On 6/20/24 22:09, kai huang wrote:
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?
You are in luck, we thought of this when we wrote step-36 :-) Take a look at
this section:
https://dealii.org/developer/doxygen/deal.II/step_36.html#step_36-EigenvaluesandDirichletboundaryconditions
Additionally, I would like to ask if isogeometric analysis can be done in
deal.II?
This depends on how exactly you define "isogeometric". We can use arbitrary
geometries (in particular NURBS-based geometries) and there are tutorial
programs about that as well (step 54, for example).
Best
W.
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Wolfgang Bangerth email: [email protected]
www: http://www.math.colostate.edu/~bangerth/
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