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

 From: julien pommier Subject: Re: [Getfem-users] gf_asm : How to use? Date: Mon, 16 Jul 2007 13:57:08 +0200 User-agent: Thunderbird 1.5.0.12 (X11/20070604)

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);

Yours

Richard George

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