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An Iterative Random Sampling Algorithm for Rapid and Scalable Estimation of Matrix Spectra 矩阵谱快速可扩展估计的迭代随机抽样算法
IF 2.3 Q1 Mathematics Pub Date : 2023-03-30 DOI: 10.1109/JMMCT.2023.3263152
Jon T. Kelley;Ali E. Yılmaz;Yaniv Brick
An easy-to-implement iterative algorithm that enables efficient and scalable spectral analysis of dense matrices is presented. The algorithm relies on the approximation of a matrix's singular values by those of a series of smaller matrices formed from uniform random sampling of its rows and columns. It is shown that, for sufficiently incoherent and rank-deficient matrices, the singular values [are expected to] decay at the same rate as those of matrices formed via this sampling scheme, which permits such matrices’ ranks to be accurately estimated from the smaller matrices’ spectra. Moreover, for such a matrix of size $m times n$, it is shown that the dominant singular values are [expected to be] $sqrt {mn} /k$ times those of a $k times k$ matrix formed by randomly sampling $k$ of its rows and columns. Starting from a small initial guess $k = {k}_0$, the algorithm repeatedly doubles $k$ until two convergence criteria are met; the criteria to ensure that $k$ is sufficiently large to estimate the singular values, to the desired accuracy, are presented. The algorithm's properties are analyzed theoretically and its efficacy is studied numerically for small to very-large matrices that result from discretization of integral-equation operators, with various physical kernels common in electromagnetics and acoustics, as well as for artificial matrices of various incoherence and rank-deficiency properties.
提出了一种易于实现的迭代算法,可以实现密集矩阵的高效和可扩展的谱分析。该算法依赖于矩阵奇异值的近似,该近似是由矩阵的行和列的均匀随机抽样形成的一系列较小矩阵的奇异值。结果表明,对于充分不相干和秩不足的矩阵,奇异值[预计]以与通过该采样方案形成的矩阵相同的速率衰减,这允许从较小矩阵的谱中准确估计此类矩阵的秩。此外,对于这样一个大小为$m * n$的矩阵,我们证明了主导奇异值[期望]为$sqrt {mn} /k$乘以由随机抽取$k$的行和列组成的$k * k$矩阵的奇异值。从一个小的初始猜测$k = {k}_0$开始,算法反复加倍$k$,直到满足两个收敛准则;给出了确保$k$足够大以估计奇异值并达到所需精度的准则。对该算法的性能进行了理论分析,并对具有电磁学和声学中常见的各种物理核的积分方程算子离散化产生的小到超大矩阵,以及具有各种非相干性和秩亏性的人工矩阵的有效性进行了数值研究。
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引用次数: 3
Accurate Prediction of Electric Fields of Nanoparticles With Deep Learning Methods 利用深度学习方法精确预测纳米粒子电场
IF 2.3 Q1 Mathematics Pub Date : 2023-03-23 DOI: 10.1109/JMMCT.2023.3260900
Mengmeng Li;Zixuan Ma
Three different deep learning models were designed in this paper, to predict the electric fields of single nanoparticles, dimers, and nanoparticle arrays. For single nanoparticles, the prediction error was 4.4%. For dimers with strong couplings, a sample self-normalization method was proposed, and the error was reduced by an order of magnitude compared with traditional methods. For nanoparticle arrays, the error was reduced from 28.8% to 5.6% compared with previous work. Numerical tests proved the validity of the proposed deep learning models, which have potential applications in the design of nanostructures.
本文设计了三种不同的深度学习模型,用于预测单纳米粒子、二聚体和纳米粒子阵列的电场。对于单个纳米颗粒,预测误差为4.4%。对于强耦合二聚体,提出了一种样本自归一化方法,与传统方法相比,误差减小了一个数量级。对于纳米粒子阵列,误差从28.8%降低到5.6%。数值实验证明了所提出的深度学习模型的有效性,在纳米结构设计中具有潜在的应用前景。
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引用次数: 0
Numerical and Experimental Investigations of Flaws Detection in Multilayer HTS Tapes by Magnetothermal Technique 磁热技术在多层高温超导带缺陷检测中的数值与实验研究
IF 2.3 Q1 Mathematics Pub Date : 2023-03-11 DOI: 10.1109/JMMCT.2023.3275321
Walid Dirahoui;Hocine Menana
This article presents a numerical and experimental studies on the non-destructive testing of high temperature superconducting (HTS) multilayer tapes at room temperature, by eddy current thermography (ECT). An experimental setup is developed in which a rotating magnet wheel inductor is used instead of electromagnetic inductors to avoid the inherent thermal disturbance. A 3-D magnetothermal modelling approach is developed for the verification of the experimental results and the simulation of situations that cannot be reproduced experimentally, in particular the verification of the detection limits as a function of the shape and location of the defects. Simulation and experimental results are in good agreement.
本文对高温超导多层带在室温下的涡流热像仪无损检测进行了数值和实验研究。建立了一种用旋转磁轮电感代替电磁电感的实验装置,以避免固有的热干扰。开发了一种三维磁热建模方法,用于验证实验结果和模拟实验无法再现的情况,特别是验证检测极限作为缺陷形状和位置的函数。仿真结果与实验结果吻合较好。
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引用次数: 0
Performance of Inexpensive Local Error Estimation Techniques for Integral Equation Numerical Solutions 积分方程数值解的廉价局部误差估计技术的性能
IF 2.3 Q1 Mathematics Pub Date : 2023-03-10 DOI: 10.1109/JMMCT.2023.3255010
Sheldon R. Steines;Brett L. Baxley;Andrew F. Peterson
The performance of several inexpensive local error estimation techniques is evaluated in connection with the Rao-Wilton-Glisson method of moments numerical solutions of the electric field integral equation. Results for 18 perfectly conducting test targets are used to evaluate the performance of the estimators. Two of the estimators produce error maps that consistently exhibit high correlations with reference solutions. These estimators are also suitable for “goal-oriented” estimation of secondary quantities, such as identifying cells that contribute the most error to the radar cross section of the target.
结合电场积分方程的Rao-Wilton-Glisson矩量法,评价了几种廉价的局部误差估计技术的性能。对18个完全传导的测试目标的结果用于评估估计器的性能。其中两个估计器产生的误差图始终显示出与参考解的高度相关性。这些估计器也适用于二次量的“目标导向”估计,例如识别对目标雷达横截面误差最大的单元。
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引用次数: 0
Multiphysics Computing of Challenging Antenna Arrays Under a Supercomputer Framework 在超级计算机框架下挑战性天线阵列的多物理场计算
IF 2.3 Q1 Mathematics Pub Date : 2023-03-10 DOI: 10.1109/JMMCT.2023.3254661
Hao-Xuan Zhang;Qiwei Zhan;Li Huang;Da-Wei Wang;Yin-Da Wang;Wei-Jie Wang;Zhen-Guo Zhao;Hai-Jing Zhou;Kai Kang;Liang Zhou;Wen-Yan Yin
A parallel multiphysics simulation solver is developed to solve electromagnetic-thermal-mechanical coupling for some challenging large-scale antenna arrays. To achieve high scalability of supercomputer architectures, we reconstruct the preconditioned BiCGSTAB method and the non-overlapping domain decomposition method, so that the most resource-intensive matrix factorization steps can be performed in parallel independently within subdomains. The electromagnetic and thermal fields are solved separately, while coupled through the dissipated power and the temperature-dependent material parameters; after thermal steady state is reached, the mechanical simulation is stimulated subject to the temperature rise. The accuracy of electromagnetic-thermal coupling and thermal stress solution are first validated, and then the strong/weak parallel scalability experiments of the developed multiphysics solver are performed on supercomputer. Finally, an extremely challenging antenna array is simulated using the proposed solver, where to our best knowledge we bring the scale of multiphysics simulations excited by frequency-domain electromagnetic fields to the order of billion unknowns for the first time.
为解决大型天线阵的电磁-热-机械耦合问题,开发了一种并行多物理场仿真求解器。为了实现超级计算机体系结构的高可扩展性,我们重构了预置的BiCGSTAB方法和不重叠的域分解方法,使资源最密集的矩阵分解步骤能够在子域内并行独立地执行。电磁场和热场分别求解,并通过耗散功率和温度相关的材料参数进行耦合;在达到热稳态后,受温度升高的影响进行力学模拟。首先验证了电磁-热耦合和热应力求解的准确性,然后在超级计算机上对所开发的多物理场求解器进行了强/弱并行可扩展性实验。最后,使用所提出的求解器模拟了一个极具挑战性的天线阵列,据我们所知,我们首次将频域电磁场激发的多物理场模拟的规模提高到数十亿个未知数。
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引用次数: 1
Investigating the Scattering Characteristics of Artificial Field-Aligned Irregularities Based on T-Matrix Algorithm 基于t矩阵算法的人工场对准不规则体散射特性研究
IF 2.3 Q1 Mathematics Pub Date : 2023-03-03 DOI: 10.1109/JMMCT.2023.3252053
Shuai S. A. Yuan;Zhu Hong Lin;Li-Bin Lv;Shu-Ji Hao;Wei E. I. Sha
The artificial field-aligned irregularity (AFAI) in ionosphere can be generated by heating the ionosphere with high-power high-frequency radio waves, and the physical structures of AFAIs are modeled as elongated multiple multilayer plasma cylinders. At relatively low frequencies, AFAIs could work as natural reflectors for long-distance communications. In order to evaluate the performance of AFAI-based communications, it is crucial to obtain the objective radar cross section (RCS) of AFAIs quickly and accurately. On account of the large electrical size of AFAIs, it would be time-consuming to calculate the objective RCS by full-wave simulations, meanwhile, the accuracies of the existing approximated methods are limited in many scenarios. In this paper, the T-matrix algorithm is used for analytically calculating the objective RCS of AFAIs after making reasonable approximations. Compared to the results obtained from full-wave simulations, the errors of objective RCS are within an acceptable range while the computation time is largely reduced. Furthermore, the scattering characteristics of AFAIs at different frequencies are investigated. The proposed method could be readily implemented for investigating and predicting the performance of AFAI-based long-wave communications.
利用高功率高频无线电波加热电离层,可产生电离层人工场向不规则(AFAI),并将其物理结构建模为细长的多层等离子体柱。在相对较低的频率下,afai可以作为长距离通信的天然反射器。为了评估基于afai的通信性能,快速准确地获得afai的目标雷达截面(RCS)是至关重要的。由于afai的电尺寸较大,采用全波模拟方法计算目标RCS耗时长,同时现有的近似方法在很多情况下精度有限。本文采用t矩阵算法,对afai进行合理近似后,解析计算目标RCS。与全波模拟结果相比,目标RCS的误差在可接受范围内,计算时间大大缩短。此外,还研究了AFAIs在不同频率下的散射特性。该方法可以很容易地用于研究和预测基于afai的长波通信的性能。
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引用次数: 1
Method of Characteristic Modes Analysis and Manipulation for Antenna Design by Using Generalized Partial Element Equivalent Circuit 基于广义部分单元等效电路的天线设计特征模态分析与处理方法
IF 2.3 Q1 Mathematics Pub Date : 2023-02-06 DOI: 10.1109/JMMCT.2023.3242714
Yuhang Dou;Hao Chen
A method of analyzing characteristic modes (CMs) of antennas with multiple lumped LC loads is proposed based on the full-wave generalized partial element equivalent circuit (GPEEC) model. Different with traditional CMs analysis methods, this method can be integrated into an optimization algorithm. With this powerful engine, we can develop a systematic method to manipulate radiation CMs of a mobile terminal while preserving its aesthetic structure features of the industrial design. This method can reveal all possible radiation structure performances as traditional methods and even create new possible radiation modes to improve antenna performance. With the GPEEC model, a comprehensive analysis of antennas can be achieved simultaneously, including but not limited to simulating time-/frequency-domain responses, evaluating radiation efficiency contributed by the self- and mutual radiated power separately, and plotting current and field distribution. Three design examples are demonstrated, including analyzing the working mechanism of the self-curing decoupling technique for mobile terminals from the view of CMs, extending the bandwidth of an antenna in LTE-A low-frequency bands, and creating a pair of MIMO antennas in the low LTE-A bands. These examples are verified theoretically and experimentally, showing the high potential of this method in analyzing and designing antennas for mobile terminals.
提出了一种基于全波广义部分单元等效电路(GPEEC)模型的多集总LC负载天线特征模态分析方法。与传统的CMs分析方法不同,该方法可集成为优化算法。通过这个强大的引擎,我们可以开发出一种系统的方法来操纵移动终端的辐射cm,同时保持其工业设计的美学结构特征。该方法可以像传统方法一样揭示所有可能的辐射结构性能,甚至可以创造新的可能的辐射模式,从而提高天线的性能。利用GPEEC模型,可以同时对天线进行综合分析,包括但不限于模拟时频域响应,分别评估自辐射功率和互辐射功率贡献的辐射效率,绘制电流和场分布。给出了三个设计实例,包括从CMs的角度分析移动终端自固化解耦技术的工作机理,扩展LTE-A低频段天线的带宽,以及在LTE-A低频段创建一对MIMO天线。通过理论和实验验证了该方法在移动终端天线分析和设计方面的巨大潜力。
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引用次数: 2
Predicting Output Responses of Nonlinear Dynamical Systems With Parametrized Inputs Using LSTM 基于LSTM的参数化非线性动力系统输出响应预测
IF 2.3 Q1 Mathematics Pub Date : 2023-02-03 DOI: 10.1109/JMMCT.2023.3242044
Lihong Feng
Long Short-Term Memory (LSTM) has been more and more used to predict time evolution of dynamics for many problems, especially the fluid dynamics. Usually, it is applied to the latent space after dimension reduction of the full dynamical system by proper orthogonal decomposition (POD), autoencoder (AE) or convolutional autoencoder (CAE). In this work, we propose to directly apply LSTM to the data of the output without dimension reduction for output response prediction. The dimension of the output is usually small, and no dimension reduction is necessary, thus no accuracy loss is caused by dimension reduction. Based on the standard LSTM structure, we propose an LSTM network with modified activation functions which is shown to be much more robust for predicting periodic waveforms. We are especially interested in showing the efficiency of LSTM for predicting the output responses corresponding to time-vary input signals, which is rarely considered in the literature. However, such systems are of great interests in electrical engineering, mechanical engineering, and control engineering, etc. Numerical results for models from circuit simulation, neuron science and a electrochemical reaction have shown the efficiency of LSTM in predicting the dynamics of output responses.
长短期记忆(LSTM)越来越多地用于预测动力学的时间演化,特别是流体动力学。通常采用正交分解(POD)、自编码器(AE)或卷积自编码器(CAE)对全动力系统降维后的潜在空间进行处理。在这项工作中,我们提出直接将LSTM应用于输出数据,而不进行降维,用于输出响应预测。输出的尺寸通常较小,不需要降维,因此不会因降维而造成精度损失。在标准LSTM结构的基础上,我们提出了一种带有修正激活函数的LSTM网络,该网络对周期波形的预测具有更强的鲁棒性。我们特别感兴趣的是展示LSTM预测时变输入信号对应的输出响应的效率,这在文献中很少考虑。然而,这类系统在电气工程、机械工程和控制工程等领域有着广泛的应用。电路仿真、神经元科学和电化学反应模型的数值结果表明,LSTM在预测输出响应的动态方面是有效的。
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引用次数: 1
Simulation of Thin-Film Cells With a Multiscale Quantum-Mechanical/Electromagnetic Method 薄膜电池的多尺度量子力学/电磁法模拟
IF 2.3 Q1 Mathematics Pub Date : 2023-02-02 DOI: 10.1109/JMMCT.2023.3241633
Lei Zhang;Hui Zeng;Zhenhong Fan;Da-Zhi Ding
This article studies the surface plasmon-enhanced effect of metal nanoparticles (NPs) in thin-film cells by using a semi-classical multiscale quantum-mechanical/electromagnetic (QM/EM) method. The QM/EM method establishes a relationship between classical electromagnetic environment and full quantum-mechanical photovoltaics with quantized vector magnetic potential on the boundary. In our theoretical framework, the EM region is solved by Maxwell equation with method of moments (MoM), and the QM region is solved by density-functional tight-binding (DFTB) theory with the nonequilibrium Green's function. The proposed method has predicted that metal NPs could generate surface plasmon enhancement and substantially improve the photovoltaic performance of thin-film cells. By comparison, we investigated the influences of different NP materials, distributions and drop-casting ratios on the current-voltage characteristics. The simulated results provide a comprehensive understanding of photoelectric interaction, which can be utilized to improve the power conversion efficiency (PCE) of thin-film cells by fast optimization design.
本文采用半经典多尺度量子力学/电磁(QM/EM)方法研究了金属纳米颗粒在薄膜电池中的表面等离子体增强效应。QM/EM方法建立了经典电磁环境与边界上量子化矢量磁势的全量子力学光伏之间的关系。在我们的理论框架中,EM区域用矩量法求解麦克斯韦方程(MoM), QM区域用非平衡格林函数求解密度泛函紧结合(DFTB)理论。该方法预测了金属NPs可以产生表面等离子体增强,并大大提高薄膜电池的光伏性能。通过比较,我们研究了不同NP材料、分布和浇铸比对电流-电压特性的影响。仿真结果提供了对光电相互作用的全面理解,可用于通过快速优化设计来提高薄膜电池的功率转换效率。
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引用次数: 0
A TF/SF Plane Wave Source Condition for the Constraint-Preserving FVTD Method 保约束FVTD方法的TF/SF平面波源条件
IF 2.3 Q1 Mathematics Pub Date : 2023-01-31 DOI: 10.1109/JMMCT.2023.3241190
Kaiser Niknam;Jamesina J. Simpson
A low-leakage total-field/scattered-field plane wave source condition capable of propagating at any incident angle is developed for a newly-developed DGTD-based FVTD method. This constraint-preserving FVTD method provides solutions up to any order of accuracy, preserves the divergence constraints imposed by Gauss’ laws, and may be easily adapted to non-conformal and unstructured meshes. In order to implement the proposed plane wave source condition, several of the steps within the updating loop of the FVTD model, including the Riemann solvers and update equations, must be adapted to ensure the field variables always remain consistent (are consistently designated as either total or scattered fields). The proposed total-field/scattered-field technique is shown to provide numerical leakage errors at the level of machine precision (−300 dB) for second-, third-, and fourth-order constraint-preserving FVTD schemes.
针对新开发的基于dgtd的FVTD方法,提出了一种能够在任意入射角下传播的低泄漏全场/散射场平面波源条件。这种保持约束的FVTD方法提供了任何精度的解,保留了高斯定律施加的散度约束,并且可以很容易地适应非保形和非结构化网格。为了实现所提出的平面波源条件,必须调整FVTD模型更新循环中的几个步骤,包括黎曼解算器和更新方程,以确保场变量始终保持一致(一致地指定为总场或分散场)。所提出的全场/散射场技术为二阶、三阶和四阶保持约束的FVTD方案提供了机器精度水平的数值泄漏误差(−300 dB)。
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引用次数: 0
期刊
IEEE Journal on Multiscale and Multiphysics Computational Techniques
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