For many wave propagation problems, it is often necessary to solve the variable coeecient Helmholtz equation in a very large domain. The one-way re-formulation based on the Dirichlet-to-Neumann (DtN) map can be used to nd the solutions of the Helmholtz equation over a large range distance. It is particularly useful for waveguide problems, since it leads to a numerical algorithm that marches in ...

We show that the Kelvin-Helmholtz instability excited by a localized perturbation yields a self-similar wave. The instability of the mixing layer was first conceived by Helmholtz as the inevitable growth of any localized irregularity into a spiral, but the search and uncovering of the resulting self-similar evolution was hindered by the technical success of Kelvin's wavelike perturbation theory...

Abstract We establish weighted $$L^p$$ Lp -Fourier extension estimates for $$O(N-k) \times O(k)$$ xmlns:mml="http://www.w3.org/1998/Math/MathML">O(N-k)×</...

In this paper, thirdand fourth-order compact finite difference schemes are proposed for solving Helmholtz equations with discontinuous media along straight interfaces in two space dimensions. To keep the compactness of the finite difference schemes and get global high order schemes, even at the interface where the wave number is discontinuous, the idea of the immersed interface method is employ...

A high-order accurate, explicit kernel-split, panel-based, Fourier–Nyström discretization scheme is developed for integral equations associated with the Helmholtz equation in axially symmetric domains. Extensive incorporation of analytic information about singular integral kernels and on-the-fly computation of nearly singular quadrature rules allow for very high achievable accuracy, also in the...

This note is concerned with a semi-analytical method for the solution of 2-D Helmholtz equation in unit square. The method uses orthogonal functions to project the problem down to finite dimensional space. After the projection, the problem simplifies to that of obtaining solutions for second order constant coefficient differential equations which can be done analytically. Numerical results indi...

We regularize the variable coefficient Helmholtz equations arising from implicit time discretizations for resistive MHD, in a way that leads to a symmetric positive-definite system uniformly in the time step. Standard centered-difference discretizations in space of the resulting PDE leads to a method that is second-order accurate, and that can be used with multigrid iteration to obtain efficien...

The paper is devoted to an integral equation algorithm for studying the scattering of plane waves by multilayer diffraction gratings under oblique incidence. The scattering problem is described by a system of Helmholtz equations with piecewise constant coefficients in R coupled by special transmission conditions at the interfaces between different layers. Boundary integral methods lead to a sys...

Many boundary integral equations for exterior boundary value problems for the Helmholtz equation suffer from a notorious instability for wave numbers related to interior resonances. The so-called combined field integral equations are not affected. However, if the boundary is not smooth, the traditional combined field integral equations for the exterior Dirichlet problem do not give rise to an L...