Dear Ivan,
Yes, if you can expand K(x,x') in \sum (a_k b_l \phi_k(x') \phi_l(x)), you can compute two separate matrices and obten what you want. But this is a case where you can approximate K(x,x') with a finite element method, which does not correspond to most of interesting cases where the kernel has singularities ... you are right. > 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? You can obtain the expression of shape function on the reference element and the expression of the transformation to the real element (in case of affine transformations). You can also interpolate the shape functions on any points. Yves. ----- Original Message ----- From: "Ivan Melikhov" <[email protected]> To: "Yves Renard" <[email protected]> Cc: [email protected] Sent: Friday, January 18, 2013 7:25:40 PM Subject: Re: [Getfem-users] Integro-differential equations Yves, Thank you for your response. 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? Thanks, Ivan 2013/1/18 Yves Renard < [email protected] > Dear Ivan, 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 \int\int(\phi_i(r')\phi_j(r')V(r,r')\phi_m(r)\phi_l(r))dr'dr 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? Thank you for answers, Ivan _______________________________________________ Getfem-users mailing list [email protected] https://mail.gna.org/listinfo/getfem-users -- Yves Renard ( [email protected] ) 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 --------- _______________________________________________ Getfem-users mailing list [email protected] https://mail.gna.org/listinfo/getfem-users
