Re: [Getfem-users] gf_asm : How to use?

[julien pommier]

Hi Richard,

Your expression for I1 is the correct one. The first index of a Base(), 
vBase(), Grad etc is always the one refering to the corresponding degree 
of freedom

a=data(#1) and a=data$1(#1) are equivalent. The '$' is only useful when 
you have more than one data argument (for example b=data$2(#1))
The #1 says that the corresponding dimension is the number of degrees of 
freedom of the mesh_fem number 1

if U lives on a mesh_fem mf, and a lives on a mesh_fem mfd (a scalar 
mesh_fem whose qdim is 1), then the expression for I2 is:

I2 = gf_asm('boundary',1,'u=data$1(#1);a=data$2(#2);
V()+=a(i).u(j).comp(vBase(#1).Base(#2).Normal())(j,k,i,k);',mim,mf,mfd,U,A);

In order to understand that, just write
a(x) = sum(a_i * Phi_i(x)) with Phi_i(x) being the scalar base 
functions of mesh_fem mf1
U(x) = sum(u_j * Psi_j(x)) with Psi_j(x) being the vector base 
functions of mf (so Psi_j(x)[k] is one of its components).

Everything that is inside the 'comp' is in the integral, so you have

sum_{i,j,k} a_i * U_j * integral(Phi_i(x) * Psi_j(x)[k] * Normal[k] dS)

I hope it is more clear now !

Best regards,
Julien

Richard George wrote:
> Hello
>
> I'd like to evaluate the integral of the normal component of a vector 
> valued mesh_fem on a boundary,
>
> I have 'U' as a vector valued function represented by a FEM_PK(3,1) 
> object, and 'a' being a scalar valued function
> that takes a constant value on each convex, represented by a 
> FEM_DISCONTINUOUS_PK(3,0) object.
>
> term
>
> term 2
>
> The code for evaluating the first integral via gf_asm is possible I 
> think by making a contraction of a vBase() with a Normal()
>
> I1 = 
> gf_asm('boundary',1,'u=data(#1);V()+=u(i).comp(vBase(#1).Normal())(i,j,j);',mim,mf,U);
>
> This appears to give the right results in some simple tests - I'm 
> assuming that i sums over nodes, while j,j sums over vector components 
> and provides
> a dot product - but I don't really understand how are the indexes on 
> the comp() function are determined ? When do the indexes all refer to 
> cartesian
> vector components, and when are they local node numbers? am I using 
> the Normal() option correctly?
>
> I think it should be possible to specify the second integral as a 
> contraction of 'a', 'U' and a tensor but
> I don't think I grasp the syntax of the gf_asm command properly.
>
> Could you explain how to specify integral I2 via gf_asm, and when it's 
> appropriate to use
>
> a=data(#1)
> a=data$1(#1)
> a=data(#1,qdim(#1))
>
> I2 = gf_asm('boundary',1,'u=data(#1);a=data(#2) 
> ;V()+=a(i).u(j,k).comp(---??---.vBase(#1).Normal())(i,j,k,l,l);',mim,mf1,mf0,U,A);
>
> Thanks for any help you can provide
>
> Yours
>
> Richard George
>
>
>
>
>
>
>
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--
Julien Pommier, bureau 111
GMM, INSA Toulouse, tél:05 61 55 93 42