计算电磁学中二维与三维单纯形插值法的探索与应用研究

批准号:
61971384
项目类别:
面上项目
资助金额:
65.0 万元
负责人:
宋继明
依托单位:
学科分类:
电磁场与波
结题年份:
2023
批准年份:
2019
项目状态:
已结题
项目参与者:
宋继明
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中文摘要
作为20世纪的十大杰出算法之一,多层快速多极子算法(MLFMA)是截至目前用于迭代求解电磁问题最快的算法,被用于仿真电大尺寸目标的电磁散射特性与阵列天线等的辐射特性。它的关键思想是将插值/反插值结合起来,导致了低计算复杂度。应用最广泛的插值方法是二维拉格朗日多项式插值乘法,其另一应用是快速计算多层介质的周期格林函数, 在实际工程问题如频率选择表面、超材料、天线的设计中起着至关重要的作用。本申请的主要目的是开发一种新型单纯形插值技术并将其应用于电磁建模工具中。首先,拟研究如何正确地将二维三角形插值应用于矩形网格或等边三角形网格中。基于最小插值误差,研究如何选择最合适的三角形用来插值。然后将有效的插值技术应用于加速MLFMA。研究在单位球面上非均匀采样点的情况下如何利用不同的变换方法,或研究出更有效的插值积分方法。对于三维单纯形插值,将研究出一种通用的途径来选择合适的四面体使插值误差降低到最小
英文摘要
As one of top 10 algorithms in the last century, the fast multipole method (FMM) and the multilevel fast multipole algorithm (MLFMA) are the fastest iterative solver for 3D electromagnetic (EM) problems up to now. The MLFMA has been implemented by many research groups and in several commercial EM software tools, has many applications such as the scattering and radiation of electrically large size objects and design and simulations of antenna arrays. One key idea in the lower complexity is the combination of the interpolation and adjoint interpolation. Currently, 2D Lagrangian polynomial interpolations are commonly in use..One of other fields using the interpolation in computational electromagnetics is the efficient evaluation of periodic Green’s functions (PGF) in layered-media, which is a key component in modeling with applications such as frequency selective surfaces (FSS), photonic crystal slabs, metamaterials, and rectarray antennas. In general, it is very time-consuming to evaluate the PGF for all observation and source points because PGF involves the Sommerfeld integral and double summations of infinite series, in spectral or space domain. To reduce the CPU time, the interpolation technique is applied to the tabulated PGF..The PI proposes to develop novel simplex interpolation techniques in EM modeling tools applicable to design and analysis of low RCS objects, antenna arrays, embedded radio frequency components, and high-speed circuits. In geometry, a simplex is a generalization of the notion of a triangle or tetrahedron to arbitrary dimensions. For example, a 2-simplex is a triangle and a 3-simplex is a tetrahedron. 2D triangular interpolations over the right triangles in the rectangular grids or over equilateral triangular grids will be studied first. The choice of triangles will be optimized basing on the minimization of the interpolation error. Then we will develop efficient triangular interpolation techniques to accelerate the MLFMA. The issue of non-uniform sampling on the unit sphere will be studied and solved using different transformations, or by developing more efficient quadrature rules for the sphere suitable for interpolation. For 3D simplex interpolations, we will develop a general approach to choose a right triangular pyramid to minimize the interpolation error and avoid the big regular tetrahedron in the middle of the interpolation cube used in the literature. .The proposed project will cut the interpolation time significantly and make the MLFMA faster and more powerful. The proposed research will provide viable, fast and efficient solutions for several key EM modeling issues in scattering and antenna radiations, in high-speed circuits such as complex sub-micron and nanoscale structures, FSS, metamaterials and metasurfaces, etc.
期刊论文列表
专著列表
科研奖励列表
会议论文列表
专利列表
Error Analysis of Higher Order Bivariate Lagrange and Triangular Interpolations in Electromagnetics
电磁学中高阶二元拉格朗日和三角插值的误差分析
DOI:10.1109/ojap.2020.3030091
发表时间:2020-10
期刊:IEEE Open Journal of Antennas and Propagation
影响因子:4
作者:Wen Luo;Jinbo Liu;Zengrui Li;Jiming Song
通讯作者:Jiming Song
DOI:10.1109/tap.2022.3209247
发表时间:2022-12
期刊:IEEE Transactions on Antennas and Propagation
影响因子:5.7
作者:Jinbo Liu;Xumeng Men;M. He;Zengrui Li;Jiming Song
通讯作者:Jinbo Liu;Xumeng Men;M. He;Zengrui Li;Jiming Song
DOI:10.1049/mia2.12051
发表时间:2021-02
期刊:IET Microwaves, Antennas & Propagation
影响因子:--
作者:Jinbo Liu;Jin Yuan;Zengrui Li;Jiming Song
通讯作者:Jinbo Liu;Jin Yuan;Zengrui Li;Jiming Song
DOI:10.1109/ojap.2023.3331217
发表时间:2023
期刊:IEEE Open Journal of Antennas and Propagation
影响因子:4
作者:Yuhua Niu;Jinbo Liu;Wen Luo;Zengrui Li;Jiming Song
通讯作者:Yuhua Niu;Jinbo Liu;Wen Luo;Zengrui Li;Jiming Song
DOI:10.1109/tap.2022.3225242
发表时间:2023-02
期刊:IEEE Transactions on Antennas and Propagation
影响因子:5.7
作者:Jinbo Liu;Wen Luo;Jiming Song;Zengrui Li
通讯作者:Jinbo Liu;Wen Luo;Jiming Song;Zengrui Li
国内基金
海外基金
