Conference paper
Higher Order Hierarchical Legendre Basis Functions for Iterative Integral Equation Solvers with Curvilinear Surface Modeling
Numerical solution of Maxwell's equations is often based on a discretization of an unknown field quantity using a set of N basis functions. A set of higher order hierarchical vector basis functions for the electric surface current in MoM codes with curvilinear quad patches is investigated. The basis is based on Legendre polynomials, modified to enforce current continuity, and are rather simple to implement in addition to allowing for a flexible selection of the polynomial order.
This flexibility is not provided by interpolatory bases that traditionally have been preferred due to the condition number of the matrix. Numerical results obtained with EFIE and CFIE show that the hierarchical Legendre basis provides a better condition number of the MoM matrix than existing interpolatory bases.
This allows for convergence in very few iterations using basis functions as high as 10th order.
Language: | English |
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Publisher: | IEEE |
Year: | 2002 |
Pages: | 618-621 |
Proceedings: | IEEE Antennas and Propagation Society International Symposium |
Journal subtitle: | 2002 Digest |
ISBN: | 0780373308 and 9780780373303 |
Types: | Conference paper |
DOI: | 10.1109/APS.2002.1017060 |
ORCIDs: | Breinbjerg, Olav |
CFIE Convergence Differential equations EFIE Integral equations Iterative methods Legendre basis functions Legendre polynomials Linear systems Maxwell equations Message-oriented middleware MoM matrix Moment methods Polynomials combined field integral equations convergence of numerical methods curvilinear surface modeling electric current electric field integral equations electric surface current electromagnetic field theory integral equations interpolation interpolatory bases iterative methods iterative solvers matrix algebra method of moments