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solving 6th order eigenvalue problem

Asked by venkatesh

I have this equation:

D^6 u - k^6 *u - 3*k^2*D^4 u + 3*k^2* D^2 u = -k^2 * R * u

R is my eigen value
k is just a constant
D is differential operator

How to write the weak statement for this equation?

the final form must be A x = R B x

can i use the demo_eigenvalue.py ?

kindly help.

cheers

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Jan Blechta
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venkatesh (venkateshgk-j) said : 		#1

i wrote my weak form according to the BC (w, Dw, D^3 w =0 at 0 and 1), so weak form and the code is (pls correct if wrong)

mesh = UnitInterval(100)

a = -1.0*dot(grad(div(grad(u))), grad(div(grad(v))))*dx-k*k*u*v*dx-3*k*k*inner(div(grad(u)),div(grad(v)))*dx-3*k*k*k*k*dot(grad(u), grad(v))*dx

b = -1.0*k*k*u*v*dx

# Assemble stiffness form
A = PETScMatrix()
B = PETScMatrix()

assemble(a, tensor=A)
assemble(b, tensor=B)

# Create eigensolver
eigensolver = SLEPcEigenSolver(A,B)

# Compute all eigenvalues of A x = \lambda B x
print "Computing eigenvalues. This can take a minute."
eigensolver.solve()

i should get R = 1707 for k = 3.117

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Best Jan Blechta (blechta) said : 		#2

On Sun, 21 Apr 2013 07:06:17 -0000
venkatesh <email address hidden> wrote:
> New question #227152 on FEniCS Project:
> https://answers.launchpad.net/fenics/+question/227152
>
> I have this equation:
>
> D^6 u - k^6 *u - 3*k^2*D^4 u + 3*k^2* D^2 u = -k^2 * R * u
>
> R is my eigen value
> k is just a constant
> D is differential operator
>
> How to write the weak statement for this equation?

I'm afraid that nobody reading this forum will give you lectures in PDR.

>
> the final form must be A x = R B x
>
> can i use the demo_eigenvalue.py ?
>
> kindly help.
>
> cheers
>
>

Revision history for this message
venkatesh (venkateshgk-j) said : 		#3

sorry for the question.