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作者： Dufva, Tommi Aalto University

学位级别：master

A variety of electromagnetic field problems can be most elegantly formulated by integral equations. A common way to search for a solution to such an integral equation is the method of moments (MoM) where the equation is discretised by expanding the unknown function in basis functions and forcing the error in the approximation to be orthogonal to test functions. Many times, the method can be enhanced by exploiting wave functions together with addition theorems for them. The thesis treats three electromagnetic field problems formulated by integral equations: one electrostatic, one magnetostatic and one time-harmonic. The geometry in the static problems consists of ring conductors, and the solution can be constructed by using sophisticated entire-domain basis functions and Galerkin''s method. The geometry in the time-harmonic problem is an extremely complex model of a pine tree, and therefore, the solution must be formed by using simple sub-domain basis functions and point matching. In each of the above solutions, wave functions together with addition theorems for them are exploited. In the static problems, the Green''s function is expanded in cylindrical wave functions, the MoM matrix terms are formulated partly in the spectral domain using addition theorems for the cylindrical wave functions, and certain integral results are derived from addition theorems for ultra-spherical wave functions. In the time-harmonic problem, the discretised problem is solved by using an iterative scheme and the calculation is accelerated by using the multilevel fast multipole algorithm (MLFMA) which is based on addition theorems for spherical wave functions. The thesis is based upon five publications. The first two publications present an efficient and accurate method for calculating the capacitances and inductances of ring conductors in a layered medium. The third publication gives a unified and transparent derivation of translational addition theorems for spherical wave functions. Th

关键词： Electrical engineering integral equations method of moments wave equation addition theorems multilevel fast multipole algorithm capacitance inductance scattering

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IMPLEMENTATION OF THE EQUIVALENCE PRINCIPLE algorithm FOR POTENTIAL INTEGRAL EQUATIONS

IMPLEMENTATION OF THE EQUIVALENCE PRINCIPLE ALGORITHM FOR PO...

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作者： ALI FARSHKARAN MIDDLE EAST TECHNICAL UNIVERSITY

学位级别：硕士

In this thesis, a domain decomposition method based on the Huygens' principle for integral equations is studied. Step-by-step development of equivalence principle al- gorithm (EPA) is described for solving arbitrary shaped perfect electric conductor (PEC) and penetrable objects. The main advantage of EPA is its efficiency thanks to the enhanced conditioning hence accelerated iterative solutions of the matrix equa- tions derived from discretizations. For further enhancing the efficiency, the multilevel fast multipole algorithm (MLFMA) is used to speed up the matrix-vector multiplica- tions (MVMs) in EPA. Following standard implementations, a novel implementation of EPA using potential integral equations (PIEs) is further presented. EPA is general- ized to be compatible with PIEs used to formulate inner problems inside equivalence surfaces. Based on the stability of PIEs at low frequencies, the resulting EPA-PIE im- plementation is suitable for low-frequency problems involving dense discretizations with respect to wavelength. Along with the formulation and demonstration of the EPA-PIE scheme, high accuracy and stability of the implementation are presented on canonical problems.

关键词： Surface Integral Equations Equivalence Principle algorithm multilevel fast multipole algorithm Potential Formulations

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Computing magnetic current on aperture surface of a target with cavities by EFIE and MLFMA

Computing magnetic current on aperture surface of a target w...

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Asia-Pacific Microwave Conference

作者： Meng Min Nie Zaiping Hu Jun Univ Elect Sci & Technol China Dept Microwave Engn Chengdu 610054 Peoples R China

ISBN: (纸本)078039433X

The solution of the electromagnetic scattering from target with electrically large aperture cavity is very important and challenging. The electric field integral equation(EFIE) with partial coupling principle presented in this paper to compute equivalent magnetic current on aperture surface is easy to understand and can expand the aperture electrical size greatly. Furthermore, a new usage of multilevel fast multipole algorithm(MLFMA) speeds up the computation.

关键词： electric field integral equation electrically large aperture multilevel fast multipole algorithm partial coupling principle

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fast solution of scattering from 3D coating object by MLFMA with diagonal element approximation method

Fast solution of scattering from 3D coating object by MLFMA ...

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IEEE Antennas-and-Propagation-Society International Symposium

作者： Hu, J Nie, ZP Lei, L Wang, J Zou, GX Univ Elect Sci & Technol China Coll Elect Engn Chengdu 610054 Peoples R China

ISBN: (纸本)0780383028

In this paper, multilevel fast multipole algorithm (MLFMA) combined with diagonal element approximation method is used to realize fast solution of scattering from 3D coating object. Impedance boundary condition (IBC) is used to approximate real boundary condition. MLFMA based on CG iteration is applied to expedite greatly the field computations from electric current sources and magnetic current sources. Diagonal element approximation (DEA) method is used to achieve efficient solution of sparse matrix equation. Numerical results show the present method is efficient for solution of scattering from 3D coating object with arbitrary shape.

关键词： electromagnetic scattering coating multilevel fast multipole algorithm impedance boundary condition sparse technique

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Computational design of nanoantennas with improved power enhancement capabilities via shape optimization

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OPTICAL ENGINEERING 2023年第1期62卷 015107-015107页

作者： Isiklar, Goktug Yazar, Sirin Ibili, Hande Onay, Gulten El Ahdab, Zeina Ergul, Ozgur Middle East Tech Univ Dept Elect & Elect Engn Ankara Turkiye Aselsan Res Ctr Ankara Turkiye

Computational design and analyses of nanoantennas obtained via surface shape optimization are presented. Starting with a kernel geometry, free deformations are applied on selected surfaces to reach optimal designs that can provide improved power enhancement capabilities at desired frequencies. An in-house implementation of genetic algorithms is efficiently combined with the multilevel fast multipole algorithm developed for accurate solutions of plasmonic problems to construct the effective optimization environment. The geometries obtained via optimization do not only represent optimal shapes within the allowed deformation limits but also reveal certain types of modifications on kernel geometries to improve their performances. (c) 2023 Society of Photo-Optical Instrumentation Engineers (SPIE)

关键词： nanoantennas optimization genetic algorithms multilevel fast multipole algorithm

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A Modified Hybrid Integral Equation to Electromagnetic Scattering from Composite PEC-Dielectric Objects Containing Closed-Open PEC Junctions

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APPLIED COMPUTATIONAL ELECTROMAGNETICS SOCIETY JOURNAL 2021年第6期36卷 642-649页

作者： Liu, Jinbo Chen, Hongyang Zhang, Hui Yuan, Jin Li, Zengrui Commun Univ China State Key Lab Media Convergence Beijing 100024 Peoples R China Commun Univ China Sch Informat & Commun Engn Beijing 100024 Peoples R China

To efficiently analyze the electromagnetic scattering from composite perfect electric conductor (PEC)-dielectric objects with coexisting closed-open PEC junctions, a modified hybrid integral equation (HIE) is established as the surface integral equation (SIE) part of the volume surface integral equation (VSIE), which employs the combined field integral equation (CFIE) and the electric field integral equation (EFIE) on the closed and open PEC surfaces, respectively. Different from the traditional HIE modeled for the objects whose closed and open PEC surfaces are strictly separate, the modified HIE can be applied to the objects containing closed-open junctions. A matrix equation is obtained by using the Galerkin's method of moments (MoM), which is augmented with the spherical harmonics expansion-based multilevel fast multipole algorithm (SE-MLFMA), improved by the mixed-potential representation and the triangle/tetrahedron-based grouping scheme. Because in the improved SE-MLFMA, the memory usage for storing the radiation patterns of basis functions is independent of the SIE type in the VSIE, it is highly appropriate for the fast solution of the VSIE that contains the HIE. Various numerical experiments demonstrate that during the calculation of composite objects containing closed-open PEC junctions, the application of the modified HIE in the VSIE can give reliable results with fast convergence speed.

关键词： fast solver integral equation method of moments multilevel fast multipole algorithm

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Convergence property of IDR variant methods in the integral equation analysis of electromagnetic scattering problems

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IEICE ELECTRONICS EXPRESS 2014年第9期11卷 20140198-20140198页

作者： Chiba, Hidetoshi Fukasawa, Toru Miyashita, Hiroaki Mitsubishi Electr Corp Informat Technol R&D Ctr Kamakura Kanagawa Japan

In this study, we investigate the performance of the variants of the induced dimension reduction (IDR) in large-scale electromagnetic scattering problems. We also focus on the tolerance to the so-call spurious convergence and convergence property of the IDR variant methods. Comparative numerical experiments, using IDR(s), Bi-IDR(s), and GIDR(s, L), reveal that GIDR(s, L) with L = 2 or 4 and an s value of around 15 shows the best performance with respect to the balance between the convergence property and the tolerance to the spurious convergence for problems with several levels of geometry complexity.

关键词： IDR variants method of moments multilevel fast multipole algorithm

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Computational study of scattering from healthy and diseased red blood cells

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JOURNAL OF BIOMEDICAL OPTICS 2010年第4期15卷 045004-045004页

作者： Ergul, Ozgur Arslan-Ergul, Ayca Gurel, Levent Univ Strathclyde Dept Math & Stat Glasgow G1 1XH Lanark Scotland Univ Strathclyde Strathclyde Inst Pharm & Biomed Sci Glasgow G4 0NR Lanark Scotland Bilkent Univ Dept Elect & Elect Engn TR-06800 Ankara Turkey Bilkent Univ Computat Electromagnet Res Ctr BiLCEM TR-06800 Ankara Turkey

We present a comparative study of scattering from healthy red blood cells (RBCs) and diseased RBCs with deformed shapes. Scattering problems involving three-dimensional RBCs are formulated accurately with the electric and magnetic current combined- field integral equation and solved efficiently by the multilevel fast multipole algorithm. We compare scattering cross section values obtained for different RBC shapes and different orientations. In this way, we determine strict guidelines to distinguish deformed RBCs from healthy RBCs and to diagnose various diseases using scattering cross section values. The results may be useful for designing new and improved flow cytometry procedures. (C) 2010 Society of Photo-Optical Instrumentation Engineers. [DOI: 10.1117/1.3467493]

关键词： red blood cell electromagnetic scattering surface formulations multilevel fast multipole algorithm

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Incomplete LU Factorization Preconditioner for the Efficient Solution of Improved Electric Field Integral Equations

Incomplete LU Factorization Preconditioner for the Efficient...

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2010 International Conference on Microwave and Millimeter Wave Technology(2010国际微波与毫米波技术会议 ICMMT2010)

作者： H. H. Zhang Z. H. Fan R. S. Chen Department of Communication Engineering Nanjing University of Science and Technology Nanjing 210094

ISBN: (纸本)9781424457052

This paper is a study on the numerical solution of linear systems arising from the discretization of the improved electric field integral equation (IEFIE) for electromagnetic scattering problems. Using incomplete LU factorization preconditioner, the IEFIE is solved by generalized minimal residual iterative method in the context of the multilevel fast multipole algorithm (MLFMA). Numerical results show that the efficiency and robustness of the solution can be significantly improved by contrast with the conventional EFIE formulation.

关键词： Improved electric field integral equation incomplete LU factorization preconditioner generalized minimal residual iterative method multilevel fast multipole algorithm

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fast Computation of Electromagnetic Scattering Based on Optimized Solution of Matrix Equations

Fast Computation of Electromagnetic Scattering Based on Opti...

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2009 9th International Conference on Electronic Measurement & Instruments（ICEMI’2009）

作者： Xiaofei Gu Jianshe Song Wenchang Sun Meng Yang (Xi’an Research Inst. of High-tech, Xi’an 710025, China)

In this paper, the characteristic basis function method (CBFM) is applied to instead of conventional MOM for MLFMA implementations. CBFM includes the mutual coupling effects among different subdomains directly by constructing the high level basis functions, Use of these basis functions leads to a significant reduction in the number of unknowns, and results in a substantial size reduction of the coupling matrix;This reduces matrix size improves the convergence properties. The MLFMA is introduced to speed up the matrix-vector multiplications. The advantages of applying the CBFM with MLFMA are illustrated with numerical simulation. The results demonstrate the efficiency and accuracy of the proposed method.

关键词： electromagnetic scattering matrix equations fast Computation method of moments characteristic basis function method multilevel fast multipole algorithm

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