Numerical Study of Inverse Problems of Nonscattering Anisotropic Shell Theory

Abstract:

The inverse problems are formulated for generalized Helmholtz equation describing propagation of acoustics waves in inhomogeneous anisotropic medium. These problems are connected with constructing nonscattering shells filled with anisotropic fluid. For solving the inverse problems we apply the nonlinear optimization techniques. Based on this approach we formulate the general control problem for the Helmholtz equation under consideration. The control problem consists of minimization of a suitable cost functional depending on the state (acoustic pressure) and unknown functions (controls). The optimality system for the general control problem is derived, the sufficient conditions for data which provide a local stability and uniqueness of control problems under study for concrete tracking-type cost functionals are discussed. The efficient numerical algorithm of solving control problem under study based on Newton's method of solving nonlinear equations and finite element for Helmholtz boundary value problems is proposed.

• Periodical: Applied Mechanics and Materials (Volumes 249-250)
• Pages: 557-562
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.249-250.557
• Online since: December 2012
• Authors: Gennady V. Alekseev, Aleksey Lobanov, Gleb Grenkin
• Keywords: Acoustic, Anisotropic Media, Cloaking Shells, Control Problem, Inverse Problem, Numerical Algorithm, Optimality System

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