[Getdp] Formulation

Gilles schaouette at free.fr
Wed Jan 10 10:05:12 CET 2007


The expression 
Galerkin { [ epsr[]*Dof{d v} , {d v} ] ; In Vol; Jacobian Vol ;  Integration Int ; }
Is a way to describe the Galerkin formulation of the problem. It is the variationnal formulation of the problem using Galerkin's assumption. You can see for example section Variationnal Formulation there:
http://www.geuz.org/getdp/wiki/WaveEquationPml     (username:getp  password:wiki)

The expression Dof{athing} means that athing is the unknown parameter (Dof: Degree Of Freedom)

The sign d is the Exterior derivative: applied to a p-form, gives a (p+1)-form. This means that applied to a scalar, d is the gradient.

> I need some help in understanding formulations. How does the following  
> line: "Galerkin { [ epsr[]*Dof{d v} , {d v} ] ; In Vol; Jacobian Vol ;  
> Integration Int ; }" translate into "div epsr[] grad v=0".
> Is the grad operation implicit in "Dof{d v}"?
> Where is the div operation specified?
> These are probably very simply questions, maybe someone can enlighten me.
>
> Tammo
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