English
Related papers

Related papers: A Stable, Accurate and Well-Conditioned Time-Domai…

200 papers

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 describes a fast direct boundary element method for elastodynamic transmission problems in two dimensions, which can be used for analyzing elastic wave scattering by an inclusion. We develop an efficient solver based on a…

Numerical Analysis · Mathematics 2026-03-24 Yasuhiro Matsumoto , Taizo Maruyama

We describe a fourth-order accurate finite-difference time-domain scheme for solving dispersive Maxwell's equations with nonlinear multi-level carrier kinetics models. The scheme is based on an efficient single-step three time-level…

We present a novel computational scheme to solve acoustic wave transmission problems over composite scatterers, i.e. penetrable obstacles possessing junctions or triple points. Our continuous problem is cast as a multiple traces time-domain…

Numerical Analysis · Mathematics 2022-04-01 Carlos Jerez-Hanckes , Ignacio Labarca

A symmetric boundary integral formulation for the transient scattering of acoustic waves off homogeneous and isotropic elastic obstacles is analyzed. Both the acoustic scattered field and the elastodynamic excited field are represented…

Numerical Analysis · Mathematics 2025-08-19 Tonatiuh Sánchez-Vizuet

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

Consider the scattering of a time-harmonic plane wave by a rigid obstacle embedded in a homogeneous and isotropic elastic medium in two dimensions. In this paper, a novel boundary integral formulation is proposed and its highly accurate…

Numerical Analysis · Mathematics 2020-07-20 Heping Dong , Jun Lai , Peijun Li

Metasurfaces, consisting of large arrays of interacting subwavelength scatterers, pose significant challenges for general-purpose computational methods due to their large electric dimensions and multiscale nature. This paper introduces an…

Computational Physics · Physics 2024-10-07 Emanuele Corsaro , Giovanni Miano , Antonello Tamburrino , Salvatore Ventre , Carlo Forestiere

We develop an unconditionally energy-stable tensor-product space-time discretization framework for the solution of a linear kinetic transport equation in one space dimension. The kinetic equation is a simplified model of radiative transfer…

Numerical Analysis · Mathematics 2026-04-24 Anita Gjesteland , Sigrun Ortleb , Salim Elghawi , David C. Del Rey Fernández

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

The Schr\"odinger equation defines the dynamics of quantum particles which has been an area of unabated interest in physics. We demonstrate how simple transformations of the Schr\"odinger equation leads to a coupled linear system, whereby…

Numerical Analysis · Computer Science 2015-03-17 Hisham bin Zubair , Bram Reps , Wim Vanroose

In this work, we present scalable balancing domain decomposition by constraints methods for linear systems arising from arbitrary order edge finite element discretizations of multi-material and heterogeneous 3D problems. In order to enforce…

Computational Engineering, Finance, and Science · Computer Science 2024-12-20 Santiago Badia , Alberto F. Martín , Marc Olm

In this work, we introduce new integral formulations based on the convolution quadrature method for the time-domain modeling of perfectly electrically conducting scatterers that overcome some of the most critical issues of the standard…

Numerical Analysis · Mathematics 2023-11-28 Pierrick Cordel , Alexandre Dély , Adrien Merlini , Francesco P. Andriulli

This paper investigates the late-time instability of marching-on-in-time solution to the time-domain PMCHWT equation. The stability analysis identifies the static solenoidal nullspace of the time-domain electric field integral operator as…

Numerical Analysis · Mathematics 2025-09-19 Van Chien Le , Viviana Giunzioni , Pierrick Cordel , Francesco P. Andriulli , Kristof Cools

The goal of this work is to study the electromagnetic scattering problem of time-domain Maxwell's equations in an unbounded structure. An exact transparent boundary condition is developed to reformulate the scattering problem into an…

Analysis of PDEs · Mathematics 2016-04-27 Yixian Gao , Peijun Li

We prove sharp wavenumber-explicit error bounds for first- or second-family-N\'ed\'elec-element (a.k.a. edge-element) conforming discretisations, of arbitrary (fixed) order, of the variable-coefficient time-harmonic Maxwell equations posed…

Numerical Analysis · Mathematics 2026-01-09 Théophile Chaumont-Frelet , Jeffrey Galkowski , Euan A. Spence

This paper provides a rigorous analysis of boundary element methods for the magnetic field integral equation on Lipschitz polyhedra. The magnetic field integral equation is widely used in practical applications to model electromagnetic…

Numerical Analysis · Mathematics 2024-09-12 Van Chien Le , Kristof Cools

We develop a structure-preserving computational framework for acoustic wave scattering by moving objects, comprising a new PML-domain-embedding model and a compatible numerical approximation. The model couples a perfectly matched layer…

Numerical Analysis · Mathematics 2026-05-28 Xuelong Gu , Qi Wang

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

In this work, we derive particle schemes, based on micro-macro decomposition, for linear kinetic equations in the diffusion limit. Due to the particle approximation of the micro part, a splitting between the transport and the collision part…

Numerical Analysis · Mathematics 2017-01-19 Anaïs Crestetto , Nicolas Crouseilles , Mohammed Lemou