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We discuss the construction of Maxwellian electrodynamics in 2+1 dimensions and some of its applications. Special emphasis is given to the problem of the retarded potentials and radiation, where substantial differences with respect to the…

Classical Physics · Physics 2021-05-19 D. Boito , L. N. S. de Andrade , G. de Sousa , R. Gama , C. Y. M. London

The CHDG method is a hybridizable discontinuous Galerkin (HDG) finite element method suitable for the iterative solution of time-harmonic wave propagation problems. Hybrid unknowns corresponding to transmission variables are introduced at…

Numerical Analysis · Mathematics 2025-05-08 Ari E. Rappaport , Théophile Chaumont-Frelet , Axel Modave

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

We consider nodal-based Lagrangian interpolations for the finite element approximation of the Maxwell eigenvalue problem. The first approach introduced is a standard Galerkin method on Powell-Sabin meshes, which has recently been shown to…

Numerical Analysis · Mathematics 2023-04-04 Daniele Boffi , Ramon Codina , Önder Türk

One way of improving the behavior of finite element schemes for classical, time-dependent Maxwell's equations, is to render them from their hyperbolic character to elliptic form. This paper is devoted to the study of the stabilized linear…

Numerical Analysis · Mathematics 2024-09-23 M. Asadzadeh , L. Beilina

We present the implementation of an implicit-explicit (IMEX) Runge-Kutta numerical scheme for general relativistic hydrodynamics coupled to an optically thick radiation field in two existing GR-hydrodynamics codes. We argue that the…

High Energy Astrophysical Phenomena · Physics 2015-06-05 Constanze Roedig , Olindo Zanotti , Daniela Alic

With the advent of PW class lasers, the very large laser intensities attainable on-target should enable the production of intense high order Doppler harmonics from relativistic laser-plasma mirrors interactions. At present, the modeling of…

Computational Physics · Physics 2017-10-11 G. Blaclard , H. Vincenti , R. Lehe , J. L. Vay

We present a collection of well-conditioned integral equation methods for the solution of electrostatic, acoustic or electromagnetic scattering problems involving anisotropic, inhomogeneous media. In the electromagnetic case, our approach…

Numerical Analysis · Mathematics 2018-05-15 Lise-Marie Imbert-Gerard , Felipe Vico , Leslie Greengard , Miguel Ferrando

We present a boundary integral formulation of electromagnetic scattering by homogeneous bodies that are characterized by linear constitutive equations in the frequency domain. By working with the Cartesian components of the electric, E and…

Computational Physics · Physics 2018-12-18 Qiang Sun , Evert Klaseboer , Derek Y. C. Chan

We couple the mixed variational problem for the generalized Hodge-Helmholtz or Hodge-Laplace equation posed on a bounded three-dimensional Lipschitz domain with the first-kind boundary integral equation arising from the latter when constant…

Analysis of PDEs · Mathematics 2022-03-01 Erick Schulz , Ralf Hiptmair

We apply boundary integral equations for the first time to the two-dimensional scattering of time-harmonic waves from a smooth obstacle embedded in a continuously-graded unbounded medium. In the case we solve the square of the wavenumber…

Numerical Analysis · Mathematics 2016-05-04 Alex. H. Barnett , Bradley J. Nelson , J. Matthew Mahoney

Consider the elastic scattering of a time-harmonic wave by multiple well separated rigid particles in two dimensions. To avoid using the complex Green's tensor of the elastic wave equation, we utilize the Helmholtz decomposition to convert…

Numerical Analysis · Mathematics 2020-08-17 Jun Lai , Peijun Li

We study a time-dependent 5D metric which contains a static 4D sub-metric whose 3D part is spherically symmetric. An expansion in the metric coefficient allow us to obtain close-to Schwarzschild approximation to a class of…

General Relativity and Quantum Cosmology · Physics 2010-05-12 Hongya Liu , Paul S. Wesson

A semi-implicit finite difference time domain (FDTD) numerical Maxwell solver is developed for full electromagnetic Particle-in-Cell (PIC) codes for the simulations of plasma-based acceleration. The solver projects the volumetric Yee…

Plasma Physics · Physics 2020-08-26 Alexander Pukhov

Although high-order Maxwell integral equation solvers provide significant advantages in terms of speed and accuracy over corresponding low-order integral methods, their performance significantly degrades in presence of non-smooth…

Numerical Analysis · Mathematics 2025-01-31 Constantine Sideris , Davit Aslanyan , Oscar P. Bruno

Boundary integral methods are attractive for solving homogeneous linear constant coefficient elliptic partial differential equations on complex geometries, since they can offer accurate solutions with a computational cost that is linear or…

Numerical Analysis · Mathematics 2023-01-25 Fredrik Fryklund , Sara Pålsson , Anna-Karin Tornberg

An exact, ray-based general treatment is shown to hold for any kind of monochromatic wave feature - including diffraction and interference - described by Helmholtz-like equations, under the coupling action of a dispersive function (which we…

Quantum Physics · Physics 2014-03-25 Adriano Orefice , Raffaele Giovanelli , Domenico Ditto

This work is concerned with an inverse problem of identifying the current source distribution of the time-harmonic Maxwell's equations from multi-frequency measurements. Motivated by the Fourier method for the scalar Helmholtz equation and…

Numerical Analysis · Mathematics 2017-08-03 Guan Wang , Fuming Ma , Yukun Guo , Jingzhi Li

Acoustic scattering of waves by bounded inhomogeneities in an unbounded homogeneous domain is considered. A symmetric coupled system of time-domain boundary integral equations and the second order formulation of the wave equation is…

Numerical Analysis · Mathematics 2022-03-03 Lehel Banjai

This article presents an ultraweak discontinuous Petrov-Galerkin (DPG) formulation of the time-harmonic Maxwell equations for the vectorial envelope of the electromagnetic field in a weakly-guiding multi-mode fiber waveguide. This…

Numerical Analysis · Mathematics 2024-11-15 Stefan Henneking , Jacob Grosek , Leszek Demkowicz