Constructive Method for Solving a Boundary Value Problem with Impedance Boundary Condition for the Helmholtz Equation

2018 ◽  
Vol 54 (4) ◽  
pp. 539-550 ◽  
Author(s):  
E. H. Khalilov
Keyword(s):  
Boundary Condition ◽  
Boundary Value Problem ◽  
Helmholtz Equation ◽  
Boundary Value ◽  
Impedance Boundary Condition ◽  
Constructive Method ◽  
Impedance Boundary

scholarly journals RELAXATION APPROXIMATION OF THE KERR MODEL FOR THE THREE-DIMENSIONAL INITIAL-BOUNDARY VALUE PROBLEM

2009 ◽  
Vol 06 (03) ◽  
pp. 577-614 ◽  
Author(s):  
GILLES CARBOU ◽  
BERNARD HANOUZET
Keyword(s):  
Boundary Value Problem ◽  
Response Time ◽  
Boundary Value ◽  
Three Dimensional ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Debye Model ◽  
Impedance Boundary Condition ◽  
Impedance Boundary ◽  
Initial Boundary Value

The electromagnetic wave propagation in a nonlinear medium is described by the Kerr model in the case of an instantaneous response of the material, or by the Kerr–Debye model if the material exhibits a finite response time. Both models are quasilinear hyperbolic and are endowed with a dissipative entropy. The initial-boundary value problem with a maximal-dissipative impedance boundary condition is considered here. When the response time is fixed, in both the one-dimensional and two-dimensional transverse electric cases, the global existence of smooth solutions for the Kerr–Debye system is established. When the response time tends to zero, the convergence of the Kerr–Debye model to the Kerr model is established in the general case, i.e. the Kerr model is the zero relaxation limit of the Kerr–Debye model.

A METHOD FOR THE TREATMENT OF A SLOPING SEA BOTTOM IN THE PARABOLIC APPROXIMATION

1996 ◽  
Vol 04 (01) ◽  
pp. 89-100 ◽  
Author(s):  
J. S. PAPADAKIS ◽  
B. PELLONI
Keyword(s):  
Boundary Condition ◽  
Helmholtz Equation ◽  
Pressure Field ◽  
Impedance Boundary Condition ◽  
Parabolic Approximation ◽  
Impedance Boundary ◽  
Local Boundary ◽  
Sea Bottom ◽  
Local Boundary Condition ◽  
Non Local

The impedance boundary condition for the parabolic approximation is derived in the case of a sea bottom profile sloping at a constant angle, as a non-local boundary condition imposed exactly at the interface. This condition is integrated into the IFD code for the numerical computation of the pressure field and implemented to test its accuracy in some benchmark cases, for which the backscattered field is negligible. It is shown that by avoiding the sloping interface, the results obtained are closer to the benchmark results given by normal mode codes solving the full Helmholtz equation, such as the 2-way COUPLE code, than those of the standard IFD or other 1-way codes, at least for problems that do not have significant backscattering effects.

scholarly journals On the approximate solution of the boundary value problem for the Helmholtz equation with impedance condition

2019 ◽  
Vol 488 (3) ◽  
pp. 233-236
Author(s):  
A. R. Aliev ◽  
R. J. Heydarov
Keyword(s):  
Integral Equation ◽  
Exact Solution ◽  
Approximate Solution ◽  
Boundary Value Problem ◽  
Error Estimate ◽  
Helmholtz Equation ◽  
Collocation Method ◽  
Boundary Value ◽  
Impedance Boundary ◽  
Impedance Condition

In this work, we present a justification of collocation method for integral equation of the impedance boundary value problem for the Helmholtz equation. We also build a sequence which converges to the exact solution of our problem and we obtain an error estimate.

scholarly journals Numerical solution to the Complex 2D Helmholtz Equation based on Finite Volume Method with Impedance Boundary Conditions

Open Physics ◽  
2016 ◽  
Vol 14 (1) ◽  
pp. 436-443 ◽  
Author(s):  
Angela Handlovičová ◽  
Izabela Riečanová
Keyword(s):  
Boundary Condition ◽  
Helmholtz Equation ◽  
Numerical Solution ◽  
Finite Volume Method ◽  
Finite Volume ◽  
Robin Boundary Condition ◽  
Impedance Boundary Condition ◽  
Impedance Boundary ◽  
Volume Method ◽  
Robin Boundary

AbstractIn this paper, the numerical solution to the Helmholtz equation with impedance boundary condition, based on the Finite volume method, is discussed. We used the Robin boundary condition using exterior points. Properties of the weak solution to the Helmholtz equation and numerical solution are presented. Further the numerical experiments, comparing the numerical solution with the exact one, and the computation of the experimental order of convergence are presented.

Analysis of Control Problems for 2-D Model of Sound Scattering

2015 ◽  
Vol 770 ◽  
pp. 531-534
Author(s):  
Valeriy Sosnov
Keyword(s):  
Boundary Condition ◽  
Helmholtz Equation ◽  
Unbounded Domain ◽  
Surface Impedance ◽  
Impedance Boundary Condition ◽  
Control Problems ◽  
Sound Scattering ◽  
Impedance Boundary ◽  
D Model

In this paper control problems for 2-D Helmholtz equation are formulated and investigated. These problems are associated with developing technology of acoustic cloaking. Helmholtz equation is considered in an unbounded domain with the impedance boundary condition. The role of control in control problems under study is played by surface impedance.

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