Far Eastern Mathematical Journal

To content of the issue


On the optimal control problem for equations of acoustic wave diffraction


Illarionova L.V.

2018, issue 2, P. 195-205


Abstract
One consider the optimal control problem for stationary equations of acoustic waves diffraction on three-dimensional inclusion in unbounded homogeneous medium. The problem is to minimize $L^2$-deviation of pressure field in inclusion from the given. The control is the field source in the exterior medium.

Keywords:
acoustic wave diffraction, optimal control problem, Helmholtz equation

Download the article (PDF-file)

References

[1] V.S. Vladimirov, Uravneniya matematicheskoy fiziki, Nauka, M., 1988, 512 s.
[2] S.I. Smagin, Integral’nyye uravneniya zadach difraktsii, Dal’nauka, Vladivostok, 1995.
[3] S.I. Smagin, “Ob odnoy sisteme integral’nykh uravneniy teorii difraktsii”, Differents. uravneniya, 26:8, (1990), 1432–1437.
[4] A.A. Samarskiy, Teoriya raznostnykh skhem, Nauka, M., 1977, 656 s.
[5] G.I. Marchuk, V.I. Agoshkov, Vvedeniye v proyektsionno-setochnyye metody, Nauka, M., 1981, 416 s.
[6] D. Kolton, R. Kress, Metody integral’nykh uravneniy v teorii rasseyaniya, Mir, M., 1987, 311 s.
[7] N.E. Ershov, L.V. Illarionova, S.I. Smagin, “CHislennoye resheniye trekhmernoy statsionarnoy zadachi difraktsii akusticheskikh voln”, Vychislitel’nyye tekhnologii, 15:1, (2010), 60–76.
[8] A.A. Kashirin, S.I. Smagin, “O chislennom reshenii zadach Dirikhle dlya uravneniya Gel’mgol’tsa metodom potentsialov”, ZH. vychisl. matem. i matem. fiz., 52:8, (2012), 1429–1505.
[9] A.A. Kashirin, S.I. Smagin, M.YU. Taltykina, “Primeneniye mozaichno-skeletonnogo metoda pri chislennom reshenii trekhmernykh zadach Dirikhle dlya uravneniya Gel’mgol’tsa v integral’noy forme”, ZH. vychisl. matem. i matem. fiz., 56:4, (2012), 625–638.
[10] A. Kirsch, “A weak bang-bang principle for the control of an exterior robin problem”, Applicable Analysis, 13, (1982), 65–75.
[11] R. Kress, W. Rundell, “Inverse scattering for shape and impedance”, Inverse Problems, 2001, № 17, 1075–1085.
[12] T.S. Angell, A. KirschOptimization methods in electromagnetic radiation, Springer, 2004, 331 s.
[13] Cao Yanzhao, D. Stanescu, “Shape optimization for noise radiation problems”, Computers and Mathenatics with Applications, 2002, № 44, 1527–1537.
[14] A. Habbal, “Nonsmooth shape optimization applied to linear acoustic”, SIAM Journal on Optimization, 8:4, (1998), 989–1006.
[15] A.A. Goryunov, A.V. Saskovets, Obratnyye zadachi rasseyaniya v akustike, Izd-vo MGU, M., 1989.
[16] J. Jahn, A. Kirsch, C. Wagner, “Optimization of rod antennas of mobile phones”, Math. Meth. Oper. Res., 2004, № 59, 37–51.
[17] L.V. Illarionova, “Zadacha optimal’nogo upravleniya dlya statsionarnykh uravneniy difraktsii akusticheskikh voln”, ZH. vychisl. matem. i matem. fiz., 48:2, (2008), 297–308.
[18] L.V. Illarionova, “CHislennoye resheniye zadachi optimal’nogo upravleniya statsionarnymi akusticheskimi polyami”, Vestnik TOGU, 23:4, (2011), 75–84.

To content of the issue