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Zero Determinant of stiffness matrix

Posted Aug 11, 2020, 10:50 a.m. EDT General, LiveLink for MATLAB, Modeling Tools & Definitions Version 5.5 4 Replies

Alexandre Arsenault
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Hello,

I am trying to evaluate the conditioning of the stiffness matrix. My simulations work fine and seem to give good results. However, when I extract the stiffness matrix into Matlab using an assembly node and LiveLink, the determinant gives zero. Why does my simulation work fine, but the stiffness matrix seems non-invertible?

Thank you,

Alex

4 Replies Last Post Aug 24, 2020, 5:21 p.m. EDT
Henrik Sönnerlind COMSOL Employee

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Posted: 4 years ago Aug 11, 2020, 5:35 p.m. EDT

If you are looking at the noneliminated stiffness matrix, this is expected, but not if you are looking at the eliminated version. What type pf physics and boundary conditions are involved?

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Henrik Sönnerlind
COMSOL
If you are looking at the noneliminated stiffness matrix, this is expected, but not if you are looking at the eliminated version. What type pf physics and boundary conditions are involved?
Alexandre Arsenault
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Posted: 4 years ago Aug 11, 2020, 9:03 p.m. EDT

Hi Henrik,

Thank you for the reply. I tried looking at both the eliminated and full stiffness matrices and both give the same result.

I am using a General Form PDE that is the same physics as the MFH module to calculate the magnetic field of a superconductor. The boundary condition used is a Dirichlet condition to set the magnetic field at the domain boundary.

Cheers,

Alex

Hi Henrik, Thank you for the reply. I tried looking at both the eliminated and full stiffness matrices and both give the same result. I am using a General Form PDE that is the same physics as the MFH module to calculate the magnetic field of a superconductor. The boundary condition used is a Dirichlet condition to set the magnetic field at the domain boundary. Cheers, Alex
Henrik Sönnerlind COMSOL Employee

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Posted: 4 years ago Aug 12, 2020, 5:38 a.m. EDT

Then it difficult to guess. With sufficient Dirichlet conditions, the eliminated matrix should be nonsingular. What are the sizes of the two matrices?

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Henrik Sönnerlind
COMSOL
Then it difficult to guess. With sufficient Dirichlet conditions, the eliminated matrix should be nonsingular. What are the sizes of the two matrices?
Alexandre Arsenault
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Posted: 4 years ago Aug 24, 2020, 5:21 p.m. EDT

Hello,

It turns out that the stiffness matrix is singular in my case since we are taking the curl of the test functions in the weak formulation (not sure why this makes the matrix singular, but I read it in a few research papers). Therefore, you need to calculate the condition number of the addition of the stiffness matrix and the damping matrix in order to consider the time-dependence of the weak formulation.

Cheers,

Alex

Hello, It turns out that the stiffness matrix is singular in my case since we are taking the curl of the test functions in the weak formulation (not sure why this makes the matrix singular, but I read it in a few research papers). Therefore, you need to calculate the condition number of the addition of the stiffness matrix and the damping matrix in order to consider the time-dependence of the weak formulation. Cheers, Alex

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