equations

[Christophe Geuzaine]

"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/