An Introduction to the Locally Corrected Nystrom Method
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This lecture provides a tutorial introduction to the Nystr?m and locally-corrected Nystr?m 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 Nystr?m method is summarized, and applied to the magnetic field equation for illustration. To obtain high order accuracy in the numerical results, the locally-corrected Nystr?m 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. Table of Contents: Introduction / Classical Quadrature Rules / The Classical Nystr?m Method / The Locally-Corrected Nystr?m Method / Generalized Gaussian Quadrature / LCN Treatment of Edge Singularities
Format:Paperback
Language:English
ISBN:3031005821
ISBN13:9783031005824
Release Date:November 2009
Publisher:Springer
Length:103 Pages
Weight:0.47 lbs.
Dimensions:0.2" x 7.5" x 9.3"
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