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element-wise generalized eigenvalue problem in X-FEM

*element-wise generalized eigenvalue problem in X-FEM*was created by

*Shaoqi*

[attachment=undefined]eigen_prob.png[/attachment]Hi ngsolve comminity,

I would like to calculate the element-wise eigenvalue k of an generalized eigenvalue problem in the case "CufFEM" or X-FEM.

The problem is stated as:

where the matrix

[attachment=undefined]eigen_prob.png[/attachment]

Could you give some instruction on implementing this problem, I tried something to calculte the integrator like:
I am not sure if I do this with function

Then with the computed integrator, How can we calculate the eigenvalue problem? I saw some demos which use the algrhitome like PINVIT?

I would like to calculate the element-wise eigenvalue k of an generalized eigenvalue problem in the case "CufFEM" or X-FEM.

The problem is stated as:

**A**_{m}**=k***x*_{e,m}**B**_{m}*x*where the matrix

**A**and**B**is written as attached figure[attachment=undefined]eigen_prob.png[/attachment]

Could you give some instruction on implementing this problem, I tried something to calculte the integrator like:

Code:

lsPOS = {"levelset": levelset, "domain_type": POS}
lsNEG = {"levelset": levelset, "domain_type": NEG}
lsIF = {"levelset": levelset, "domain_type": IF}
space_flux = HDiv(mesh, order=2)
f = GridFunction(space_flux, "flux")
flux = grad(f)
#intf = Integrate(lsPOS, mesh=mesh, cf=flux, element_wise=True)
intf = Integrate(lsNEG, mesh=mesh, cf=flux, element_wise=True)
intf = Integrate(lsIF, mesh=mesh, cf=flux, element_wise=True)
intf = Integrate(flux, mesh, VOL, element_wise=True)

**Integrate**or with**symbolic integrators**Then with the computed integrator, How can we calculate the eigenvalue problem? I saw some demos which use the algrhitome like PINVIT?

#### Attachment not found

Last edit: 3 years 4 months ago by Shaoqi. Reason: add image

Replied by

*schruste*on topic*element-wise generalized eigenvalue problem in X-FEM*
Hi,

I cannot see the picture, i.e. I don't know the eigenvalue problem that you want to solve, yet.

Best,

Christoph

I cannot see the picture, i.e. I don't know the eigenvalue problem that you want to solve, yet.

Best,

Christoph

Replied by

*Shaoqi*on topic*element-wise generalized eigenvalue problem in X-FEM*
[attachment=undefined]eigen_prob.png[/attachment]

Last edit: 3 years 4 months ago by Shaoqi.

Replied by

*Shaoqi*on topic*element-wise generalized eigenvalue problem in X-FEM*
Hi Christoph,

Here is the picture

Best,

Shaoqi

Here is the picture

Best,

Shaoqi

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Last edit: 3 years 4 months ago by Shaoqi. Reason: add image

Replied by

*Shaoqi*on topic*element-wise generalized eigenvalue problem in X-FEM*
The integrations are defined on the levelset interface elements and the entire elements respectively.

Thanks Christoph!

Thanks Christoph!

Last edit: 3 years 4 months ago by Shaoqi.

Replied by

*schruste*on topic*element-wise generalized eigenvalue problem in X-FEM*
Hi Shaoqi,

You should setup the matrices A_m and B_m as you would do for solving a PDE problem. Hence, use symoblic integrators or differential symbols to describe the two bilinear forms and assemble the matrices

Afterwards you can use pinvit as done in the i-tutorials (e.g. 2.4.1) to compute the eigenvalues.

Best,

Christoph

You should setup the matrices A_m and B_m as you would do for solving a PDE problem. Hence, use symoblic integrators or differential symbols to describe the two bilinear forms and assemble the matrices

Afterwards you can use pinvit as done in the i-tutorials (e.g. 2.4.1) to compute the eigenvalues.

Best,

Christoph

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