Shape and material optimization for antenna applications

Doctoral thesis, 2009

In this thesis, a gradient-based method for shape and material optimization for two antenna applications is presented: minimization of the active reflection coefficient for conformal array antennas; and minimization of the total scattering cross section for cylindrical scatterers. The sensitivity of the objective function with respect to changes of the shape and material of the geometry is expressed in terms of the original field problem and an adjoint field problem. This makes the computational cost of calculating the sensitivity independent of the number of design variables used to parameterize the geometry of the problem. Moreover, since the sensitivity is based on the continuum form of Maxwell's equations, the method is flexible with respect to the choice of field solver. The problem of minimizing the active reflection coefficient for conformal array antennas is tested in two dimensions for antenna elements that conform to a circular cylinder. Both uniform arrays and arrays where the antenna elements only cover part of the cylinder are considered. The minimization problem for the total scattering cross section is tested in two dimensions for metal cylinders and metal cylinders coated with a dielectric material. For both applications, the objective function is reduced significantly in a relatively small number of iterations. A finite element approach to treating curved boundaries in a finite-difference scheme on a Cartesian mesh is presented. It is based on Nitsche's method of applying boundary conditions for interfaces that do not conform to the mesh and uses explicit time stepping for the elements that are not cut by the interface and implicit time stepping for the elements that are cut by the interface. The method is tested for an eigenvalue problem in two dimensions and second-order convergence is observed.