Dear all,
I have a question regarding constrained dofs that are themselves constrained by
other dofs within the same element. Apparently, this leads to a non-symmetric
constrained element matrix which I illustrate here by a small example:
I consider an element with dof indices = (0,1,2,3). I impose the following
contraint rows
{
constrained_dof_index = 0;
constraint_row[1] = 1.0;
constraint_row[2] = -1.0;
}
{
constrained_dof_index = 1;
constraint_row[0] = 1.0;
constraint_row[3] = -1.0;
}
using
system.get_dof_map().add_constraint_row( constrained_dof_index, constraint_row,
0., true);
Since dof 1 is also constrained, these constraints get preprocessed so that
dof_map.print_dof_constraints();
yields
Constraints for DoF 0: (0,1) (2,-1) (3,-1) rhs: 0
Constraints for DoF 1: (2,-1) (3,-2) rhs: 0
This means that the following constraint matrix is generated:
C =
1 0 -1 -1
0 0 -1 -2
0 0 1 0
0 0 0 1
Assume now that the (symmetric) element matrix K is given by
K =
1 2 3 4
2 3 4 5
3 4 5 6
4 5 6 7
Then
C^T*K*C =
1 0 0 -1
0 0 0 0
0 0 -1 -1
-1 0 -1 0
This means that
dof_map.constrain_element_matrix(K, dof_indices,
/*asymmetric_constraint_rows*/false);
generates the (non-symmetric) constrained matrix
K_constrained =
1 0 0 0
0 1 0 0
0 0 -1 -1
-1 0 -1 0
because the first two rows are replaced by unit rows.
My question would be if this cannot be avoided so that I also have to use a
non-symmetric solver in this case.
Best,
Jonas
------------------------------------------------------------------------------
Check out the vibrant tech community on one of the world's most
engaging tech sites, Slashdot.org! http://sdm.link/slashdot
_______________________________________________
Libmesh-users mailing list
[email protected]
https://lists.sourceforge.net/lists/listinfo/libmesh-users
