[Getdp] function space for 3D a-v-formulation, and higher order approximation ?

Christophe Geuzaine cag32 at case.edu
Sun May 14 01:14:57 CEST 2006


Thomas Jung wrote:
> Hi,
> 
> I would be grateful if someone could give me a little help on this:
> 
> First, would the following be a correct declaration of a function space for 
> the 3D magnetic vector potential ?
> 
> FunctionSpace {
> 
>   // Magnetic vector potential a (b = curl a)
>   { Name Hcurl_a_Mag_3D; Type Form1;
>     BasisFunction {
> 	{ Name se; NameOfCoef ae; Function BF_Edge;
>         Support Domain_Mag; Entity EdgesOf[ All ]; }
>     }
>     Constraint {
> 	{ NameOfCoef ae; EntityType EdgesOf;NameOfConstraint a; }
> 	{ NameOfCoef ae; EntityType EdgesOfTreeIn; EntitySubType 
> StartingOn;NameOfConstraint Gauge; }
>     }
>   }
> 
> }
> 
> with the Gauge constraint like this:
> 
>   { Name Gauge; Type Assign;
>   Case {
> 	{ Region Domain_Mag ; SubRegion OuterBoundary; Value 0.; }
>     }
>   }


Looks good to me.

> 
> 
> If that would be o.k., how would one do a higher order approximation?
> 

You need to add the higher order basis functions in the function space: 
BF_Edge_2E, BF_Edge_2F, etc.


> 
> Thank you very much !
> 
> 
> Thomas Jung
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> 


-- 
Christophe Geuzaine
Assistant Professor, Case Western Reserve University, Mathematics
http://www.case.edu/artsci/math/geuzaine



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