $\psi=u(x)e^{-i\omega t}$ in equilibrium with a purely electrostatic field $\mathbf{E}=-\nabla\phi(x)$. We…

Analysis of PDEs · Mathematics 2019-12-04 Pietro d'Avenia , Lorenzo Pisani , Gaetano Siciliano

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…

Numerical Analysis · Mathematics 2020-03-23 Marcella Bonazzoli , Victorita Dolean , Frédéric Hecht , Francesca Rapetti

In this work, we are interested in the analysis of time-harmonic Maxwell's equations in presence of a conical tip of a material with negative dielectric constants. When these constants belong to some critical range, the electromagnetic…

Analysis of PDEs · Mathematics 2020-10-19 Anne-Sophie Bonnet-Ben Dhia , Lucas Chesnel , Mahran Rihani

We discuss a time-harmonic inverse scattering problem for the Helmholtz equation with compactly supported penetrable and possibly inhomogeneous scattering objects in an unbounded homogeneous background medium, and we develop a monotonicity…

Analysis of PDEs · Mathematics 2021-03-01 Roland Griesmaier , Bastian Harrach

This paper presents an integral formulation for Helmholtz problems with mixed boundary conditions. Unlike most integral equation techniques for mixed boundary value problems, the proposed method uses a global boundary charge density. As a…

Numerical Analysis · Mathematics 2016-01-12 Adrianna Gillman

We propose a new concept of weak solution to the equations of compressible magnetohydrodynamics driven by large boundary data. The system of the underlying field equations is solvable globally in time in the out of equilibrium regime…

Analysis of PDEs · Mathematics 2023-04-04 Eduard Feireisl , Piotr Gwiazda , Young-Sam Kwon , Agnieszka Świerczewska-Gwiazda

We consider the inverse problem of determining different type of information about a diffusion process, described by ordinary or fractional diffusion equations stated on a bounded domain, like the density of the medium or the velocity field…

Analysis of PDEs · Mathematics 2019-07-05 Yavar Kian , Zhiyuan Li , Yikan Liu , Masahiro Yamamoto

We study time-dependent acoustic and electromagnetic waves governed by the scalar wave equation or Maxwell's equations in a bounded three-dimensional domain. We establish the existence of time-dependent boundary excitations that can be…

Analysis of PDEs · Mathematics 2026-03-03 Roland Griesmaier , Soumen Senapati

The concept of weak invariants is examined in the thermodynamic context. Discussions are made about the temporally-local equilibrium states, corrections to them, and isoenergetic processes based on the quantum master equations of the…

Statistical Mechanics · Physics 2019-05-06 Congjie Ou , Sumiyoshi Abe

The properties of the modified Maxwell electrodynamics (ModMax) are investigated in presence of external and uniform electric and magnetic fields. We expand the non-linear theory around an electromagnetic background up to second order in…

High Energy Physics - Theory · Physics 2023-04-20 M. J. Neves , Patricio Gaete , L. P. R. Ospedal , J. A. Helayël-Neto

Solution of Helmholtz equation with impedance boundary condition on finite interval is equivalently reformulated as steady state of initial boundary value problem for first order hyperbolic system of partial differential equations.…

Numerical Analysis · Mathematics 2018-06-19 Ramaz Botchorishvili , Tamar Janelidze

A novel approach to computing time-harmonic solutions of Maxwell's equations by time-domain simulations is presented. The method, EM-WaveHoltz, results in a positive definite system of equations which makes it amenable to iterative solution…

Numerical Analysis · Mathematics 2022-08-17 Zhichao Peng , Daniel Appelö

In this paper, we investigate whether Variational Principles can be associated with the Helmholtz equation subject to impedance (absorbing) boundary conditions. This model has been extensively studied in the literature from both…

Numerical Analysis · Mathematics 2025-11-18 G. Makrakis , C. Makridakis , D. Mitsoudis , M. Plexousakis , T. Pryer

In this paper we consider the transmission eigenvalue problem for Maxwell's equations corresponding to non-magnetic inhomogeneities with contrast in electric permittivity that changes sign inside its support. We formulate the transmission…

Analysis of PDEs · Mathematics 2015-06-02 Fioralba Cakoni , Houssem Haddar , Shixu Meng

We study the Boltzmann equation near a global Maxwellian in the case of bounded domains. We consider the boundary conditions to be either specular reflections or Maxwellian diffusion. Starting from the reference work of Guo in…

Mathematical Physics · Physics 2016-11-30 Marc Briant

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…

Numerical Analysis · Mathematics 2014-06-11 Elena Beretta , Maarten V. de Hoop , Lingyun Qiu , Otmar Scherzer

In the present paper we consider an inverse source problem for time-fractional mixed parabolic-hyperbolic equation with the Caputo derivative. In case, when hyperbolic part of the considered mixed type equation is wave equation, the…

Analysis of PDEs · Mathematics 2015-12-08 Pengbin Feng , E. T. Karimov