Topology optimization of metallic devices for microwave applications

In electromagnetic optimization problems of metallic radio-frequency devices, such as antennas and resonators for wireless energy transfer, the volumetric distribution of good conductors, e.g. copper, has been known to cause numerical bottlenecks. In finite element analysis the limiting factor is the skin depth, which calls for highly refined meshing in order to capture the physics. The skin depth problem has therefore prohibited the application of topology optimization to this class of problem. We present a design parameterization that remedies these numerical issues, by the interpolation of Maxwell's equations and a fictitious element impedance condition. The validity of the proposed design parameterization is confirmed by several numerical examples. Copyright © 2010 John Wiley & Sons, Ltd.

[1]  James K. Guest,et al.  Achieving minimum length scale in topology optimization using nodal design variables and projection functions , 2004 .

[2]  Ole Sigmund,et al.  A topology optimization method for design of negative permeability metamaterials , 2010 .

[3]  M. Bendsøe.  Optimal shape design as a material distribution problem , 1989 .

[4]  J. Petersson,et al.  Topology optimization of fluids in Stokes flow , 2003 .

[5]  Ole Sigmund,et al.  Geometric properties of optimal photonic crystals. , 2008, Physical review letters.

[6]  K. Svanberg.  The method of moving asymptotes—a new method for structural optimization , 1987 .

[7]  Yu Zhu,et al.  Multigrid Finite Element Methods for Electromagnetic Field Modeling , 2006 .

[8]  O. Sigmund.  Morphology-based black and white filters for topology optimization , 2007 .

[9]  N. Kikuchi,et al.  Topology optimization of dielectric substrates for filters and antennas using SIMP , 2004 .

[10]  Jakob S. Jensen,et al.  Systematic design of photonic crystal structures using topology optimization: Low-loss waveguide bends , 2004 .

[11]  Jakob S. Jensen,et al.  Topology optimization and fabrication of photonic crystal structures. , 2004, Optics express.

[12]  M. Bendsøe,et al.  Generating optimal topologies in structural design using a homogenization method , 1988 .

[13]  Alessandro Reali,et al.  Isogeometric Analysis of Structural Vibrations , 2006 .

[14]  M. Soljačić,et al.  Wireless Power Transfer via Strongly Coupled Magnetic Resonances , 2007, Science.

[15]  O. Sigmund,et al.  Three-dimensional topology optimized electrically-small conformal antenna , 2008, 2008 IEEE Antennas and Propagation Society International Symposium.

[16]  T. E. Bruns,et al.  Topology optimization of non-linear elastic structures and compliant mechanisms , 2001 .

[17]  J. Volakis,et al.  Multiobjective Optimal Antenna Design Based on Volumetric Material Optimization , 2007, IEEE Transactions on Antennas and Propagation.

[18]  B. Bourdin.  Filters in topology optimization , 2001 .