Error bounds for inverse electromagnetic problems in soil mechanics

Inverse Electromagnetic Problems

Error Bounds for Regularizedcomplementarity Problems

An approach to solving a complementarity problem entails regular-izing/perturbing the problem by adding to the given mapping another mapping multiplied by a small positive parameter. We study properties of the limit point of the solution to the regularized problem. We also derive local error bounds on the distance from the solution to its limit point, expressed in terms of the regularization pa...

Inverse Medium Scattering Problems for Electromagnetic Waves

Consider a time-harmonic electromagnetic plane wave incident on a medium enclosed by a bounded domain in R3. In this paper, existence and uniqueness of the variational problem for forward scattering are established. An energy estimate for the scattered field with a uniform bound with respect to the wavenumber is obtained in the case of low frequency on which the Born approximation is based. A c...

Shape Optimization for Inverse Electromagnetic Casting Problems

In this paper we present an algorithm for inverse optimization problems concerning electromagnetic casting of molten metals. We are interested in locating suitable inductors around the molten metal so that the equilibrium shape be as near as possible to a desired target shape. A Simultaneous Analysis and Design (SAND) mathematical programming formulation is stated for the inverse problem. The r...

Piecewise smooth models for electromagnetic inverse problems

This paper presents a new method for constructing onedimensional electrical conductivity models of the Earth from surface electromagnetic measurements. The construction of these models is a nonlinear inverse problem that can be approached by linearization techniques combined with iterative methods and Tikhonov’s regularization. The standard application of these techniques usually leads to smoot...