Properties of the Gram Matrices Associated with Loop-flower Basis Functions
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 Calder(o)n 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 Calder(o)n 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.
Yibei Hou Gaobiao Xiao
Key Laboratory of Ministry of Education of Design and Electromagnetic Compatibility of High-Speed Electronic Systems,Shanghai Jiao Tong University,Shanghai,China
国际会议
Progress in Electromagnetics Research Symposium 2014(2014年电磁学研究新进展学术研讨会)
广州
英文
2316-2321
2014-08-01（万方平台首次上网日期，不代表论文的发表时间）