Cloaking via impedance boundary condition for the 2-D Helmholtz equation

被引：20

作者：

Alekseev, G. V. ^{[1
,2
]}

机构：

[1] Far Eastern Fed Univ, Sch Nat Sci, Vladivostok, Russia

[2] Inst Appl Math FEB RAS, Vladivostok, Russia

来源：

APPLICABLE ANALYSIS | 2014年 / 93卷 / 02期

基金：

俄罗斯基础研究基金会;

关键词：

Helmholtz equation; mixed boundary value problem; impedance; control problem; boundary control; solvability; stability estimates; 35R30; 35Q60; 35J15; 78A25; SCATTERING; SHAPE;

D O I：

10.1080/00036811.2013.768340

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider control problems for the 2-D Helmholtz equation in an unbounded domain with partially coated boundary. Dirichlet boundary condition is given on one part of the boundary and the impedance boundary condition is imposed on another its part. The role of control in control problem under study is played by boundary impedance. Quadratic tracking-type functionals for the field play the role of cost functionals. Solvability of control problems is proved. The uniqueness and stability of optimal solutions with respect to certain perturbations of both cost functional and incident field are established.

引用

页码：254 / 268

页数：15

共 50 条

[31] A BOUNDARY INTEGRAL EQUATION FORMULATION FOR OPTIMIZATION OF 2D ACOUSTIC CLOAKING
Iemma, Umberto
Burghignoli, Lorenzo
PROCEEDINGS OF THE 17TH INTERNATIONAL CONGRESS ON SOUND AND VIBRATION, 2010,
[32] Helmholtz equation for a Neumann condition on a curved boundary: spurious resonances
Wirgin, Armand
APPLICABLE ANALYSIS, 2022, 101 (11) : 3841 - 3857
[33] An algebraic solution for a 2-D partial differential energy equation with a Robin boundary condition generated from the simpler solution for a dirichlet boundary condition
Campo, A
Campo, L
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 1997, 34 (10) : 101 - 114
[34] The Analyses of 2-D EM Cloaking Problem
Larkina, Olga
2014 INTERNATIONAL CONFERENCE ON COMPUTER TECHNOLOGIES IN PHYSICAL AND ENGINEERING APPLICATIONS (ICCTPEA), 2014, : 90 - 90
[35] WEAK GALERKIN METHOD FOR THE HELMHOLTZ EQUATION WITH DTN BOUNDARY CONDITION
Hu, Qingjie
He, Yinnian
Wang, Kun
INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING, 2020, 17 (05) : 643 - 661
[36] Numerical solution to the Complex 2D Helmholtz Equation based on Finite Volume Method with Impedance Boundary Conditions
Handlovicova, Angela
Riecanova, Izabela
OPEN PHYSICS, 2016, 14 (01): : 436 - 443
[37] The Dirichlet problem for the 2-D Helmholtz equation in a multiply connected domain with cuts
Krutitskii, PA
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK, 1997, 77 (12): : 883 - 890
[38] Dirichlet problem for the 2-D Helmholtz equation in a multiply connected domain with cuts
Krutitskii, P.A.
Zeitschrift fuer Angewandte Mathematik und Mechanik, ZAMM, Applied Mathematics and Mechanics, 77 (12):
[39] Implementation of a PEMC Boundary Condition in the 2-D FDTD Technique
Nayyeri, Vahid
Soleimani, Mohammad
Dehmollaian, Mojtaba
2012 IEEE ANTENNAS AND PROPAGATION SOCIETY INTERNATIONAL SYMPOSIUM (APSURSI), 2012,
[40] Nonlinear impedance boundary condition for 2D BEM
de Falco, Carlo
Di Rienzo, Luca
Ida, Nathan
Yuferev, Sergey
COMPEL-THE INTERNATIONAL JOURNAL FOR COMPUTATION AND MATHEMATICS IN ELECTRICAL AND ELECTRONIC ENGINEERING, 2018, 37 (02) : 772 - 783

← 1 2 3 4 5 →