Abdel M. A. Alsnayyan;Leo Kempel;Shanker Balasubramaniam
{"title":"Manifold Harmonics and Their Application to Computational Electromagnetics","authors":"Abdel M. A. Alsnayyan;Leo Kempel;Shanker Balasubramaniam","doi":"10.1109/JMMCT.2022.3199612","DOIUrl":"https://doi.org/10.1109/JMMCT.2022.3199612","url":null,"abstract":"The eigenfunctions of the Laplace-Beltrami operator (LBO), or manifold harmonic basis (MHB), have many applications in mathematical physics, differential geometry, machine learning, and topological data analysis. MHB allows us to associate a frequency spectrum to a function on a manifold, analogous to the Fourier decomposition. This insight can be used to build a framework for analysis. The purpose of this paper is to review and illustrate such possibilities for computational electromagnetics as well as chart a potential path forward. To this end, we introduce three features of MHB: (a) enrichment for analysis of multiply connected domains, (b) local enrichment (L-MHB) and (c) hierarchical MHB (H-MHB) for reuse of data from coarser to fine geometry discretizations. Several results highlighting the efficacy of these methods are presented.","PeriodicalId":52176,"journal":{"name":"IEEE Journal on Multiscale and Multiphysics Computational Techniques","volume":null,"pages":null},"PeriodicalIF":2.3,"publicationDate":"2022-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49950113","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A Hybrid EM/QM Framework Based on the ADHIE-FDTD Method for the Modeling of Nanowires","authors":"Pieter Decleer;Dries Vande Ginste","doi":"10.1109/JMMCT.2022.3198750","DOIUrl":"https://doi.org/10.1109/JMMCT.2022.3198750","url":null,"abstract":"A new modeling formalism to compute the time-dependent behavior of combined electromagnetic (EM) and quantum mechanical (QM) systems is proposed. The method is geared towards highly multiscale geometries, which is vital for the future design of nanoelectronic devices. The advocated multiphysics modeling formalism leverages the alternating-direction hybrid implicit-explicit (ADHIE) finite-difference time-domain (FDTD) method for the EM fields and is combined with a novel ADHIE method for the EM potentials. Additionally, we tackle the QM problem using a new split real and imaginary part formulation that includes higher-order spatial differences and arbitrary time-dependent EM potentials. The validity of the proposed formalism is theoretically discussed by deriving its stability condition and calculating the numerical dispersion relation. Furthermore, the applicability of our modeling approach is proven through several numerical experiments, including a single-particle Maxwell-Schrödinger (MS) system as well as a many-particle Maxwell-Kohn-Sham (MKS) system within the time-dependent density-functional theory (TDDFT) framework. These experiments confirm that the novel ADHIE method drastically decreases the computation time while retaining the accuracy, leading to efficient and accurate simulations of light-matter interactions in multiscale nanoelectronic devices.","PeriodicalId":52176,"journal":{"name":"IEEE Journal on Multiscale and Multiphysics Computational Techniques","volume":null,"pages":null},"PeriodicalIF":2.3,"publicationDate":"2022-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49950265","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Space-Mapping Based Automatic Design of SIW-Based Directional Coupler With Arbitrary Power Ratio","authors":"Tianrui Qiao;Jun Zhang;Qingsha S. Cheng","doi":"10.1109/JMMCT.2022.3194934","DOIUrl":"https://doi.org/10.1109/JMMCT.2022.3194934","url":null,"abstract":"In this paper, an automatic design method allowing efficient design of substrate integrated waveguide (SIW) directional coupler with any given power ratio between 3 dB and 20 dB has been proposed. Due to excessive electromagnetic (EM) simulation time of SIW structure, the space mapping technique is exploited to accelerate the design process. An EM-simulation based dielectric rectangular waveguide (RWG) model acts as the surrogate to reduce the simulation time. A two-stage optimization scheme including a differential evolution (DE) algorithm and a Nelder-Mead (NM) simplex algorithm is used to obtain initial surrogate design. Suitable objective functions are proposed for surrogate optimization and for parameter extraction procedure of space mapping technique. Our proposed method is verified with an X band SIW directional coupler with four different power ratio designs, which are 3 dB, 10 dB, 15 dB and 20 dB. The experimental results confirm the effectiveness and efficiency of the method.","PeriodicalId":52176,"journal":{"name":"IEEE Journal on Multiscale and Multiphysics Computational Techniques","volume":null,"pages":null},"PeriodicalIF":2.3,"publicationDate":"2022-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49950342","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"FDTD Method With Explicit Non-Iterative and Second Order Treatment for Kerr Nonlinearities","authors":"Jinjie Liu;Jason Cornelius;Moysey Brio","doi":"10.1109/JMMCT.2022.3193051","DOIUrl":"https://doi.org/10.1109/JMMCT.2022.3193051","url":null,"abstract":"The finite-difference time-domain (FDTD) method is a very popular numerical method used to solve Maxwell's equations in various types of materials, including those with nonlinear properties. When solving the nonlinear constitutive equation that models Kerr media, Newton's iterative method is accurate but computationally expensive, while the conventional explicit non-iterative method is less expensive but not very accurate. In this work, we propose a new explicit non-iterative algorithm to solve the Kerr nonlinear constitutive equation that achieves a quadratic convergence rate. This method attains a similar accuracy to Newton's method but does with a significant reduction in computational cost. To demonstrate the accuracy and efficiency of our method, we provide several numerical examples, including the simulations of four-wave mixing and soliton propagation in one and two dimensions.","PeriodicalId":52176,"journal":{"name":"IEEE Journal on Multiscale and Multiphysics Computational Techniques","volume":null,"pages":null},"PeriodicalIF":2.3,"publicationDate":"2022-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49950341","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Fahimeh Sepehripour;Martijn C. van Beurden;Bastiaan P. de Hon
{"title":"Direct Computation of the PEC Body of Revolution Modal Green Function for the Electric Field Integral Equation","authors":"Fahimeh Sepehripour;Martijn C. van Beurden;Bastiaan P. de Hon","doi":"10.1109/JMMCT.2022.3190789","DOIUrl":"https://doi.org/10.1109/JMMCT.2022.3190789","url":null,"abstract":"We propose a five-term recurrence relation for the direct computation of the modal Green function (MGF) arising in the electric field integral equations (EFIE), when solving the scattering of PEC bodies of revolution. It is shown that, by considering it as an infinite penta-diagonal matrix, the proposed five-term recurrence relation can be solved in a stable manner in \u0000<inline-formula><tex-math>$O(M)$</tex-math></inline-formula>\u0000 steps for \u0000<inline-formula><tex-math>$M$</tex-math></inline-formula>\u0000 modes with high and controllable accuracy. By evaluating the performance of the proposed five-term recurrence relation for several scatterers of different geometries, we show that the proposed approach enables an accurate computation with a simple algorithm.","PeriodicalId":52176,"journal":{"name":"IEEE Journal on Multiscale and Multiphysics Computational Techniques","volume":null,"pages":null},"PeriodicalIF":2.3,"publicationDate":"2022-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49950340","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"An Effective Global Approach for Assessment of Decoupling Capacitors on Mixed Planar and Transmission Line PDNs","authors":"Ihsan Erdin;Ramachandra Achar","doi":"10.1109/JMMCT.2022.3189229","DOIUrl":"https://doi.org/10.1109/JMMCT.2022.3189229","url":null,"abstract":"A global analysis technique is proposed to calculate the effectiveness of decoupling capacitors on practical power delivery networks (PDN). The proposed method is based on separation of a PDN into its power transmission lines (PTL) and non-PTL sections. The PTL section consists of circuit components with the highest impact on the impedance of the specified power pin, including the pin itself, the nearest capacitor and segments of PTL on both sides of the capacitor. The rest of the PDN makes up the non-PTL section which could be composed of planar shapes, PTLs or a mixture of both. The non-PTL section is characterized as a distributed circuit, preferably using an electromagnetic (EM) simulator. The effectiveness of the capacitor is measured by the self-impedance of the pin which depends on the distance between them. The pin impedance is cast in a transcendental equation in the PTL section including the impedance of the non-PTL section. The optimal placement of the capacitor is calculated using an iterative approach. With the proposed method, the use of an EM simulation at each step of the iteration is eliminated, significantly speeding up the computation process. The proposed method is validated on real-life design cases.","PeriodicalId":52176,"journal":{"name":"IEEE Journal on Multiscale and Multiphysics Computational Techniques","volume":null,"pages":null},"PeriodicalIF":2.3,"publicationDate":"2022-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49950339","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Shakirudeen O. Lasisi;Trevor M. Benson;Mark T. Greenaway;Gabriele Gradoni;Kristof Cools
{"title":"Modeling of Resonant Tunneling Diode Oscillators Based on the Time-Domain Boundary Element Method","authors":"Shakirudeen O. Lasisi;Trevor M. Benson;Mark T. Greenaway;Gabriele Gradoni;Kristof Cools","doi":"10.1109/JMMCT.2022.3187022","DOIUrl":"https://doi.org/10.1109/JMMCT.2022.3187022","url":null,"abstract":"We demonstrate how the coupling of a full-wave time-domain boundary element method (BEM) solver with a circuit solver can be used to model 1) the generation of high frequency oscillations in resonant tunneling diode (RTD) oscillators, and 2) the mutual coupling and synchronization of non-identical RTDs with significant differences in frequencies to achieve coherent power combination. Numerical simulations show a combined output power of up to 3.7 times a single oscillator in synchronized devices. The non-differential conductance of the RTD is modeled as a lumped component with a non-linear current-voltage relationship. The lumped element is coupled to the radiating structure using a finite-gap model in a consistent and discretisation independent manner. The resulting circuit equations are solved simultaneously and consistently with time-domain electric field integral equations that model the transient scattering of electromagnetic (EM) fields from conducting surfaces that make up the device. This paper introduces three novel elements: (i) the application of a mesh independent feed line to the modelling of feed lines of RTD devices, (ii) the coupling of the radiating system to a strongly non-linear component with negative differential resistance, and (iii) the verification of this model with circuit models where applicable and against the experimental observation of synchronisation when two RTDs are placed in close proximity. These three elements provide a methodology that create the capacity to model RTD sources and related technology.","PeriodicalId":52176,"journal":{"name":"IEEE Journal on Multiscale and Multiphysics Computational Techniques","volume":null,"pages":null},"PeriodicalIF":2.3,"publicationDate":"2022-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49950337","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Efficient Numerical Evaluation of Singular Integrals in Volume Integral Equations","authors":"Cedric Münger;Kristof Cools","doi":"10.1109/JMMCT.2022.3185531","DOIUrl":"https://doi.org/10.1109/JMMCT.2022.3185531","url":null,"abstract":"We present a method for the numerical evaluation of 6D and 5D singular integrals appearing in Volume Integral Equations. It is an extension of the Sauter-Schwab/Taylor-Duffy strategy for singular triangle-triangle interaction integrals to singular tetrahedron-tetrahedron and triangle-tetrahedron interaction integrals. The general advantages of these kind of quadrature strategy is that they allow the use of different kinds of kernel and basis functions. They also work on curvilinear domains. They are all based on relative coordinates tranformation and splitting the integration domain into subdomains for which quadrature rules can be constructed. We show how to build these tensor-product quadrature rules in 6D and 5D and further show how to improve their efficiency by using quadrature rules defined over 2D, 3D and 4D simplices. Compared to the existing approach, which computes the integral over the subdomains as a sequence of 1D integrations, significant speedup can be achieved. The accuracy and convergence properties of the method are demonstrated by numerical experiments for 5D and 6D singular integrals. Additionally, we applied the new quadrature approach to the triangle-triangle interaction integrals appearing in Surface Integral Equations.","PeriodicalId":52176,"journal":{"name":"IEEE Journal on Multiscale and Multiphysics Computational Techniques","volume":null,"pages":null},"PeriodicalIF":2.3,"publicationDate":"2022-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49950338","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Error-Controllable Scheme for the LOD-FDTD Method","authors":"Tasuku Nakazawa;Di Wu;Seiya Kishimoto;Jun Shibayama;Junji Yamauchi;Shinichiro Ohnuki","doi":"10.1109/JMMCT.2022.3181568","DOIUrl":"https://doi.org/10.1109/JMMCT.2022.3181568","url":null,"abstract":"The implicit locally one-dimensional finite-difference time-domain (LOD-FDTD) method is useful for designing plasmonic devices and waveguide structures. By using a large timestep size, the implicit LOD-FDTD method can reduce the computational time; however, this involves a trade-off with accuracy. To overcome this trade-off, we propose an error-controllable scheme for the LOD-FDTD method, wherein the fast inverse Laplace transform is employed to generate the electromagnetic field in arbitrary time domain from that in complex frequency domain. Compared to the conventional LOD-FDTD method, our scheme provides higher accuracy with more efficient calculations.","PeriodicalId":52176,"journal":{"name":"IEEE Journal on Multiscale and Multiphysics Computational Techniques","volume":null,"pages":null},"PeriodicalIF":2.3,"publicationDate":"2022-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/iel7/7274859/9715154/09793664.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49950349","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"RCS Optimization of Surface Geometry With Physics Inspired Neural Networks","authors":"Xu Zhang;Jiaxin Wan;Zhuoyang Liu;Feng Xu","doi":"10.1109/JMMCT.2022.3181606","DOIUrl":"https://doi.org/10.1109/JMMCT.2022.3181606","url":null,"abstract":"Radar cross section (RCS) optimization is important to object geometry design, for example seeking a low-scattering structure. However, it is difficult to obtain a geometry with particular RCS quickly due to the complex geometry, low-efficient RCS calculation, or lack of effective automatic optimization methods. In this paper, a RCS optimization method is proposed based on physics inspired neural network named electromagnetic fully connected neural network (EM-FCNN). It employs the principles of MoM to transform the slow numerical calculation method into the fast neural network calculation. To reduce the complexity of surface geometry characterization, a low-dimensional surface hyperparametric modulation method (SHMM) is formulated to characterize object surfaces by introducing a modulation factor into rough surfaces. In this regard, the ultra-high-dimensional target surfaces can be characterized by only a few hyperparameters. To accelerate the optimization process, a dimensional reduction optimization algorithm (DROA) is further designed to simplify the multi-dimensional hyperparameters optimization problem to a series of one-dimensional optimization problems. The efficacy of the proposed method is validated with a RCS reduction task of a simplified aircraft model. This is generalized to solve the RCS optimization and it can be used to handle object geometry design for other application areas.","PeriodicalId":52176,"journal":{"name":"IEEE Journal on Multiscale and Multiphysics Computational Techniques","volume":null,"pages":null},"PeriodicalIF":2.3,"publicationDate":"2022-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49950262","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}