Dear all,
I am working on some problems involving eigenvalues and eigenvectors.
I am having some issues when assembling the stiffness matrix. Generally,
there are three methods to handle Dirichlet boundary conditions, such as
the penalty method (multiplying by a large number); setting the diagonal
elements to 1 and the remaining elements to zero; or removing the
corresponding degrees of freedom from the stiffness matrix. However, the
penalty method (multiplying by a large number) can cause the matrix to
become ill-conditioned. Setting the diagonal elements to 1 and the
remaining elements to zero can affect the computation of lower-order
eigenvalues, leading to eigenvalues of 1 that might not be the desired
eigenvalues. The best method for solving eigenvalue problems is to remove
the corresponding degrees of freedom from the stiffness matrix, as this not
only saves computational effort but also avoids the aforementioned issues.
However, in sparse matrices, this method is not easy to handle. Is there a
function in deal.II that can manage this?
Additionally, I would like to ask if isogeometric analysis can be done
in deal.II?
*Thank you for your great kindness and generosity.*
Best
Huang
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