相关论文: Stable approximation of Helmholtz solutions in the…
The two-dimensional propagation of small-amplitude waves through an infinite periodic array of freely-floating rectangular floes is considered under the assumptions of inviscid linearised wave theory. Fluid gaps between adjacent floes allow…
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 present a novel neural network architecture for the efficient prediction of sound fields in two and three dimensions. The network is designed to automatically satisfy the Helmholtz equation, ensuring that the outputs are physically…
A new method of solution is proposed for solution of the wave equation in one space dimension with continuously-varying coefficients. By considering all paths along which information arrives at a given point, the solution is expressed as an…
This paper is a short guideline to the decomposition of a compressible velocity into vortical and compressible structures using standard flow solvers. In particular, this is a fast solution to get an idea of the compressible fields inside…
This paper is concerned with solving the Helmholtz exterior Dirichlet and Neumann problems with large wavenumber $k$ and smooth obstacles using the standard second-kind boundary integral equations. We consider Galerkin and collocation…
This study employs spectral methods to capture the behaviour of wave equation with dispersive-nonlinearity. We describe the evolution of hump initial data and track the conservation of the mass and energy functionals. The…
We give integral formulas to approximate solutions of Dirichlet and Neumann problems for Helmholtz equation at high frequencies. These approximations are valid in the complementary of a union of convex compact obstacles. The first step of…
We study traveling wave solutions of an equation for surface waves of moderate amplitude arising as a shallow water approximation of the Euler equations for inviscid, incompressible and homogenous fluids. We obtain solitary waves of…
In this paper we investigate the dispersive properties of the solutions of the two dimensional water-waves system. First we prove Strichartz type estimates with loss of derivatives at the same low level of regularity we were able to…
We consider the numerical approximation of the ill-posed data assimilation problem for stationary convection-diffusion equations and extend our previous analysis in [Numer. Math. 144, 451--477, 2020] to the convection-dominated regime.…
We present a new numerical scheme to solve the Helmholtz equation in a wave-guide. We consider a medium that is bounded in the $x_2$-direction, unbounded in the $x_1$-direction and $\varepsilon$-periodic for large $|x_1|$, allowing…
We study wave propagation phenomena modelled in the frequency domain by the Helmholtz equation in heterogeneous media with focus on media with discontinuous, highly oscillating wave speed. We restrict to problems with spherical symmetry and…
High-frequency wave propagation is often modelled by nonlinear Friedrichs systems where both the differential equation and the initial data contain the inverse of a small parameter $\varepsilon$, which causes oscillations with wavelengths…
We present a method to obtain explicit solutions of the complex eikonal equation in the plane. This equation arises in the approximation of Helmholtz equation by the WKBJ or EWT methods. We obtain the complex-valued solutions (called…
In this paper, an efficient solver for the Helmholtz equation using a noval approximation space is developed. The ingradients of the method include the approximation space recently proposed, a discontinuous Galerkin scheme extensively used,…
A weak Galerkin (WG) method is introduced and numerically tested for the Helmholtz equation. This method is flexible by using discontinuous piecewise polynomials and retains the mass conservation property. At the same time, the WG finite…
This paper is devoted to study the wave propagation and its stability for a class of two-component discrete diffusive systems. We first establish the existence of positive monotone monostable traveling wave fronts. Then, applying the…
This paper introduces planewave density interpolation methods for the regularization of weakly singular, strongly singular, hypersingular and nearly singular integral kernels present in 3D Helmholtz surface layer potentials and associated…
We use the work of Milton, Seppecher, and Bouchitt\'{e} on variational principles for waves in lossy media to formulate a finite element method for solving the complex Helmholtz equation that is based entirely on minimization. In…