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We devise a new high order local absorbing boundary condition (ABC) for radiating problems and scattering of time-harmonic acoustic waves from obstacles of arbitrary shape. By introducing an artificial boundary $S$ enclosing the scatterer,…

Computational Physics · Physics 2020-07-01 Vianey Villamizar , Sebastian Acosta , Blake Dastrup

Transparent boundary conditions for the time-dependent Schrodinger equation are implemented using the R-matrix method. The employed scattering formalism is suitable for describing open quantum systems and provides the framework for the…

Mesoscale and Nanoscale Physics · Physics 2016-09-20 G. A. Nemnes , Alexandra Palici , A. Manolescu

We prove spatiotemporal algebraically decaying estimates for the density of the solutions of the linearly damped nonlinear Schr\"odinger equation with localized driving, when supplemented with vanishing boundary conditions. Their derivation…

Mathematical Physics · Physics 2019-12-10 G. Fotopoulos , N. I. Karachalios , V. Koukouloyannis , K. Vetas

We propose a new Nitsche-type approach for weak enforcement of normal velocity boundary conditions for a Lagrangian discretization of the compressible shock-hydrodynamics equations using high-order finite elements on curved boundaries.…

Numerical Analysis · Mathematics 2023-09-06 Nabil M. Atallah , Vladimir Z. Tomov , Guglielmo Scovazzi

Generalized impedance boundary conditions are effective, approximate boundary conditions that describe scattering of waves in situations where the wave interaction with the material involves multiple scales. In particular, this includes…

Numerical Analysis · Mathematics 2020-05-29 Lehel Banjai , Christian Lubich , Joerg Nick

We consider the Schr\"odinger equation on a half space in any dimension with a class of nonhomogeneous boundary conditions including Dirichlet, Neuman and the so-called transparent boundary conditions. Building upon recent local in time…

Analysis of PDEs · Mathematics 2017-02-23 Corentin Audiard

The Schroedinger equation with an energy-dependent complex absorbing potential, associated with a scattering system, can be reduced for a special choice of the energy-dependence to a harmonic inversion problem of a discrete pseudo-time…

Chemical Physics · Physics 2009-11-07 A. Neumaier , V. A. Mandelshtam

The time-dependent form of Tappert's range refraction parabolic equation is derived using Daletskiy-Krein formula form noncommutative analysis and proposed as an artificial boundary condition for the wave equation in a waveguide. The…

Mathematical Physics · Physics 2015-05-13 P. S. Petrov , M. Yu. Trofimov

We present an absorbing boundary condition for electromagnetic frequency domain simulations of photonic crystals and metamaterials. This boundary condition can simultaneously absorb multiple Bloch-Floquet eigenmodes of a periodic crystal,…

Optics · Physics 2015-06-16 Chris Fietz

The problem of boundary behaviour at the origin of coordinates is discussed for D-dimensional Schrodinger equation in the framework of hyper spherical formalism, which have been often considered last time. We show that the Dirichlet…

Quantum Physics · Physics 2022-06-02 Anzor Khelashvili , Teimuraz Nadareishvili

This work is devoted to the structure of the time-discrete Green-Naghdi equations including bathymetry. We use the projection structure of the equations to characterize homogeneous and inhomogeneous boundary conditions for which the…

Numerical Analysis · Mathematics 2022-04-25 Sebastian Noelle , Martin Parisot , Tabea Tscherpel

We propose a boundary integral formulation for the dynamic problem of electromagnetic scattering and transmission by homogeneous dielectric obstacles. In the spirit of Costabel and Stephan, we use the transmission conditions to reduce the…

Numerical Analysis · Mathematics 2025-05-20 Tonatiuh Sánchez-Vizuet

This article proves the well posedness of the boundary value problemthat arises when PML algorithms are applied to Pauli's equationswith a three dimensional rectangle as computational domain. The absorptionsare positive near the boundary…

Analysis of PDEs · Mathematics 2022-02-18 Laurence Halpern , Jeffrey Rauch

It is shown that exterior complex scaling provides for complete absorption of outgoing flux in numerical solutions of the time-dependent Schr\"odinger equation with strong infrared fields. This is demonstrated by computing high harmonic…

Computational Physics · Physics 2014-05-19 Armin Scrinzi

Firstly, a systematic procedure is derived for obtaining three-dimensional bound-state equations from four-dimensional ones. Unlike ``quasi-potential approaches'' this procedure does not involve the use of delta-function constraints on the…

Nuclear Theory · Physics 2008-11-26 D. R. Phillips , S. J. Wallace

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…

Numerical Analysis · Mathematics 2024-08-27 Samardhi Yadav , Vishal Vaibhav

Theoretical treatments of strong-field physics have long relied on the numerical solution of the time-dependent Schr\"odinger equation. The most effective such treatments utilize a discrete spatial representation---a grid. Since most…

Computational Physics · Physics 2018-05-09 Youliang Yu , B. D. Esry

We consider an inverse problem of recovering all spatial dependent coefficients in the time dependent Schr\"odinger equation defined on an open bounded domain in $\mathbb{R}^n$, $n\geq 2$, with smooth enough boundary. We show that by…

Analysis of PDEs · Mathematics 2025-03-19 Shitao Liu , Antonio Pierrottet

The large time $t$ asymptotics for scalar, constant coefficient,linear, third order, dispersive equations are obtained for asymptotically time-periodic Dirichlet boundary data and zero initial data on the half-line modeling a wavemaker…

Analysis of PDEs · Mathematics 2023-07-28 Yifeng Mao , Dionyssios Mantzavinos , Mark A. Hoefer

The study of nonlinear Schr\"odinger-type equations with nonzero boundary conditions define challenging problems both for the continuous (partial differential equation) or the discrete (lattice) counterparts. They are associated with…