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We propose a novel on-surface radiation condition to approximate the outgoing solution to the Helmholtz equation in the exterior of several impenetrable convex obstacles. Based on a local approximation of the Dirichlet-to-Neumann operator…

Computational Physics · Physics 2021-02-01 Sebastian Acosta

The space-time adaptive ADER-DG finite element method with LST-DG predictor and a posteriori sub-cell ADER-WENO finite-volume limiting was used for simulation of multidimensional reacting flows with detonation waves. The presented numerical…

Fluid Dynamics · Physics 2024-09-23 I. S. Popov

We propose and analyze a general framework for space-time finite element methods that is based on least-squares finite element methods for solving a first-order reformulation of the thick parabolic obstacle problem. Discretizations based on…

Numerical Analysis · Mathematics 2025-03-12 José Joaquín Carvajal , Davood Damircheli , Thomas Führer , Francisco Fuica , Michael Karkulik

In this paper, we study the convergence behavior of the diffuse domain method (DDM) for solving a class of second-order parabolic partial differential equations with Neumann boundary condition posed on general irregular domains. The DDM…

Numerical Analysis · Mathematics 2025-10-06 Wenrui Hao , Lili Ju , Yuejin Xu

In this paper we propose a new finite element method for solving elliptic optimal control problems with pointwise state constraints, including the distributed controls and the Dirichlet or Neumann boundary controls. The main idea is to use…

Numerical Analysis · Mathematics 2023-06-07 Wei Gong , Zhiyu Tan

We treat an inverse electrical conductivity problem which deals with the reconstruction of nonlinear electrical conductivity starting from boundary measurements in steady currents operations. In this framework, a key role is played by the…

We study the time-harmonic scattering by a heterogeneous object covered with a thin layer of randomly distributed sound-soft nanoparticles. The size of the particles, their distance between each other and the layer's thickness are all of…

Analysis of PDEs · Mathematics 2026-01-13 Amandine Boucart , Sonia Fliss , Laure Giovangigli

The Discontinuous Galerkin time-domain method is well suited for adaptive algorithms to solve the time-domain Maxwell's equations and depends on robust and economically computable drivers. Adaptive algorithms utilize local indicators to…

Computational Physics · Physics 2025-05-02 Apurva Tiwari , Avijit Chatterjee

We propose a novel a posteriori error estimator for the N\'ed\'elec finite element discretization of time-harmonic Maxwell's equations. After the approximation of the electric field is computed, we propose a fully localized algorithm to…

Numerical Analysis · Mathematics 2024-02-28 T. Chaumont-Frelet

In \cite{cheung2019optimally}, the authors presented two finite element methods for approximating second order boundary value problems on polytopial meshes with optimal accuracy without having to utilize curvilinear mappings. This was done…

Numerical Analysis · Mathematics 2023-01-11 James Cheung

We propose a time-domain boundary integral method to model linear wave propagation with refractive, focusing, and Doppler effects arising from medium heterogeneities and moving obstacles. In contrast to existing techniques, our method…

Numerical Analysis · Mathematics 2026-05-13 Raaghav Ramani

In this contribution we develop a cut finite element method with boundary value correction of the type originally proposed by Bramble, Dupont, and Thomee. The cut finite element method is a fictitious domain method with Nitsche type…

Numerical Analysis · Mathematics 2015-07-14 Erik Burman , Peter Hansbo , Mats G. Larson

Maxwell equations describe the propagation of electromagnetic waves and are therefore fundamental to understanding many problems encountered in the study of antennas and electromagnetics. The aim of this paper is to propose and analyse an…

Numerical Analysis · Mathematics 2022-10-13 Bin Wang , Yaolin Jiang

The paper is concerned with the three-dimensional electromagnetic scattering from a large open rectangular cavity that is embedded in a perfectly electrically conducting infinite ground plane. By introducing a transparent boundary…

Numerical Analysis · Mathematics 2021-04-28 Yanli Chen , Xue Jiang , Jun Lai , Peijun Li

This paper presents a robust numerical solution to the electromagnetic scattering problem involving multiple multi-layered cavities in both transverse magnetic and electric polarizations. A transparent boundary condition is introduced at…

Numerical Analysis · Mathematics 2023-08-14 Peijun Li , Xiaokai Yuan

We present a novel Discontinuous Galerkin Finite Element Method for wave propagation problems. The method employs space-time Trefftz-type basis functions that satisfy the underlying partial differential equations and the respective…

Computational Physics · Physics 2015-05-19 Fritz Kretzschmar , Sascha Schnepp , Igor Tsukerman , Thomas Weiland

This work proposes a nonlinear finite element method whose nodal values preserve bounds known for the exact solution. The discrete problem involves a nonlinear projection operator mapping arbitrary nodal values into bound-preserving ones…

Numerical Analysis · Mathematics 2023-04-04 Gabriel Barrenechea , Emmanuil Georgoulis , Tristan Pryer , Andreas Veeser

We present a high order, Fourier penalty method for the Maxwell's equations in the vicinity of perfect electric conductor boundary conditions. The approach relies on extending the smooth non-periodic domain of the equations to a periodic…

Numerical Analysis · Mathematics 2016-01-20 Ryan Galagusz , David Shirokoff , Jean-Christophe Nave

A reduction of the Maxwell's system to a Fredholm second-kind integral equation with weakly singular kernel is given for electromagnetic (EM) wave scattering by one and many small bodies. This equation is solved asymptotically as the…

Mathematical Physics · Physics 2009-11-13 A. G. Ramm

The inverse scattering problem for biharmonic waves, governing flexural vibrations of elastic plates, presents fundamental analytical challenges distinct from acoustic inverse problems due to the fourth-order differential operator and…

Numerical Analysis · Mathematics 2026-05-05 Tielei Zhu , Zhihao Ge , Bangmin Wu