Abstract
This paper discusses the application of loop-flower basis functions for solving surface integral equations involved in electromagnetic scattering problems on perfectly electrically conducting surfaces. Flower-shaped basis functions are proposed to replace the conventional star basis functions. The flower basis functions are defined based on mesh nodes instead of surface triangles. It is shown that the loop-flower basis functions not only can be used to handle the electromagnetic scattering problems at very low frequencies, but also can be directly used to implement Calderon preconditioners for EFIEs.
Highlights
The Rao-Wilton-Glisson (RWG) basis functions are wellused low-order basis functions for solving surface integral equations (SIEs) [1], such as in solving the widely-used electric field integral equation (EFIE)
Solving EFIE with RWG basis functions usually suffers from two problems: low frequency breakdown and the ill-conditioning of the coefficient matrix in the corresponding discrete system
Solving EFIE with RWG basis functions cannot provide accurate solutions to the electric currents. This is known as the low frequency breakdown problem and can be overcome using several techniques such as performing a quasi-Helmholtz decomposition [2,3,4,5]: expanding the surface currents with loop-tree or loop-star basis functions so that the surface currents are approximately divided into a solenoidal part and a nonsolenoidal part
Summary
The Rao-Wilton-Glisson (RWG) basis functions are wellused low-order basis functions for solving surface integral equations (SIEs) [1], such as in solving the widely-used electric field integral equation (EFIE). Solving EFIE with RWG basis functions cannot provide accurate solutions to the electric currents This is known as the low frequency breakdown problem and can be overcome using several techniques such as performing a quasi-Helmholtz decomposition [2,3,4,5]: expanding the surface currents with loop-tree or loop-star basis functions so that the surface currents are approximately divided into a solenoidal part and a nonsolenoidal part. A safe choice is to use the loop basis functions for the solenoidal currents and find a set of basis functions for Jirr, making the total number of degrees of freedom of these two set of bases equal to that of the RWG bases. Detailed descriptions on implementing Calderon preconditioners using loop-flower basis functions are provided, together with discussions on the properties of the flower basis functions
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