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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

The interface problem describing the scattering of time-harmonic electromagnetic waves by a dielectric body is often formulated as a pair of coupled boundary integral equations for the electric and magnetic current densities on the…

Numerical Analysis · Mathematics 2011-02-28 Martin Costabel , Frédérique Le Louër

An accurate force calculation with the Poisson-Boltzmann equation is challenging, as it requires the electric field on the molecular surface. Here, we present a calculation of the electric field on the solute-solvent interface that is exact…

Chemical Physics · Physics 2023-01-13 Ian Addison-Smith , Horacio V. Guzmán , Christopher D. Cooper

Fourth-order differential equations play an important role in many applications in science and engineering. In this paper, we present a three-field mixed finite-element formulation for fourth-order problems, with a focus on the effective…

Numerical Analysis · Mathematics 2022-10-13 Patrick E. Farrell , Abdalaziz Hamdan , Scott P. MacLachlan

In this paper, we consider the numerical approximation for a diffuse interface model of the two-phase incompressible inductionless magnetohydrodynamics problem. This model consists of Cahn-Hilliard equations, Navier-Stokes equations and…

Numerical Analysis · Mathematics 2022-02-01 Xiaorong Wang , Xiaodi Zhang

We consider the variational formulation of the electric field integral equation (EFIE) on bounded polyhedral open or closed surfaces. We employ a conforming Galerkin discretization based on div-conforming Raviart-Thomas boundary elements…

Numerical Analysis · Mathematics 2009-07-31 Alexei Bespalov , Norbert Heuer , Ralf Hiptmair

This paper is concerned with a numerical solution to the scattering of a time-harmonic electromagnetic wave by a bounded and impenetrable obstacle in three dimensions. The electromagnetic wave propagation is modeled by a boundary value…

Numerical Analysis · Mathematics 2022-02-21 Gang Bao , Mingming Zhang , Xue Jiang , Peijun Li , Xiaokai Yuan

Boundary integral equation methods for analyzing electromagnetic scattering phenomena typically suffer from several of the following problems: (i) ill-conditioning when the frequency is low; (ii) ill-conditioning when the discretization…

Computational Physics · Physics 2020-06-24 Adrien Merlini , Yves Beghein , Kristof Cools , Eric Michielssen , Francesco P. Andriulli

We propose a new class of finite element approximations to ideal compressible magnetohydrodynamic equations in smooth regime. Following variational approximations developed for fluid models in the last decade, our discretizations are built…

Numerical Analysis · Mathematics 2024-02-29 Valentin Carlier , Martin Campos-Pinto

A robust and efficient field-only nonsingular surface integral method to solve Maxwell's equations for the components of the electric field on the surface of a dielectric scatterer is introduced. In this method, both the vector Helmholtz…

Optics · Physics 2020-02-19 Qiang Sun , Evert Klaseboer , Alex J. Yuffa , Derek Y. C. Chan

We consider the scattering problem on locally perturbed periodic penetrable dielectric layers, which is formulated in terms of the full vector-valued time-harmonic Maxwell's equations. The right-hand side is not assumed to be periodic. At…

Analysis of PDEs · Mathematics 2019-08-23 Alexander Konschin

A full multigrid finite element method is proposed for semilinear elliptic equations. The main idea is to transform the solution of the semilinear problem into a series of solutions of the corresponding linear boundary value problems on the…

Numerical Analysis · Mathematics 2017-03-29 Hehu Xie , Fei Xu

This paper is devoted to the numerical validation of an explicit finite-difference scheme for the integration in time of Maxwell's equations in terms of the sole electric field, using standard linear finite elements for the space…

Numerical Analysis · Mathematics 2019-05-10 L. Beilina , V. Ruas

We propose an unfitted finite element method for numerically solving the time-harmonic Maxwell equations on a smooth domain. The model problem involves a Lagrangian multiplier to relax the divergence constraint of the vector unknown. The…

Numerical Analysis · Mathematics 2022-07-13 Fanyi Yang , Xiaoping Xie

The use of boundary integral equations in modeling boundary value problems-such as elastic, acoustic, or electromagnetic ones-is well established in the literature and widespread in practical applications. These equations are typically…

Computational Engineering, Finance, and Science · Computer Science 2025-05-28 Viviana Giunzioni , Adrien Merlini , Francesco P. Andriulli

We propose a high-order adaptive numerical solver for the semilinear elliptic boundary value problem modelling magnetic plasma equilibrium in axisymmetric confinement devices. In the fixed boundary case, the equation is posed on curved…

Computational Physics · Physics 2021-05-28 Tonatiuh Sánchez-Vizuet , Manuel E. Solano , Antoine J. Cerfon

A finite element approach for approximating the solution of a mathematical model for the response of a penetrable, bounded object (obstacle) to the excitation by an external electromagnetic field is presented and investigated. The model…

Numerical Analysis · Mathematics 2026-04-16 Lutz Angermann

Wave propagation problems have many applications in physics and engineering, and the stochastic effects are important in accurately modeling them due to the uncertainty of the media. This paper considers and analyzes a fully discrete finite…

Numerical Analysis · Mathematics 2021-06-30 Yukun Li , Shuonan Wu , Yulong Xing

This paper treats the time-harmonic electro-magnetic scattering or radiation problem governed by Maxwell's equations in an exterior weak Lipschitz domain divided into two disjoint weak Lipschitz parts We will present a solution theory using…

Analysis of PDEs · Mathematics 2019-04-30 Frank Osterbrink , Dirk Pauly

The quad-curl term is an essential part of the resistive magnetohydrodynamic (MHD) equation and the fourth order inverse electromagnetic scattering problem, which are both of great significance in science and engineering. It is desirable to…

Numerical Analysis · Mathematics 2020-02-25 Gang Chen , Weifeng Qiu , Liwei Xu