相关论文: Helmholtz equation and non-singular boundary eleme…
We analyse and implement a quasi-Monte Carlo (QMC) finite element method (FEM) for the forward problem of uncertainty quantification (UQ) for the Helmholtz equation with random coefficients, both in the second-order and zero-order terms of…
We consider the Helmholtz equation with real analytic coefficients on a bounded domain $\Omega\subset\mathbb{R}^{d}$. We take $d+1$ prescribed boundary conditions $f^{i}$ and frequencies $\omega$ in a fixed interval $[a,b]$. We consider a…
This paper focuses on the well-posedness (or lack thereof) of three-dimensional time-harmonic wave propagation problems modeled by the Helmholtz equation. It is well-known that if the problem is set in bounded domain with Dirichlet boundary…
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…
The boundary integral method (BIM) is a formulation of Helmholtz equation in the form of an integral equation suitable for numerical discretization to solve the quantum billiard. This paper is an extensive numerical survey of BIM in a…
The calculation of the acoustic field in or around objects is an important task in acoustic engineering. To numerically solve this task, the boundary element method (BEM) is a commonly used method especially for infinite domains. The open…
Most problems in electrodynamics do not have an analytical solution so much effort has been put in the development of numerical schemes, such as the finite-difference method, volume element methods, boundary element methods, and related…
Solving Helmholtz problems using finite elements leads to the resolution of a linear system which is challenging to solve for classical computers. In this paper, we investigate how quantum annealers could address this challenge. We first…
A method is presented for the analytical evaluation of the singular and near-singular integrals arising in the Boundary Element Method solution of the Helmholtz equation. An error analysis is presented for the numerical evaluation of such…
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…
This paper is concerned with reconstruction issue of some typical inverse problems and consists of three parts. First a framework of the enclosure method for an inverse source problem governed by the Helmholtz equation at a fixed wave…
Acoustic scattering of waves by bounded inhomogeneities in an unbounded homogeneous domain is considered. A symmetric coupled system of time-domain boundary integral equations and the second order formulation of the wave equation is…
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,…
The behavior of classical monochromatic waves in stationary media is shown to be ruled by a novel, frequency-dependent function which we call Wave Potential, and which we show to be encoded in the structure of the Helmholtz equation. An…
We show that the properties of the lower part of the spectrum of the Helmholtz equation for an heterogeneous system in a finite region in $d$ dimensions, where the solutions to the homogeneous problems are known, can be systematically…
We are interested in time-harmonic acoustic scattering by an impenetrable obstacle in a medium where the wavenumber is constant in an exterior unbounded subdomain and is possibly heterogeneous in a bounded subdomain. The associated…
A new numerical method to solve an inverse source problem for the Helmholtz equation in inhomogenous media is proposed. This method reduces the original inverse problem to a boundary value problem for a coupled system of elliptic PDEs, in…
The design, implementation and analysis of a free library for boundary element calculations is presented. The library is free in the sense of the GNU General Public Licence and is intended to allow users to solve a wide range of problems…
We study the spectrum of the Helmholtz equation in a two-dimensional infinite waveguide, containing a weak heterogeneity localized at an internal point, and obeying Dirichlet boundary conditions at its border. We prove that, when the…
The radiation condition is the key question in the mathematical modelling for scattering problems in unbounded domains. Mathematically, it plays the role as the "boundary condition" at the infinity, which guarantees the well-posedness of…