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A nonlinear Helmholtz (NLH) equation with high frequencies and corner singularities is discretized by the linear finite element method (FEM). After deriving some wave-number-explicit stability estimates and the singularity decomposition for…

Numerical Analysis · Mathematics 2024-05-28 Run Jiang , Haijun Wu , Yifeng Xu , Jun Zou

Meshing of geometric domains having curved boundaries by affine simplices produces a polytopial approximation of those domains. The resulting error in the representation of the domain limits the accuracy of finite element methods based on…

Numerical Analysis · Mathematics 2018-02-09 James Cheung , Mauro Perego , Pavel Bochev , Max Gunzburger

A preasymptotic error analysis of the finite element method (FEM) and some continuous interior penalty finite element method (CIP-FEM) for Helmholtz equation in two and three dimensions is proposed. $H^1$- and $L^2$- error estimates with…

Numerical Analysis · Mathematics 2014-01-20 Yu Du , Haijun Wu

In this paper, we proposed two new types of edge multiscale methods motivated by \cite{GL18} to solve Partial Differential Equations (PDEs) with high-contrast heterogeneous coefficients: Edge spectral multiscale Finte Element method…

Numerical Analysis · Mathematics 2019-09-04 Shubin Fu , Eric Chung , Guanglian Li

In this paper, we develop an accurate and efficient framework for computing subwavelength guided modes in high-contrast periodic media with line defects, based on a tight-binding approximation. The physical problem is formulated as an…

Mathematical Physics · Physics 2026-01-21 Habib Ammari , Erik Orvehed Hiltunen , Ping Liu , Borui Miao , Yi Zhu

An isogeometric boundary element method (BEM) is presented to solve scattering problems in an isotropic homogeneous medium. We consider wave problems governed by the scalar wave equation as in acoustics and the Lam\'e-Navier equations for…

Computational Engineering, Finance, and Science · Computer Science 2025-10-09 Thomas Kramer , Benjamin Marussig , Martin Schanz

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 2017-05-16 Marcella Bonazzoli , Victorita Dolean , Frédéric Hecht , Francesca Rapetti

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

This study introduces the first 3D spectral-element method (SEM) simulation of ultrasonic wave propagation in a bottlenose dolphin (Tursiops truncatus) head. Unlike traditional finite-element methods (FEM), which struggle with…

Computational Engineering, Finance, and Science · Computer Science 2025-07-01 Carlos García A. , Vladimiro Boselli , Aida Hejazi Nooghabi , Andrea Colombi , Lapo Boschi

In this work, we are concerned with the mathematical modeling of the electromagnetic (EM) scattering by arbitrarily shaped non-magnetic nanoparticles with high refractive indices. When illuminated by visible light, such particles can…

Mathematical Physics · Physics 2021-08-13 Habib Ammari , Bowen Li , Jun Zou

The boundary element method (BEM) enables the efficient electromagnetic modelling of lossy conductors with a surface-based discretization. Existing BEM techniques for conductor modelling require either expensive dual basis functions or the…

Computational Physics · Physics 2020-12-29 Shashwat Sharma , Piero Triverio

In our recent work [AIP Adv. 11, 095006], we presented an efficient numerical method to compute dispersions and spatial mode profiles of spin waves propagating in waveguides with translationally invariant equilibrium magnetization. Using a…

Mesoscale and Nanoscale Physics · Physics 2024-06-12 Lukas Körber , Alexander Hempel , Andreas Otto , Rodolfo Gallardo , Yves Henry , Jürgen Lindner , Attila Kákay

In this paper, we consider a pressure-velocity formulation of the heterogeneous wave equation and employ the constraint energy minimizing generalized multiscale finite element method (CEM-GMsFEM) to solve this problem. The proposed method…

Numerical Analysis · Mathematics 2020-10-06 Eric Chung , Sai-Mang Pun

We present a Fourier finite element modeling of light emission of dipolar emitters coupled to infinitely long waveguides. Due to the translational symmetry, the three-dimensional (3D) coupled waveguide-emitter system can be decomposed into…

Optics · Physics 2015-12-01 Yangxin Ou , David Pardo , Yuntian Chen

In this paper, we provide the constraint energy minimization generalized multiscale finite element method (CEM-GMsFEM) to solve Helmholtz equations in heterogeneous medium. This novel multiscale method is specifically designed to overcome…

Numerical Analysis · Mathematics 2024-07-09 Xingguang Jin , Changqing Ye , Eric T. Chung

We introduce discontinuous spectral-element methods of arbitrary order that are well balanced, conservative of mass, and conservative or dissipative of total energy (i.e., a mathematical entropy function) for a covariant flux formulation of…

Numerical Analysis · Mathematics 2026-02-10 Tristan Montoya , Andrés M. Rueda-Ramírez , Gregor J. Gassner

We present 2-D, 3-D, and spherical mesh generators for the Finite Element Method (FEM) using triangular and tetrahedral elements. The mesh nodes are treated as if they were linked by virtual springs that obey Hooke's law. Given the desired…

Computational Geometry · Computer Science 2017-11-20 J. M. Taramón , J. P. Morgan , C. Shi , J. Hasenclever

Hyperbolic metamaterials are strongly anisotropic artificial composite materials at a subwavelength scale and can greatly widen the engineering feasibilities for manipulation of wave propagation. However, limited by the empirical structure…

Classical Physics · Physics 2018-11-09 Hao-Wen Dong , Sheng-Dong Zhao , Yue-Sheng Wang , Chuanzeng Zhang

For any inhomogeneous compactly supported electromagnetic (EM) medium, it is shown that there exists an infinite set of linearly independent electromagnetic waves which generate nearly vanishing scattered wave fields. If the inhomogeneous…

Analysis of PDEs · Mathematics 2017-03-08 Hongyu Liu , Yuliang Wang , Shuhui Zhong

This work investigates finite element approximations for a general class of elliptic hemivariational inequalities arising in semipermeable media. The proposed model incorporates non-isotropic and heterogeneous diffusion coefficients,…

Numerical Analysis · Mathematics 2026-05-05 Ban Li , Bangmin Wu