A novel grid-robust higher order vector basis function for the method of moments

A set of novel, grid-robust, higher order vector basis functions is proposed for the method-of-moments (MoM) solution of integral equations for three-dimensional (3-D) electromagnetic (EM) problems. These basis functions are defined over curvilinear triangular patches and represent the unknown elect...

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Bibliographic Details
Published in:IEEE transactions on antennas and propagation 2001-06, Vol.49 (6), p.908-915
Main Authors: Gang Kang, Jiming Song, Weng Cho Chew, Donepudi, K.C., Jian-Ming Jin
Format: Article
Language:English
Subjects:
Basis functions
Computational electromagnetics
Convergence of numerical methods
Current
Density
Integral equations
Interpolation
Lagrangian functions
Mathematical analysis
Mathematical models
Moment methods
Patch antennas
Polynomials
Robustness
Solid modeling
Studies
Vectors (mathematics)
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Summary:A set of novel, grid-robust, higher order vector basis functions is proposed for the method-of-moments (MoM) solution of integral equations for three-dimensional (3-D) electromagnetic (EM) problems. These basis functions are defined over curvilinear triangular patches and represent the unknown electric current density within each patch using the Lagrange interpolation polynomials. The highlight of these basis functions is that the Lagrange interpolation points are chosen to be the same as the nodes of the well-developed Gaussian quadratures. As a result, the evaluation of the integrals in the MoM is greatly simplified. Additionally, the surface of an object to be analyzed can be easily meshed because the new basis functions do not require the side of a triangular patch to be entirely shared by another triangular patch, which is a very stringent requirement for traditional vector basis functions. The proposed basis functions are implemented with point matching for the MoM solution of the electric-field integral equation, the magnetic-field integral equation, and the combined-field integral equation. Numerical examples are presented to demonstrate the higher order convergence and the grid robustness for defective meshes using the new basis functions.
ISSN:0018-926X
1558-2221
DOI:10.1109/8.931148