An introduction to the locally-corrected Nyström method

• 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
• Item Description: Part of: Synthesis digital library of engineering and computer science.; Title from PDF t.p. (viewed on January 11, 2010).; Series from website.
• Physical Description: 1 electronic text (xi, 103 p. : ill.) : digital file.; Also available in print.
• Format: Mode of access: World Wide Web.; System requirements: Adobe Acrobat reader.
• Bibliography: Includes bibliographical references.
• ISBN: 9781608453009 (electronic bk.); 9781608452996 (pbk.)
• ISSN: 1932-1716
• Access: Abstract freely available; full-text restricted to subscribers or individual document purchasers.

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.