Topology optimization for three-dimensional electromagnetic waves using an edge element-based finite-element method
Topology optimization for three-dimensional electromagnetic waves using an edge element-based finite-element method
复制标题
使用基于边缘元的有限元方法进行三维电磁波拓扑优化
DOI：
10.1098/rspa.2015.0835
复制
发表时间：
2016-05-01
影响因子：
3.5
通讯作者：
Korvink, Jan G.
中科院分区：
文献类型：
--
作者：
Deng, Yongbo;Korvink, Jan G.
本文提出了一种基于边缘单元有限元方法的三维电磁波拓扑优化方法。与二维情况不同，三维电磁波必须包含一个附加的场变量的无散度条件。采用基于边界元的有限元方法对波动方程进行离散化，并执行无散度条件。对于用磁场描述的波在广泛使用的一类非磁性材料中的传播，施加了磁场的无发散条件。这自然导致了节点拓扑优化方法的出现。当用电场描述波的传播时，必须对电位移施加无散度条件。在这种情况下，设计域中的材料被假定为分段均匀的，以在电场上施加无散度条件。这将导致基于元素的拓扑优化算法。利用Helmholtz滤波和阈值投影法将拓扑优化问题正则化，并使用连续伴随方法进行分析。为了保证滤波器在单元拓扑优化中的适用性，提出了一种正则化方法，将节点投影到单元物理密度变量中。
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.