Inverse source problem and active shielding for composite domains

The problem of active shielding (AS) for a multiply connected domain consists of constructing additional sources of the field (e.g., acoustic) so that all individual subdomains can either communicate freely with one another or otherwise be shielded from their peers. This problem can be interpreted as a special inverse source problem for the differential equation (or system) that governs the field. In the paper, we obtain general solution for a discretized composite AS problem and show that it reduces to solving a collection of auxiliary problems for simply connected domains. c

[1]  J. Burgess.  Active adaptive sound control in a duct: A computer simulation , 1981 .

[2]  J. Loncaric,et al.  Quadratic optimization in the problems of active control of sound , 2002 .

[3]  V. Ryaben'kii.  Faithful transfer of difference boundary conditions , 1990 .

[4]  Philip A. Nelson,et al.  Active Control of Sound , 1992 .

[5]  Semyon Tsynkov,et al.  Optimization of power in the problems of active control of sound , 2004, Math. Comput. Simul..

[6]  B. Widrow,et al.  Adaptive inverse control , 1987, Proceedings of 8th IEEE International Symposium on Intelligent Control.

[7]  Semyon Tsynkov,et al.  On the Definition of Surface Potentials for Finite-Difference Operators , 2003, J. Sci. Comput..

[8]  Semyon Tsynkov,et al.  Active Shielding and Control of Noise , 2001, SIAM J. Appl. Math..

[9]  M. O. Tokhi,et al.  Active Sound and Vibration Control: Theory and Applications [Book Review] , 2004, IEEE Control Systems.

[10]  Sue Wright,et al.  Active Control of Environmental Noise , 1996 .

[11]  A. Devaney,et al.  Nonuniqueness in inverse source and scattering problems , 1982 .

[12]  A. J. Devaney,et al.  Radiating and nonradiating classical current distributions and the fields they generate , 1973 .

[13]  Victor Isakov,et al.  Inverse Source Problems , 1990 .

[14]  Rex K. Kincaid,et al.  Reactive Tabu Search and Sensor Selection in Active Structural Acoustic Control Problems , 1998, J. Heuristics.

[15]  Sue Wright,et al.  ACTIVE CONTROL OF ENVIRONMENTAL NOISE, II: NON-COMPACT ACOUSTIC SOURCES , 1997 .

[16]  N. K. Kulman,et al.  Method of difference potentials and its applications , 2001 .

[17]  Colin H. Hansen,et al.  Active control of vibration , 1996 .

[18]  Semyon Tsynkov,et al.  Optimization of Acoustic Source Strength in the Problems of Active Noise Control , 2003, SIAM J. Appl. Math..

[19]  Rex K. Kincaid,et al.  Quelling Cabin Noise in Turboprop Aircraft via Active Control , 1997, J. Comb. Optim..

[20]  Stephen J. Elliott,et al.  A multiple error LMS algorithm and its application to the active control of sound and vibration , 1987, IEEE Trans. Acoust. Speech Signal Process..