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

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...

Table of Contents:

• 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.