The integral in my previous message is correct. But forget it. Let the 1D equation involves term \int(K(x,x')u(x'))dx' where K is known kernel and u is unknown function we are solving for. So to solve it with FEM, one needs to assemble matrix \int\int(K(x,x')\phi_i(x')phi_j(x))dx'dx. Do you mean that I can expand K(x,x') in \sum (a_k b_l \phi_k(x') \phi_l(x)), compute two separable integral and multiply their values?
Another problem is that my kernel has singularity, so it isn't interpolated well by polynomial base functions. The best way I see is to compute the whole matrix not in getFEM but in matlab or mathematica. To do it I need some data from FEM. Exactly, I need base functions and coordinates of area it's defined on. Can getFEM provide this data?
Unfortunately, the assembly procedure of Getfem is not designed to
compute such integro-differential term.
May be if you have specific _expression_ for the kernel (if it is
simple or can be expressed on a FEM) it should be possible to
adapt something.
Yves.
Le 18/01/2013 12:24, Ivan Melikhov a écrit :
Hello!
I need to solve an integro-differential eigenvalue problem
and I have trouble with integral term. Generally, I need to
assemble a 4D matrix with elements
I suppose it is
\int\int(\phi_i(r)\phi_j(r')V(r,r')\phi_m(r)\phi_l(r))dr'dr
(\phi_i(r) instead of \phi_i(r')) ?
where V(r,r') is known function, \phi_i is the ith base
function, dr is dxdy, dr' is dx'dy'. The question is how can I
compute an inner integral inside comp command in
generic_assembly::set?
--
Yves Renard (address@hidden) tel : (33) 04.72.43.87.08
Pole de Mathematiques, INSA-Lyon fax : (33) 04.72.43.85.29
20, rue Albert Einstein
69621 Villeurbanne Cedex, FRANCE
http://math.univ-lyon1.fr/~renard
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