Topology optimization for three-dimensional electromagnetic waves using an edge element-based finite-element method.
This paper develops a topology optimization procedure for three-dimensional electromagnetic waves with an edge element-based finite-element method. In contrast to the two-dimensional case, three-dimensional electromagnetic waves must include an additional divergence-free condition for the field variables. The edge element-based finite-element method is used to both discretize the wave equations and enforce the divergence-free condition. For wave propagation described in terms of the magnetic field in the widely used class of non-magnetic materials, the divergence-free condition is imposed on the magnetic field. This naturally leads to a nodal topology optimization method. When wave propagation is described using the electric field, the divergence-free condition must be imposed on the electric displacement. In this case, the material in the design domain is assumed to be piecewise homogeneous to impose the divergence-free condition on the electric field. This results in an element-wise topology optimization algorithm. The topology optimization problems are regularized using a Helmholtz filter and a threshold projection method and are analysed using a continuous adjoint method. In order to ensure the applicability of the filter in the element-wise topology optimization version, a regularization method is presented to project the nodal into an element-wise physical density variable.
State Key Laboratory of Applied Optics , Changchun Institute of Optics, Fine Mechanics and Physics (CIOMP), Chinese Academy of Sciences , Dongnanhu Road 3888, Changchun 130033, People's Republic of China.
Yongbo
0000-0002-1237-040X
Y
Deng
Institute of Microstructure Technology , Karlsruhe Institute of Technology (KIT) , Hermann-von-Helmholtzplatz 1, 76344 Eggenstein-Leopoldshafen, Germany.
Jan G
JG
Korvink
divergence-free condition; edge element; electromagnetic wave; three-dimensional; topology optimization