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Dear Marianne,
It is not very clear for me what is the problem you try to solve.
The term Grad(uf) is a priori a vector one since the term uf is a
scalar one. May be you can clarify a bit. Moreover, in order to
solve an eigenvalue problem, you have to perform the assembly of
the stiffness matrix, the mass matrix and then search the
eigenvalues.
Best regards,
Yves.
Le 05/03/2015 08:47, Marianne Petersen a écrit :
Dear community,
I am trying to implement the following problem Laplacian
eigenvalue problem:
\int Grad(<f,u>) dA = \lambda \int u*f dA
with Dirichlet boundary conditions and a Neumann condition.
Since this problem is observed on a mesh with n Triangles The
equation is to be solved on every triangle and the corresponding
fem.
Is my idea of using the following _expression_ for the lhs
correct?
getfem::mesh mymesh;
// finite element method
getfem::mesh_fem mf(mymesh);
getfem::pfem pf = getfem::fem_descriptor("FEM_PK(2,1)");
mf.set_finite_element(mymesh.convex_index(), pf);
// integration method
getfem::mesh_im intm(mymesh);
getfem::pintegration_method ppi =
getfem::int_method_descriptor("IM_TRIANGLE(7)");
intm.set_integration_method(ppi);
getfem::ga_workspace workspace;
getfem::size_type nbdof = mf.nb_dof();
getfem::base_vector U(nbdof);
// left hand side: A
workspace.add_fem_variable("u", mf, gmm::sub_interval(0,
nbdof), U);
workspace.add_fem_variable("f", mf, gmm::sub_interval(0,
nbdof), U);
workspace.add_expression("f.Test_u", intm);
getfem::base_vector skalprod(nbdof);
workspace.set_assembled_vector(skalprod);
workspace.assembly(0);
workspace.clear_expressions();
workspace.add_fem_variable("skp", mf, gmm::sub_interval(0,
nbdof), skalprod);
workspace.add_expression("Grad_skp", intm);
getfem::model_real_sparse_matrix A(nbdof, nbdof);
workspace.set_assembled_matrix(A);
workspace.assembly(2);
I am really unsure about how to implement this problem.
Do you have an idea? Or should I use the "bricks"? Although I am
not sure either if this would work..
How can I make sure that the problem is for real implemented on
each trinagle of the mesh?
Thank you already very much in advance :)
Best regards
Marianne Petersen
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--
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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