Shape Optimization for Electromagnetic and Quasimagnetostatic Applications

Licentiate thesis, 2006

This thesis uses a continuum formulation of sensitivity for shape optimization in two-dimensional microwave scattering and quasimagnetostatic problems. The continuum sensitivity is obtained by solving an appropriate adjoint problem. For microwave scattering problems, the optical theorem is used to obtain the total scattering cross section from the forward scattering. Shape optimization is performed on a 2D cross section of a strut used in antenna design and a FEM-FDTD time-domain solver is used to solve the field problem. The continuum gradient-based optimization algorithm, in conjunction with the optical theorem and the FEM-FDTD solver, yields an efficient algorithm for minimizing the total scattered power caused by the antenna strut. A continuum gradient-based shape optimization algorithm is also applied to the quasimagnetostatic problem of conductors in multi-layer components, where the objective is to increase the inductance or to reduce the magnetic field in certain regions. An efficient FEM solver, based on Nitsche's method, is also developed, which uses basic Cartesian grids in the computational domain, and lets interfaces cut through elements where necessary.