Proceedings of 2015 Photonics & Electromagnetics Research Symposium, Prague, July 6 - 9,Page(s)2316-2321
Abstract
In this paper, loop-flower basis functions are addressed to solve the electric field
integral equation (EFIE) in electromagnetic scattering issues that rise from perfectly conducting
objects. A loop basis function and a flower basis function are both defined as the sum of a set
of modified RWG basis functions associated with a node in triangular meshes. Moreover, they
could also be represented by node based Lagrange interpolation polynomials. A flower basis
function, which also resembles the star basis function, is named after its shape. In contrast
to all previous quasi-Helmholtz decomposition, loop-flower decomposition holds several good
characteristics. First, loop-flower decomposition can be used to cure low-frequency breakdown of
EFIE spectrum. Second, it can also be directly used to implement Calderón preconditioners for
EFIE. Last but not least, the unknown number corresponding with loop-flower basis functions
reduces to approximately two thirds of the one associated with RWG. Given that the property
of a Calderón preconditioner is largely affected by the Gram matrix that links the range and
domain of EFIE operator, this paper will focus on the properties of Gram matrices associated
with loop-flower basis function. Analysis shows that the Gram matrices associated with loop-
flower basis functions are invertible, and their condition numbers are approximately of the order
of (h−2 ), in which h is the characteristic dimension of a triangular mesh. The theoretical analysis
will be demonstrated by several numerical examples.
Citation
Yibei Hou,
and
Gaobiao Xiao,
"Properties of the Gram Matrices Associated with Loop-flower Basis Functions," Proceedings of 2015 Photonics & Electromagnetics Research Symposium, Prague, July 6 - 9,Page(s)2316-2321