Evaluation of Hierarchical Vector Basis Functions for Quadrilateral Cells

Author

Peterson, Andrew F. ; Graglia, Roberto D.

Author_Institution

Sch. of Electr. & Comput. Eng., Georgia Inst. of Technol., Atlanta, GA, USA

Volume

47

Issue

5

fYear

2011

fDate

5/1/2011 12:00:00 AM

Firstpage

1190

Lastpage

1193

Abstract

New hierarchical vector basis functions for quadrilateral cells are introduced, and the matrix condition numbers associated with their use are compared to those of existing vector basis families to assess the relative linear independence of the functions. Scale factors are employed to improve the condition numbers. In addition, the proper use of subsets of these families to transition from one order to another (as needed for adaptive p-refinement) without exciting spurious modes is considered.

Keywords

Helmholtz equations; Jacobian matrices; Legendre polynomials; eigenvalues and eigenfunctions; electromagnetic fields; finite element analysis; functions; transfer function matrices; vectors; Jacobi polynomials; Legendre polynomials; adaptive p-refinement; eigenfunctions; eigenvalues; electromagnetic field; finite-element analysis; hierarchical vector basis functions; matrix condition numbers; quadrilateral cell discretization; scale factors; transition functions; vector Helmholtz equation; Antennas; Cavity resonators; Eigenvalues and eigenfunctions; Polynomials; Vectors; Boundary elements; Helmholtz equation; hierarchical basis functions; vector finite elements;

fLanguage

English

Journal_Title

Magnetics, IEEE Transactions on

Publisher

ieee

ISSN

0018-9464

Type

jour

DOI

10.1109/TMAG.2010.2089500

Filename

5754747