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Related papers: A time-domain preconditioner for the Helmholtz equ…

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This paper deals with balanced domain decomposition by constraints (BDDC) method for solving large-scale linear systems of algebraic equations arising from the space-time finite element discretization of parabolic initial-boundary value…

Numerical Analysis · Mathematics 2018-10-30 Ulrich Langer , Huidong Yang

We design a primal-dual stabilized finite element method for the numerical approximation of a data assimilation problem subject to the acoustic wave equation. For the forward problem, piecewise affine, continuous, finite element functions…

Numerical Analysis · Mathematics 2023-05-10 Erik Burman , Ali Feizmohammadi , Lauri Oksanen

This article considers a unilateral contact problem for the wave equation. The problem is reduced to a variational inequality for the Dirichlet-to-Neumann operator for the wave equation on the boundary, which is solved in a saddle point…

Numerical Analysis · Mathematics 2018-02-06 Heiko Gimperlein , Fabian Meyer , Ceyhun Oezdemir , Ernst P. Stephan

In this paper we consider a class of robust multilevel precontioners for the Helmholtz equation with high wave number. The key idea in this work is to use the continuous interior penalty finite element methods (CIP-FEM) studied in…

Numerical Analysis · Mathematics 2013-04-26 Huangxin Chen , Haijun Wu , Xuejun Xu

The dispersive character of the Hall-MHD solutions, in particular the whistler waves, is a strong restriction to numerical treatments of this system. Numerical stability demands a time step dependence of the form $\Delta t\propto (\Delta…

Computational Physics · Physics 2009-11-13 Lukas Arnold , Juergen Dreher , Rainer Grauer

The Wave Based Method (WBM) is a Trefftz method for the simulation of wave problems in vibroacoustics. Like other Trefftz methods, it employs a non-standard discretisation basis consisting of solutions of the partial differential equation…

Numerical Analysis · Mathematics 2018-02-06 Daan Huybrechs , Anda-Elena Olteanu

A method of numerically solving the Maxwell equations is considered for modeling harmonic electromagnetic fields. The vector finite element method makes it possible to obtain a physically consistent discretization of the differential…

Numerical Analysis · Mathematics 2026-01-05 Andrew V. Terekhov

In this paper, we consider an efficient iterative approach to the solution of the discrete Helmholtz equation with Dirichlet, Neumann and Sommerfeld-like boundary conditions based on a compact sixth order approximation scheme and…

Numerical Analysis · Mathematics 2012-12-07 Yury Gryazin

This paper deals with bathymetry-oriented optimization in the case of long waves with small amplitude. Under these two assumptions, the free-surface incompressible Navier-Stokes system can be written as a wave equation where the bathymetry…

Optimization and Control · Mathematics 2020-03-23 Pierre-Henri Cocquet , Sebastián Riffo , Julien Salomon

The paper is concerned with well-posedness of TE and TM polarizations of time-harmonic electromagnetic scattering by perfectly conducting periodic surfaces and periodically arrayed obstacles with local perturbations. The classical Rayleigh…

Analysis of PDEs · Mathematics 2024-02-20 Guanghui Hu , Andreas Kirsch

This paper presents a numerical investigation of acoustic wave propagation in an obstacle with periodically time-modulated material parameters. We focus on the numerical construction of Floquet$-$Bloch solutions, which are quasi-periodic…

Numerical Analysis · Mathematics 2025-07-22 Jörg Nick , Ralf Hiptmair , Habib Ammari

We prove strong convergence for a large class of finite element methods for the time-dependent Joule heating problem in three spatial dimensions with mixed boundary conditions on Lipschitz domains. We consider conforming subspaces for the…

Numerical Analysis · Mathematics 2018-01-31 Max Jensen , Axel Målqvist , Anna Persson

We propose a novel numerical homogenization method based on the edge multiscale approach for solving indefinite time-harmonic Maxwell equations in heterogeneous media with large wavenumber. Numerical methods for these equations in…

Numerical Analysis · Mathematics 2026-04-27 Yueqi Wang , Wing Tat Leung , Guanglian Li

Solving the wave equation is one of the most (if not the most) fundamental problems we face as we try to illuminate the Earth using recorded seismic data. The Helmholtz equation provides wavefield solutions that are dimensionally reduced,…

Geophysics · Physics 2021-06-04 Tariq Alkhalifah , Chao Song , Umair bin Waheed , Qi Hao

A robust multilevel preconditioner based on the hybridizable discontinuous Galerkin method for the Helmholtz equation with high wave number is presented in this paper. There are two keys in our algorithm, one is how to choose a suitable…

Numerical Analysis · Mathematics 2014-03-05 Huangxin Chen , Peipei Lu , Xuejun Xu

Time-spectral solution of ordinary and partial differential equations is often regarded as an inefficient approach. The associated extension of the time domain, as compared to finite difference methods, is believed to result in…

Computational Physics · Physics 2017-04-14 Jan Scheffel , Kristoffer Lindvall

In this article, we are concerned with the analysis on the numerical reconstruction of the spatial component in the source term of a time-fractional diffusion equation. This ill-posed problem is solved through a stabilized nonlinear…

Numerical Analysis · Mathematics 2020-05-06 Daijun Jiang , Yikan Liu , Dongling Wang

We study the boundary control of solutions of the Helmholtz and Maxwell equations to enforce local non-zero constraints. These constraints may represent the local absence of nodal or critical points, or that certain functionals depending on…

Analysis of PDEs · Mathematics 2015-08-26 Giovanni S. Alberti

In this paper, we focus on a new wave equation described wave propagation in the attenuation medium. In the first part of this paper, based on the time-domain space fractional wave equation, we formulate the frequency-domain equation named…

Analysis of PDEs · Mathematics 2021-02-23 Junxiong Jia , Shigang Yu , Jigen Peng , Jinghuai Gao

We consider the inverse problem of reconstructing inhomogeneities by performing a finite number of scattering measurements of acoustic type in the time-harmonic setting. We set up the reconstruction as a fully discrete variational problem…

Analysis of PDEs · Mathematics 2026-02-24 Daniela Di Donato , Luca Rondi