equations
Christophe Geuzaine
Christophe.Geuzaine at ulg.ac.be
Fri Aug 20 15:43:36 CEST 1999
"Marius S. Birsan" wrote:
>
> Hi Chris,
>
> I still have problems figuring out the equation symbolism. In the example below, once appear [ {d a} , {d a} ], and next is [ {js} , {a} ] . What is the idea behind this notation ? Thank you,
>
> Marius B.
>
> Equation {
> Galerkin { [ nu[] * Dof{d a} , {d a} ] ; In Domain_Mag ;
> Jacobian Vol ; Integration CurlCurl ; }
> Galerkin { [ - Dof{js} , {a} ] ; In DomainS_Mag ;
> Jacobian Vol ; Integration CurlCurl ; }
> }
Hi,
'd' stands for the exterior derivative operator in differential
geometry. If 'a' is a 1-form (say one kind of vector field), 'd' stands
for 'curl', and the equations are equivalent to:
Galerkin { [ nu[] * Dof{Curl a} , {Curl a} ] ; In Domain_Mag ;
Jacobian Vol ; Integration CurlCurl ; }
Galerkin { [ - Dof{js} , {a} ] ; In DomainS_Mag ;
Jacobian Vol ; Integration CurlCurl ; }
which means "Integrate the scalar product of 'mu*Curl(a)' by 'Curl(a)'
minus the scalar product of 'js' by 'a'". The notation [x,x] is one of
the classical notations for a scalar product in a function space (here
the scalar product relative to the L2 norm).
--
Christophe Geuzaine
Tel: +32-(0)4-366.37.10 mailto:Christophe.Geuzaine at ulg.ac.be
Fax: +32-(0)4-366.29.10 http://www.montefiore.ulg.ac.be/~geuzaine/