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Mapped vector basis functions for electromagnetic integral equations

The method-of-moments solution of the electric field and magnetic field integral equations (EFIE and MFIE) is extended to conducting objects modeled with curved cells. These techniques are important for electromagnetic scattering, antenna, radar signature, and wireless communication applications. Ve...

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Bibliographic Details
Main Author: Peterson, Andrew F., 1960-
Format: Electronic
Language:English
Published: San Rafael, Calif. (1537 Fourth Street, San Rafael, CA 94901 USA) : Morgan & Claypool Publishers, c2005.
Edition:1st ed.
Series:Synthesis lectures on computational electromagnetics (Online), #1.
Subjects:
Boundary element methods.
Electromagnetism > Mathematical models.
Integral equations > Numerical solutions.
Moments method (Statistics)
Online Access:Abstract with links to full text
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020 # # |a 1598290126 (electronic bk.) 
020 # # |a 9781598290127 (electronic bk.) 
024 7 # |a 10.2200/S00008ED1V01Y200508CEM001  |2 doi 
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082 0 4 |a 537/.01/515  |2 21 
100 1 # |a Peterson, Andrew F.,  |d 1960- 
245 1 0 |a Mapped vector basis functions for electromagnetic integral equations  |c Andrew F. Peterson.  |h [electronic resource] / 
250 # # |a 1st ed. 
260 # # |a San Rafael, Calif. (1537 Fourth Street, San Rafael, CA 94901 USA) :  |b Morgan & Claypool Publishers,  |c c2005. 
300 # # |a 1 electronic text (viii, 115 p. : ill.) :  |b digital file. 
490 1 # |a Synthesis lectures on computational electromagnetics,  |v [#1]  |x 1932-1716 ; 
500 # # |a Part of: Synthesis digital library of engineering and computer science. 
500 # # |a Title from PDF t.p. (viewed Oct. 19, 2008). 
500 # # |a Series from website. 
504 # # |a Includes bibliographical references. 
505 0 # |a 1. Introduction -- 1.1. Integral equations -- 1.2. The method of moments -- 2. The surface model -- 2.1. Differential geometry -- 2.2. Mapping from square cells using Lagrangian interpolation polynomials -- 2.3. A specific example : quadratic polynomials mapped from a square reference cell -- 2.4. Mapping from triangular cells via interpolation polynomials -- 2.5. Example : quadratic polynomials mapped from a triangular reference cell -- 2.6. Constraints on node distribution -- 2.7. Hermitian mapping from square cells -- 2.8. Connectivity -- 3. Divergence-conforming basis functions -- 3.1. Characteristics of vector fields and vector basis functions -- 3.2. What does divergence-conforming mean? -- 3.3. History of the use of divergence-conforming basis functions -- 3.4. Basis functions of order p = 0 for a square reference cell -- 3.5. Basis functions of order p = 0 for a triangular reference cell -- 3.6. Nedelec's mixed-order spaces and the EFIE -- 3.7. Higher-order interpolatory functions for square cells -- 3.8. Higher-order interpolatory functions for triangular cells -- 3.9. Higher-order hierarchical functions for square cells -- 3.10. Higher-order hierarchical functions for triangular cells -- 4. Curl-conforming basis functions -- 4.1. What does curl-conforming mean? -- 4.2. History of the use of curl-conforming basis functions -- 4.3. Relation between the divergence-conforming and curl-conforming functions -- 4.4. Basis functions of order p = 0 for a square reference cell -- 4.5. Basis functions of order p = 0 for a triangular reference cell -- 4.6. Higher-order interpolatory functions for square cells -- 4.7. Higher-order interpolatory functions for triangular cells -- 4.8. Higher-order hierarchical functions for square cells -- 4.9. Higher-order hierarchical functions for triangular cells -- 5. Transforming vector basis functions to curved cells -- 5.1. Base vectors and reciprocal base vectors -- 5.2. Jacobian relations -- 5.3. Representation of vector fields -- 5.4. Restriction to surfaces -- 5.5. Curl-conforming basis functions on curvilinear cells -- 5.6. Divergence-conforming basis functions on curvilinear cells -- 5.7. The implementation of vector derivatives -- 5.8. Summary -- 6. Use of divergence-conforming basis functions with the electric field integral equation -- 6.1. Tested form of the EFIE -- 6.2. The subsectional model -- 6.3. Mapped MoM matrix entries -- 6.4. Normalization of divergence-conforming basis functions -- 6.5. Treatment of the singularity of the Green's function -- 6.6. Quadrature rules -- 6.7. Example : scattering cross section of a sphere -- 7. Use of curl-conforming bases with the magnetic field integral equation -- 7.1. Tested form of the MFIE -- 7.2. Entries of the MoM matrix -- 7.3. Mapped MoM matrix entries -- 7.4. Normalization of curl-conforming basis functions -- 7.5. Treatment of the singularity of the Green's function -- 7.6. Results. 
506 # # |a Abstract freely available; full-text restricted to subscribers or individual document purchasers. 
510 0 # |a Compendex 
510 0 # |a INSPEC 
510 0 # |a Google scholar 
510 0 # |a Google book search 
520 # # |a The method-of-moments solution of the electric field and magnetic field integral equations (EFIE and MFIE) is extended to conducting objects modeled with curved cells. These techniques are important for electromagnetic scattering, antenna, radar signature, and wireless communication applications. Vector basis functions of the divergence-conforming and curl-conforming types are explained, and specific interpolatory and hierarchical basis functions are reviewed. Procedures for mapping these basis functions from a reference domain to a curved cell, while preserving the desired continuity properties on curved cells, are discussed in detail. For illustration, results are presented for examples that employ divergence-conforming basis functions with the EFIE and curl-conforming basis functions with the MFIE. The intended audience includes electromagnetic engineers with some previous familiarity with numerical techniques. 
530 # # |a Also available in print. 
538 # # |a Mode of access: World Wide Web. 
538 # # |a System requirements: Adobe Acrobat Reader. 
650 # 0 |a Boundary element methods. 
650 # 0 |a Electromagnetism  |x Mathematical models. 
650 # 0 |a Integral equations  |x Numerical solutions. 
650 # 0 |a Moments method (Statistics) 
690 # # |a Boundary element method. 
690 # # |a Computational electromagnetics. 
690 # # |a Integral equations. 
690 # # |a Method of moments. 
690 # # |a Parametric mapping. 
730 0 # |a Synthesis digital library of engineering and computer science. 
830 # 0 |a Synthesis lectures on computational electromagnetics (Online),  |v #1.  |x 1932-1716 ; 
856 4 2 |u https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.2200/S00008ED1V01Y200508CEM001  |3 Abstract with links to full text 

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