Numerical Method Of Interaction Model Between An Elastic Body And An Electromagnetic Field

This paper deals with a time-harmonic problem that models the interaction between an elastic body and an electromagnetic field. We consider a solid occupying a bounded region and assume that it is subject to a given incident electromagnetic wave. Penetration and scattering occurs on the boundary of the elastic object. The boundary of this object will be reconstructed by far field pattern of the scattering field.In Chapter2, the mathematical model of the forward problem about the interaction between electromagnetic field and elastic body is established. We consider a suitable transmission problem holding between the solid and a annular region surrounding it, and aim to compute both the electron component of the scattered wave and the stresses that take place in the obstacle. Vligt’s model turn interaction condition to two transmission conditions. Uniqueness of solution has been proved by Relich’s theorem. Then regularization methods for ill-posed problem is introduced which is used in reconstruction of elastic object.In Chapter3, formulas of numerical solution for forward problem is derived. By using artificial boundary conditions we can cut off unbounded area for a bounded domain. A DtN mapping simulate the scattering wave of the infinity throught the artificial boundary. By using lagrange multiplier, a coupled variational formulation is established. In addition we define the corresponding Galerkin scheme by using lagrange finite element in the solid and the edge finite elements of Nedelec in the electromagnetic region. Due to the curl operator has a null space Maxwell problem does not fit in any classical theory for proving well-posedness. A Helmholtz type decomposition of the electromagnetic field is usually proposed in order to reveal hidden compactness properties to deal with the study of this problem through a classical analysis. Then we show that the resulting Galerkin scheme is uniquely solvable by using Sobolev space theory.In Chapter4, elastic target boundary reconstruct by electromagnetic far field pattern. The far field patterns as artificial data simulate by the numerical solution of the forward problem. We shall consider a model inverse scattering problem for the interaction between an elastic body and an electromagnetic field. Our wish is developing a method to determine the shape of the scatter by useing multistage far-field data. By this we mean that the far-field pattern of the scattered field is known for incident plane waves from any direction and any polarization. In fact, in numerical implementation, only a finite numbler of plane waves is used. And the far-field pattern is known in a discrete set of directions. The approach used is the linear sampling method which does not require a priori knowledge of the characteristics of the elastic object. Finally some numerical results are showed that validate the method for reconstructing elastic scatterer.