相关论文: Evanescent Plane Wave Approximation of Helmholtz S…

The extended plane wave expansion (EPWE) formulation is derived to obtain the complex band structure of flexural waves in viscoelastic thin phononic crystal plates considering the Kirchhoff-Love plate theory. The presented formulation…

An overlapped continuous model framework, for the Helmholtz wave propagation problem in unbounded regions comprising bounded heterogeneous media, was recently introduced and analyzed by the authors ({\tt J. Comput. Phys., {\bf 403}, 109052,…

We present a numerical study to investigate the conditioning of the plane wave discontinuous Galerkin discretization of the Helmholtz problem. We provide empirical evidence that the spectral condition number of the plane wave basis on a…

This paper investigates the critical quintic wave equation in a 3D bounded domain subject to locally distributed Kelvin-Voigt damping. The study tackles two major mathematical challenges: the severe loss of derivatives induced by the…

We study the increasing stability of an inverse source problem for the Helmholtz equation from limited-aperture far field data at multiple wave numbers. The measurement data are givenby the far field patterns $u^\infity(\hat{x},k)$ for all…

Electromagnetic waves interacting with three--dimensional periodic structures occur in many applications of great scientific and engineering interest. These three dimensional interactions are extremely complicated and subtle, so it is…

We consider certain estimates involving averaging operators over curves and hypersurfaces that can be cast into a combinatorial framework. We show that hypersurfaces with nonzero rotational curvature satisfy the usual restricted weak-type…

We present a stability and convergence theory for the lossy Helmholtz equation and its Galerkin discretization. The boundary conditions are of Robin type. All estimates are explicit with respect to the real and imaginary part of the complex…

We present stability estimates for the inverse source problem of the stochastic Helmholtz equation in two and three dimensions by either near-field or far-field data. The random source is assumed to be a microlocally isotropic generalized…

Trefftz schemes are high-order Galerkin methods whose discrete spaces are made of elementwise exact solutions of the underlying PDE. Trefftz basis functions can be easily computed for many PDEs that are linear, homogeneous, and have…

We consider the numerical solution of time-harmonic acoustic scattering by obstacles with uncertain geometries for Dirichlet, Neumann, impedance and transmission boundary conditions. In particular, we aim to quantify diffracted fields…

This paper introduces a class of approximate transparent boundary conditions for the solution of Helmholtz-type resonance and scattering problems on unbounded domains. The computational domain is assumed to be a polygon. A detailed…

This paper is concerned with the study, by computational means, of the generation and stability of solitary-wave solutions of generalized versions of the Benjamin equation. The numerical generation of the solitary-wave profiles is…

We consider the logarithmic Schr{\"o}dinger equations with damping, also called Schr{\"o}dinger-Langevin equation. On a periodic domain, this equation possesses plane wave solutions that are explicit. We prove that these solutions are…

The displacement field for three dimensional dynamic elasticity problems in the frequency domain can be decomposed into a sum of a longitudinal and a transversal part known as a Helmholtz decomposition. The Cartesian components of both the…

A nonlinear Helmholtz equation (NLH) with high wave number and Sommerfeld radiation condition is approximated by the perfectly matched layer (PML) technique and then discretized by the linear finite element method (FEM).…

In recent years, several numerical methods for solving the unique continuation problem for the wave equation in a homogeneous medium with given data on the lateral boundary of the space-time cylinder have been proposed. This problem enjoys…

Trefftz methods are high-order Galerkin schemes in which all discrete functions are elementwise solution of the PDE to be approximated. They are viable only when the PDE is linear and its coefficients are piecewise constant. We introduce a…

In this paper, we investigate the upward overshooting by three-dimensional numerical simulations. We find that the above convectively stable zone can be partitioned into three layers: the thermal adjustment layer (mixing both entropy and…

A new domain decomposition method is introduced for the heterogeneous 2-D and 3-D Helmholtz equations. Transmission conditions based on the perfectly matched layer (PML) are derived that avoid artificial reflections and match incoming and…