Shape optimization for inverse electromagnetic casting problems

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...

Isogeometric Shape Optimization for Electromagnetic Scattering Problems

We consider the benchmark problem of magnetic energy density enhancement in a small spatial region by varying the shape of two symmetric conducting scatterers. We view this problem as a prototype for a wide variety of geometric design problems in electromagnetic applications. Our approach for solving this problem is based on shape optimization and isogeometric analysis. One of the major difficu...

A new method for inverse electromagnetic casting problems based on the topological derivative

The inverse electromagnetic casting problem consists in looking for a suitable set of electric wires such that the electromagnetic field induced by an alternating current passing through them, makes a given mass of liquid metal acquire a predefined shape. In this paper we propose a method for the topology design of such inductors. The inverse electromagnetic casting problem is formulated as an ...

Inverse Electromagnetic Problems

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...