The Huygens subgridding for the numerical solution of the Maxwell equations

The Huygens subgridding (HSG) is a subgridding technique developed for the numerical solution of the Maxwell equations. It relies on the theoretical equivalence of any physical volume with two or more fictitious volumes connected by equivalent currents. The application of this concept to the finite-difference time-domain (FDTD) method has been previously published in the one dimensional and two dimensional cases. In this paper the HSG is extended to the general three dimensional case, the exchange of the electromagnetic energy between the two FDTD grids is investigated theoretically, and some modifications to the HSG algorithm are presented with the objective of simplifying its implementation.     

基于JASMIN平台的复合材料方舱SE快速评估

在时域有限差分（FDTD）法中采用亚网格边界条件（SGBC）法对复合材料薄层结构进行建模,可以突破复合材料薄层对空间步长的限制从而大大降低计算成本。基于大规模并行化平台JASMIN实现了SGBC-FDTD算法,通过对复合材料薄层结构的自动建模和适配,实现对复合材料薄层的快速并行化处理。利用所开发的并行SGBC-FDTD算法计算分析了含不同电磁特性复合材料薄层方舱在0.1～1.0 GHz内的电磁屏蔽效能,结果表明采用并行SGBC-FDTD算法的计算结果与全波分析软件计算结果吻合完好,且计算效率显著提升。     

Novel subgridding technique for the analysis of optical devices

A novel subgridding algorithm for the Method of Lines is presented. It enables to refine a mesh in subgridded regions by any positive integer number. High-accuracy of the proposed algorithm is achieved by second-order finite difference operators. The interpolation of the missing field components at the interface coarse/fine grid is performed with second-order accuracy as well. Numerical results are provided to check the accuracy of the proposed formulation.     

Treatment of metal for the FDTD analysis of terahertz devices

A terahertz stop band filter and a resonator consisting of metal gratings are analyzed using the finite-difference time-domain (FDTD) method, with special attention to the treatment of metal. Numerical results based on a perfect electric conductor (PEC) approximation are compared to those with a metal dispersion being taken into account by the Drude model. It is shown that the results of the resonator for the PEC model are favorably compared with those for the Drude model at frequencies of less than 1 THz. However, care must be taken at higher frequencies, since not only the transmittance at the resonance remarkably reduces for the Drude model, but also its resonance frequency deviates, in comparison with those for the PEC model. Metal mesh structures are also investigated using the periodic FDTD. The differences are found to be relatively small, due to the weak confinement of THz waves in metal mesh structures. The results can serve as a guideline for the FDTD analysis of THz devices consisting of metal.     

Electric and magnetic losses modeled by a stable hybrid with explicit–implicit time-stepping for Maxwell’s equations

A stable hybridization of the finite-element method (FEM) and the finite-difference time-domain (FDTD) scheme for Maxwell’s equations with electric and magnetic losses is presented for two-dimensional problems. The hybrid method combines the flexibility of the FEM with the efficiency of the FDTD scheme and it is based directly on Ampère’s and Faraday’s law. The electric and magnetic losses can be treated implicitly by the FEM on an unstructured mesh, which allows for local mesh refinement in order to resolve rapid variations in the material parameters and/or the electromagnetic field. It is also feasible to handle larger homogeneous regions with losses by the explicit FDTD scheme connected to an implicitly time-stepped and lossy FEM region. The hybrid method shows second-order convergence for smooth scatterers. The bistatic radar cross section (RCS) for a circular metal cylinder with a lossy coating converges to the analytical solution and an accuracy of 2% is achieved for about 20 points per wavelength. The monostatic RCS for an airfoil that features sharp corners yields a lower order of convergence and it is found to agree well with what can be expected for singular fields at the sharp corners. A careful convergence study with resolutions from 20 to 140 points per wavelength provides accurate extrapolated results for this non-trivial test case, which makes it possible to use as a reference problem for scattering codes that model both electric and magnetic losses.     

分析端接频变负载的多导体传输线FDTD新方法

提出了一种新的有效求解端接频变负载的时域有限差分法（FDTD）.该方法将频域导纳经矢量匹配后以有理式表示,通过逆傅里叶变换将其转换到时域,基于分段线性递归卷积法,推导出该导纳两端的电压和电流关系,将其代入到传输线FDTD模型中,得到了求解端接频变负载多导体（MTL）传输线FDTD的一般公式.对一典型电路进行了仿真,和以状态变量法求解任意负载的结果进行了对比,两者基本重合,说明该方法用来求解频变负载是有效的. 关键词： 多导体传输线 分段线性递归卷积 时域有限差分法 任意负载     

Efficient mesh motion using radial basis functions with data reduction algorithms

Mesh motion using radial basis functions has been demonstrated previously by the authors to produce high quality meshes suitable for use within unsteady and aeroelastic CFD codes. In the aeroelastic case the structural mesh may be used as the set of control points governing the deformation, which is efficient since the structural mesh is usually small. However, as a stand alone mesh motion tool, where the surface mesh points control the motion, radial basis functions may be restricted by the size of the surface mesh, as an update of a single volume point depends on all surface points. In this paper a method is presented that allows an arbitrary deformation to be represented to within a desired tolerance by using a significantly reduced set of surface points intelligently identified in a fashion that minimises the error in the interpolated surface. This method may be used on much larger cases and is successfully demonstrated here for a 10⁶ cell mesh, where the initial solve phase cost reduces by a factor of eight with the new scheme and the mesh update by a factor of 55. It has also been shown that the number of surface points required to represent the surface is only geometry dependent (i.e. grid size independent), and so this reduction factor actually increases for larger meshes.     

基于目标三角面元模型生成FDTD共形网格的方法

 提出了一种基于目标三角面元数据的FDTD共形网格生成方法，该方法通过投影求交计算得到目标表面各三角面元与网格线的交点，将每条网格线与三角面元的交点按坐标进行排序，根据交点的坐标及其编号的奇偶性确定FDTD共形网格的位置，并生成相应的共形FDTD计算所需的元段长度。结合处理理想导体曲面的CFDTD方法修正共形网格上的磁场递推式。数值结果证实了共形网格生成方法的正确性和在提高FDTD方法计算精度方面的有效性。     

Theoretical Reflection Coefficient of Metal Grid Reflectors at a Dielectric Interface

Reflection properties of square apertures metal mesh mirrors are studied theoretically with the Finite-Difference Time-Domain (FDTD) method associated to Floquet Boundary Conditions. The reflector is illuminated by a normally incident plane wave and is located at an interface between two semi infinite low loss dielectric materials. Reflectivity and phase of the reflection coefficient are given in the non diffraction region for a wide range of square apertures, and for the four situations corresponding to an interface between free space and fused quartz.     

A high-sensitivity terahertz sensing method using a metallic mesh with unique transmission properties

Metallic meshes work as band-pass filters in the terahertz (THz) region, with their transmission spectra acutely affected by the refractive index of the material inside and above the metallic-mesh openings. We used a metallic mesh for high-sensitivity observations by focusing on the “dip,” that is, a sudden change in transmittance that only appeared when the THz wave was obliquely incident onto the metallic mesh. Here we consider the interference between apertures of the metallic mesh in the diagonal direction and explain the dip using finite-difference time-domain (FDTD) electromagnetic simulations.     

周期对称结构R-FDTD方法及其减元优化

论述减缩时域有限差分方法(R-FDTD)中暂存场分量边值补充计算的必要性,提出周期对称结构R-FDTD方法,基于对称关系和周期边界条件(PBC),给出需要补充计算的暂存分量表达式.利用对称性,将计算空间缩减为原来的1/4,对称面外侧场分量由对称关系得到,1/4空间周期对称结构R-FDTD可更进一步将计算区域的内存使用量降为FDTD算法的1/6,且不影响计算精度.计算无限大钢筋网和钢筋混凝土墙壁的电磁脉冲响应,结果与FDTD的计算结果吻合.改进的算法在内存使用和计算时间上具有明显的优势.     

一种基于波动方程的新高阶FDTD方法

 提出了一种基于二阶波动方程的（2M,4）高阶时域有限差分(FDTD)方法，通过使用辛积分传播子(SIP)在时域上获得4阶精度，使用离散奇异卷积(DSC)方法在空域上达到2M阶精度。与已有的(2M，4) 阶FDTD方法相比，虽然两者都采用SIP和DSC方法，但是此二者的不同点在于：第一，新方法基于二阶波动方程；第二，在离散计算空间时使用单一网格而不是传统的Yee网格；第三，单独计算某一场分量从而节约内存并减少计算量。数值计算结果表明，与传统高阶算法相比，基于波动方程的高阶FDTD方法耗费的机时只有它的50%,内存消耗下降10%, 而两者的计算结果之间相对误差小于5‰。     

基于曲四面体单元剖分的CN E-H TDFEM方法

从采用Crank-Nicolson差分格式的基于麦克斯韦旋度方程的E-H时域有限元方法出发,将展开电场和磁场的叠层矢量基函数与曲四面体单元相结合.对金属球谐振腔及介质填充的圆柱形谐振腔的数值模拟表明：相较于规则四面体单元,在剖分单元数目相同的情况下,曲四面体单元离散表面弯曲结构可以获得更高的计算精度.同时,与0.5阶基函数结合曲四面体单元相比,1.0阶基函数与曲四面体单元结合可以用更少的单元数及未知量数目来获得更高的计算精度.     

嵌入式薄片模型在时域有限差分算法中的应用

将一等效薄片模型嵌入到时域有限差分算法（FDTD）中,以快速而有效地解决复合材料薄片在电磁计算中的多尺度问题。在该嵌入式薄片模型中,薄片不需要被剖分网格,而是被嵌入到相邻的网格间,从而可以使用相对较大的网格剖分周围物体,进而可节省大量的计算资源。在这一模型中,薄片被等效为一段传输线,并用其频域的导纳矩阵代替。使用数字滤波器理论以及逆Z变换可将频域的导纳矩阵转换到时域,并将其嵌入到时域有限差分算法中。该嵌入式薄片模型被用来计算一单层碳纤维复合材料薄片的反射以及透射性能,并与其解析解进行对比,从而验证该模型的准确性、收敛性以及高效性。该模型被用来计算三种具有不同电参数的单层碳纤维复合材料薄片的屏蔽性能,以研究各电参数对其屏蔽性能的影响。     

粒子模拟中的时偏FDTD算法

给出一种能自动对高频噪声进行过滤的时域有限差分(FDTD)算法,称为时偏FDTD算法.在中心差分FDTD算法的基础上,引入时间偏置和松弛迭代处理,得到该算法的计算公式,并进行稳定性与收敛性分析.通过对相对论磁控管的计算,与中心差分FDTD算法比较,验证了该算法的滤波特性.     

耦合径向基函数与多项式基函数的无网格方法

耦合径向基函数和多项式基函数,形成一种新的近似函数.该近似函数对散乱分布的离散数据点进行逼近时,只需节点信息,不需要划分网格.详细描述了耦合近似函数的建立、属性、插值行为及其形函数和形函数导数的性质.最后引入修正变分原理和单位分解积分技术求解边值问题,并给出了计算实例,表明耦合径向基函数和多项式基函数是一种非常有效的方法.     

Solution of Hartree-Fock equations in coordinate space for axially symmetric nuclei

As an alternative to the conventional deformed harmonic oscillator basis expansion, a method is developed in which the coupled integro-differential Hartree-Fock equations are solved directly in coordinate space for a simple effective interaction. The single particle wave functions are obtained on a finite mesh by minimizing a discretized energy functional and solving the resulting finite difference equations using the Lanczos algorithm. Expressions to correct the total energy to second order in the mesh spacing are derived, and the accuracy of the method is demonstrated by numerical comparison with spherical results. Applications and advantages of this new technique are briefly discussed.     

An Efficient Dynamic Mesh Generation Method for Complex Multi-Block Structured Grid

Aiming at a complex multi-block structured grid, an efficient dynamic mesh generation method is presented in this paper, which is based on radial basis functions (RBFs) and transfinite interpolation (TFI). When the object is moving, the multi-block structured grid would be changed. The fast mesh deformation is critical for numerical simulation. In this work, the dynamic mesh deformation is completed in two steps. At first, we select all block vertexes with known deformation as center points, and apply RBFs interpolation to get the grid deformation on block edges. Then, an arc-lengthbased TFI is employed to efficiently calculate the grid deformation on block faces and inside each block. The present approach can be well applied to both two-dimensional (2D) and three-dimensional (3D) problems. Numerical results show that the dynamic meshes for all test cases can be generated in an accurate and efficient manner.     

2D FDTD Algorithm for the Analysis of Lossy and Dispersive Millimeter-Wave Coplanar Waveguide

The dispersion and loss characteristics of millimeter-wave coplanar waveguides (CPWs) are analyzed by using an efficient two-dimensional finite-difference time-domain (2D FDTD) algorithm. Combined with graded mesh technique, alternating direction implicit technique and curve-fitting technique, this proposed algorithm verifies its accuracy and efficiency through an example of infinite-ground CPW. Moreover, the influence of ground-plane width on CPW's loss characteristics is analyzed. Bulk micromachined CPWs with low loss are also analyzed by the proposed algorithm.     

Scattering phase functions of horizontally oriented hexagonal ice crystals

Finite-difference time domain (FDTD) solutions are first compared with the corresponding T-matrix results for light scattering by circular cylinders with specific orientations. The FDTD method is then utilized to study the scattering properties of horizontally oriented hexagonal ice plates at two wavelengths, 0.55 and 12 μm. The phase functions of horizontally oriented ice plates deviate substantially from their counterparts obtained for randomly oriented particles. Furthermore, we compute the phase functions of horizontally oriented ice crystal columns by using the FDTD method along with two schemes for averaging over the particle orientations. It is shown that the phase functions of hexagonal ice columns with horizontal orientations are not sensitive to the rotation about the principal axes of the particles. Moreover, hexagonal ice crystals and circular cylindrical ice particles have similar optical properties, particularly, at a strongly absorbing wavelength, if the two particle geometries have the same length and aspect ratio defined as the ratio of the radius or semi-width of the cross section of a particle to its length. The phase functions for the two particle geometries are slightly different in the case of weakly absorbing plates with large aspect ratios. However, the solutions for circular cylinders agree well with their counterparts for hexagonal columns.