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An introduction to the locally-corrected Nyström method

This lecture provides a tutorial introduction to the Nyström and locally-corrected Nyström methods when used for the numerical solutions of the common integral equations of two-dimensional electromagnetic fields. These equations exhibit kernel singularities that complicate their numerical solution...

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Bibliographic Details
Main Author: Peterson, Andrew F., 1960-
Other Authors: Bibby, Malcolm M.
Format: Electronic
Language:English
Published: San Rafael, Calif. (1537 Fourth Street, San Rafael, CA 94901 USA) : Morgan & Claypool Publishers, c2010.
Series:Synthesis lectures on computational electromagnetics (Online), # 25.
Subjects:
Integral equations.
Electromagnetic fields > Mathematics.
Gaussian quadrature formulas.
Online Access:View fulltext via EzAccess
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020 # # |a 9781608453009 (electronic bk.) 
020 # # |a 9781608452996 (pbk.) 
024 7 # |a 10.2200/S00217ED1V01Y200910CEM025  |2 doi 
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040 # # |a CaBNvSL  |c CaBNvSL  |d CaBNvSL 
050 # 4 |a QC665.E4  |b P484 2010 
082 0 4 |a 530.1/41/0151  |2 21 
100 1 # |a Peterson, Andrew F.,  |d 1960- 
245 1 3 |a An introduction to the locally-corrected Nyström method  |h [electronic resource] /Andrew F. Peterson and Malcolm M. Bibby. 
260 # # |a San Rafael, Calif. (1537 Fourth Street, San Rafael, CA 94901 USA) :  |b Morgan & Claypool Publishers,  |c c2010. 
300 # # |a 1 electronic text (xi, 103 p. : ill.) :  |b digital file. 
490 1 # |a Synthesis lectures on computational electromagnetics,  |v # 25  |x 1932-1716 ; 
500 # # |a Part of: Synthesis digital library of engineering and computer science. 
500 # # |a Title from PDF t.p. (viewed on January 11, 2010). 
500 # # |a Series from website. 
504 # # |a Includes bibliographical references. 
505 0 # |a 1. Introduction : 1.1. The Nyström method; 1.2. The locally-corrected Nyström method; 1.3. A look ahead; References -- 2. Classical quadrature rules : 2.1. Trapezoid rule [2, 3]; 2.2. Romberg integration rules; 2.3. Gauss-Legendre quadrature rules; 2.4. Gauss-Lobatto quadrature; 2.5. Relative performance of quadrature rules; References -- 3. The classical Nyström method : 3.1. The magnetic field integral equation; 3.2. Flat-faceted discretization; 3.3. Discretization using exact models of a circular cylinder; 3.4. Nyström discretizations using closed quadrature rules; 3.5. Summary; References -- 4. The locally-corrected Nyström method : 4.1. The locally-corrected Nyström method; 4.2. Application of the LCN to the MFIE; 4.3. Alternate interpretation of the LCN; 4.4. Application of the LCN to the TM EFIE; 4.5. Application of the LCN to the TE EFIE; 4.6. Alternate LCN implementation of the TE EFIE using Gauss-Lobatto quadrature; 4.7. Initial application of the LCN to cylindrical structures with edge singularities; 4.8. Summary; References -- 5. Generalized Gaussian quadrature : 5.1. Introduction; 5.2. Example: development of "Lin-Log" rules; 5.3. High order representation of current density at edges in two-dimensions; 5.4. Quadrature rules for the singular degrees of freedom in table 5.1; 5.5. Summary; References -- 6. LCN treatment of edge singularities : 6.1. TM scattering from a triangular cylinder, revisited; 6.2. TM scattering from a square cylinder; 6.3. TE scattering from a square cylinder; 6.4. Input impedance of a hollow, linear dipole antenna; 6.5. Summary; References -- A. Parametric description of curved cell models-- B. Basis functions and quadrature rules for edge cells -- C. Reference data for square cylinder -- Authors' biographies. 
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 This lecture provides a tutorial introduction to the Nyström and locally-corrected Nyström methods when used for the numerical solutions of the common integral equations of two-dimensional electromagnetic fields. These equations exhibit kernel singularities that complicate their numerical solution. Classical and generalized Gaussian quadrature rules are reviewed. The traditional Nyström method is summarized, and applied to the magnetic field equation for illustration. To obtain high order accuracy in the numerical results, the locally-corrected Nyström method is developed and applied to both the electric field and magnetic field equations. In the presence of target edges, where current or charge density singularities occur, the method must be extended through the use of appropriate singular basis functions and special quadrature rules. This extension is also described. 
530 # # |a Also available in print. 
538 # # |a Mode of access: World Wide Web. 
538 # # |a System requirements: Adobe Acrobat reader. 
650 # 0 |a Integral equations. 
650 # 0 |a Electromagnetic fields  |x Mathematics. 
650 # 0 |a Gaussian quadrature formulas. 
700 1 # |a Bibby, Malcolm M. 
730 0 # |a Synthesis digital library of engineering and computer science. 
830 # 0 |a Synthesis lectures on computational electromagnetics (Online),  |v # 25.  |x 1932-1716 ; 
856 4 2 |u https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.2200/S00217ED1V01Y200910CEM025  |z View fulltext via EzAccess 

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