“Raviart–Thomas basis functions”的意思、由来-开放百科全书

In applied mathematics, Raviart–Thomas basis functions are vector basis functions used in finite element and boundary element methods. They are regularly used as basis functions when working in electromagnetics. They are sometimes called Rao-Wilton-Glisson basis functions.^[1]

The space

spanned by the Raviart–Thomas basis functions of order

is the smallest polynomial space such that the divergence maps

onto

, the space of piecewise polynomials of order

.^[2]

Order 0 Raviart-Thomas Basis Functions in 2D

In two-dimensional space, the lowest order Raviart Thomas space,

, has degrees of freedom on the edges of the elements of the finite element mesh. The

th edge has an associated basis function defined by^[3]

where

is the length of the edge,

and

are the two triangles adjacent to the edge,

and

are the areas of the triangles and

and

are the opposite corners of the triangles.

References

1. ^{{cite journal|last=Andriulli|first=Francasco P. |author2=Cools |author3=Bagci |author4=Olyslager |author5=Buffa |author6=Christiansen |author7=Michelssen |date=2008|title=A Mulitiplicative Calderon Preconditioner for the Electric Field Integral Equation|journal=IEEE Transactions on Antennas and Propagation|volume=56|issue=8|pages=2398–2412|doi=10.1109/tap.2008.926788}}
2. ^{{cite web|url=http://www.logg.org/anders/pub/papers/KirbyLoggEtAl2012a.pdf|title=Common and Unusual Finite Elements|last=Kirby|first=Robert C. |author2=Anders Logg |author3=Andy R . Terrel |date=2010|accessdate=2 October 2015}}
3. ^{{Cite journal|last1=Bahriawati |first1=C. |last2=Carstensen |first2=C. |date=2005 |title=Three MATLAB Implementations Of The Lowest-Order Raviart-Thomas MFEM With a Posteriori Error Control |url=http://www2.mathematik.hu-berlin.de/~cc/cc_homepage/download/2005-BC_CC-Three_MATLAB_Implementations_Lowest-Order_Raviart-Thomas_MFEM.pdf |journal=Computational Methods in Applied Mathematics |volume=5 |issue=4 |pages=331–361 |access-date=8 October 2015 |doi=10.2478/cmam-2005-0016}}