Juhani Kataja

Shape Sensitivity Analysis and Gradient-Based Optimization of Large Structures Using MLFMA

A fast method for computing the action of shape-differentiated electric field integral equation (EFIE) system matrix to a vector is derived exploiting the multilevel fast multipole algorithm (MLFMA). The proposed method is used in conjunction with the adjoint-variable method (AVM) to compute the shape gradient of arbitrary objective functions depending on shape of a metallic scatterer. The method is demonstrated numerically by optimizing the shape of a parabolic reflector illuminated with a half-wave dipole.

Analytical Shape Derivatives of the MFIE System Matrix Discretized With RWG Functions

An analytical formula for the shape derivative of the magnetic field integral equation (MFIE) method of moments (MoM) system matrix (or impedance matrix) is derived and validated against finite difference formulas. The motivation for computing the shape derivatives stems from adjoint variable methods (AVM). The Galerkin system matrix is constructed by means of Rao-Wilton-Glisson (RWG) basis and testing functions. The shape derivative formula yields an integral representation which is of same singularity order as the integrals appearing in the traditional MFIE system matrix.

The Parametric Optimization of Wire Dipole Antennas

The shape representation of planar wire dipole antennas of fixed radius is discussed. Away from the feed point the shape can be always represented as a arc-length parametrizable Lipschitz-continuously differentiable curve. The representation is applied to classical directivity optimization design problems as well as impedance optimization problems. By such an optimization, it is shown that directive wire dipoles of length (3/2)λ can be tuned by shape optimization and that the real part of input impedance of λ/2 dipole is bounded from above if the imaginary part must be small.

A Least Squares Finite Element Method for the Extended Maxwell System

A flnite element method based on the flrst order system LL ⁄ (FOSLL ⁄ ) approach is derived for time harmonic Maxwells equations in three dimensional domains. The flnite element solution is a potential for the original fleld in a sense that the original fleld U is given by U = L ⁄ u. The Maxwellian boundary data appears as natural boundary condition. Homogeneous Dirichlet boundary conditions for the potential must be imposed, and they are circumvented with weak enforcement of boundary conditions and it is proved that the sesquilinear form of the flnite element system is elliptic in the space where the Dirichlet boundary conditions are satisfled weakly.

On shape optimization of wire dipole antennas

Representation of dipole antennas as arc-length parametrized curves is presented and such representation is used to find optimal antenna shapes of given size constraints and impedance in two and three dimensions.