相关论文: A spectral approach to a constrained optimization …
We study a new approach to the problem of transparent boundary conditions for the Helmholtz equation in unbounded domains. Our approach is based on the minimization of an integral functional arising from a volume integral formulation of the…
We consider a constrained optimization problem arising from the study of the Helmholtz equation in unbounded domains. The optimization problem provides an approximation of the solution in a bounded computational domain. In this paper we…
This paper is concerned with the Fourier-Bessel method for the boundary value problems of the Helmholtz equation in a smooth simply connected domain. Based on the denseness of Fourier-Bessel functions, the problem can be approximated by…
We develop a spectral method for solving univariate singular integral equations over unions of intervals by utilizing Chebyshev and ultraspherical polynomials to reformulate the equations as almost-banded infinite-dimensional systems. This…
The recent development of spectral method has been praised for its high-order convergence in simulating complex physical problems. The combination of embedded boundary method and spectral method becomes a mainstream way to tackle…
We consider the Helmholtz equation defined in unbounded domains, external to 2D bounded ones, endowed with a Dirichlet condition on the boundary and the Sommerfeld radiation condition at infinity. To solve it, we reduce the infinite region,…
We present a regularization strategy that leads to well-conditioned boundary integral equation formulations of Helmholtz equations with impedance boundary conditions in two-dimensional Lipschitz domains. We consider both the case of…
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…
Finding point configurations, that yield the maximum polarization (Chebyshev constant) is gaining interest in the field of geometric optimization. In the present article, we study the problem of unconstrained maximum polarization on compact…
This paper presents a theoretical discussion as well as novel solution algorithms for problems of scattering on smooth two-dimensional domains under Zaremba boundary conditions for which Dirichlet and Neumann conditions are specified on…
A new construction of an absorbing boundary condition for indefinite Helmholtz problems on unbounded domains is presented. This construction is based on a near-best uniform rational interpolant of the inverse square root function on the…
In order to solve Prandtl-type equations we propose a collocation-quadrature method based on VP filtered interpolation at Chebyshev nodes. Uniform convergence and stability are proved in a couple of Holder - Zygmund spaces of locally…
This paper tackles the data completion problem related to the Helmholtz equation. The goal is to identify unknown boundary conditions on parts of the boundary that cannot be accessed directly, by making use of measurements collected from…
This paper is concerned with the cavity scattering problem in an infinite thin plate, where the out-of-plane displacement is governed by the two-dimensional biharmonic wave equation. Based on an operator splitting, the scattering problem is…
In the formulation of the problem of scattering of monochromatic waves and the numerical simulation of the solution to the Helmholtz equation, there is a computational inconvenience: the calculation is performed on a finite grid of…
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…
In this paper, we propose a numerical method to approximate the solution of partial differential equations in irregular domains with no-flux boundary conditions by means of spectral methods. The main features of this method are its…
We study a minimization problem with free boundary, resulting in hybrid quadrature domains for the Helmholtz equation, as well as some application to inverse scattering problem.
A finite element approach for approximating the solution of a mathematical model for the response of a penetrable, bounded object (obstacle) to the excitation by an external electromagnetic field is presented and investigated. The model…
In this article, we discuss the efficient ways of implementing the transparent boundary condition (TBC) and its various approximations for the free Schr\"{o}dinger equation on a hyperrectangular computational domain in $\field{R}^d$ with…