A radiation condition arising from the limiting absorption principle for a closed full- or half-waveguide problem

2018 ◽  
Vol 41 (10) ◽  
pp. 3955-3975 ◽  
Author(s):  
Andreas Kirsch ◽  
Armin Lechleiter
Keyword(s):  
Radiation Condition ◽  
Limiting Absorption Principle ◽  
Waveguide Problem

AN ABSTRACT RADIATION CONDITION AND APPLICATIONS TO N-BODY SYSTEMS

2000 ◽  
Vol 12 (05) ◽  
pp. 767-803 ◽  
Author(s):  
JACOB SCHACH MØLLER
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Stark Effect ◽  
Schrödinger Operators ◽  
Radiation Condition ◽  
Schrodinger Operators ◽  
Limiting Absorption Principle ◽  
Inhomogeneous Schrödinger Equation

In the setting of Mourre [18] we characterize the "outgoing" and "incoming" solutions, to the abstract inhomogeneous Schrödinger equation (H-E)u=v, given by the Limiting Absorption Principle. The characterization is in terms of an abstract radiation condition and as an application we give a characterization, in the framework of weighted L2-spaces, of the outgoing and incoming solutions for N-body Schrödinger operators with and without Stark effect. The abstract radiation condition translates in the application into a radiation condition considered by Isozaki in [13].

Radiation condition and limiting amplitude principle for acoustic propagators with two unbounded media

1998 ◽  
Vol 128 (1) ◽  
pp. 173-192 ◽  
Author(s):  
Bo Zhang
Keyword(s):  
Unique Solution ◽  
Smooth Surface ◽  
Diffraction Problem ◽  
Propagation Speed ◽  
Radiation Condition ◽  
Resolvent Estimate ◽  
Limiting Absorption Principle ◽  
Low Frequencies ◽  
Unbounded Media

Consider the diffraction problem for perturbed acoustic propagators with perturbations decreasing slowly at infinity. The propagation speed is discontinuous at the interface of two unbounded media, and the interface may be an arbitrary and smooth surface locally. A Sommerfeld radiation condition is introduced for the acoustic propagator, and is then used to establish the limiting absorption principle and the resolvent estimate at low frequencies for such an operator. Furthermore, we prove the existence of a unique solution to the diffraction problem and the validity of the limiting amplitude principles for the acoustic propagator.

scholarly journals Limiting absorption principle for the electromagnetic Helmholtz equation with singular potentials

2014 ◽  
Vol 144 (4) ◽  
pp. 857-890 ◽  
Author(s):  
Miren Zubeldia
Keyword(s):  
Helmholtz Equation ◽  
Unique Solution ◽  
A Priori ◽  
Radiation Condition ◽  
Singular Potentials ◽  
Absorption Method ◽  
Limiting Absorption Principle ◽  
Electric Potentials ◽  
Image Position

We study the Helmholtz equationin ℝd with magnetic and electric potentials that are singular at the origin and decay at ∞. We prove the existence of a unique solution satisfying a suitable Sommerfeld radiation condition, together with some a priori estimates. We use the limiting absorption method and a multiplier technique of Morawetz type.

A transmission problem for the reduced wave equation in inhomogeneous media with an infinite interface

1992 ◽  
Vol 436 (1896) ◽  
pp. 121-140 ◽  
Keyword(s):  
Wave Equation ◽  
Existence Of Solutions ◽  
Radiation Condition ◽  
Inhomogeneous Media ◽  
Transmission Problem ◽  
Surface Integral ◽  
Limiting Absorption Principle ◽  
Unique Existence

In this paper, we consider the transmission problem in R n ( n ≽ 2) for the reduced wave equation in inhomogeneous media with an infinite interface. A new radiation condition involving a surface integral over the interface, which is different from the well-known Rellich-Sommerfeld radiation condition, is introduced to ensure the uniqueness of the solutions. It is then used together with the limiting absorption principle to establish the unique existence of solutions to the problem in the various media.

VERY HIGH-ORDER SPATIALLY IMPLICIT SCHEMES FOR COMPUTATIONAL ACOUSTICS ON CURVILINEAR MESHES

2001 ◽  
Vol 09 (04) ◽  
pp. 1259-1286 ◽  
Author(s):  
MIGUEL R. VISBAL ◽  
DATTA V. GAITONDE
Keyword(s):  
Three Dimensional ◽  
Radiation Condition ◽  
Higher Order ◽  
High Order ◽  
High Frequencies ◽  
Decomposition Strategies ◽  
The Impact ◽  
Spurious Modes ◽  
Very High ◽  
Computational Strategy

A high-order compact-differencing and filtering algorithm, coupled with the classical fourth-order Runge–Kutta scheme, is developed and implemented to simulate aeroacoustic phenomena on curvilinear geometries. Several issues pertinent to the use of such schemes are addressed. The impact of mesh stretching in the generation of high-frequency spurious modes is examined and the need for a discriminating higher-order filter procedure is established and resolved. The incorporation of these filtering techniques also permits a robust treatment of outflow radiation condition by taking advantage of energy transfer to high-frequencies caused by rapid mesh stretching. For conditions on the scatterer, higher-order one-sided filter treatments are shown to be superior in terms of accuracy and stability compared to standard explicit variations. Computations demonstrate that these algorithmic components are also crucial to the success of interface treatments created in multi-domain and domain-decomposition strategies. For three-dimensional computations, special metric relations are employed to assure the fidelity of the scheme in highly curvilinear meshes. A variety of problems, including several benchmark computations, demonstrate the success of the overall computational strategy.

scholarly journals The Computation of the Magnitude of the Far Field for an Eccentric Circular Cylinder

2015 ◽  
Vol 2015 ◽  
pp. 1-8
Author(s):  
Bülent Yılmaz
Keyword(s):  
Circular Cylinder ◽  
Plane Wave ◽  
Radiation Condition ◽  
Higher Order ◽  
Numerical Results ◽  
Surface Radiation ◽  
Far Field ◽  
Condition Method ◽  
Radiation Conditions

The specific case of scattering of a plane wave by a two-layered penetrable eccentric circular cylinder has been considered and it is about the validity of the on surface radiation condition method and its applications to the scattering of a plane wave by a two-layered penetrable eccentric circular cylinder. The transformation of the problem of scattering by the eccentric circular cylinder to the problem of scattering by the concentric circular cylinder by using higher order radiation conditions, is observed. Numerical results presented the magnitude of the far field.

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