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Tim Atherton (tjatherton)
New member
Username: tjatherton

Post Number: 2
Registered: 06-2005
Posted on Monday, October 17, 2005 - 12:29 pm:   

I'm trying to solve a pair of coupled DEs with value boundary conditions. Please see the attached script:
application/octet-stream1D Nematic Cartesian with Lagrange Multipler
1DLagrangeMulitplierSteadyState.pde (1.7 k)


A bit about the problem to be solved: The variables NX and NZ are the components of a unit vector field which is constrained to specific values at either end of a line. The equations to be solved are the euler-lagrange equations which arise from a free energy. In order to enforce the constraint nx^2+nz^2=1, I introduce an auxiliary functional into the free energy with associated lagrange multiplier LAGRANGE. This contributes additional terms to the E-L equations of the form -2*LAGRANGE*NX. The expression for lagrange arises from making NX and NZ the subject of the E-L equations, substituting into nx^2+nz^2=1 and solving for LAGRANGE. The constants K11 and K33 are material parameters, and since the actual values are very small, we scale the energy by dividing by K11.

Since the problem can also be solved by parameterizing the unit vector field by a single angle THETA, the solution is also represented by a plot of this angle (for comparison with another script).

However, as you can see for moderately different values of K11/K33 you get a crazy wobble effect. I've tried the following
1. Make K11=K33 - works fine and gives a straight line in THETA (correct)
2. Use STAGED to wind up K33 - only for K33 up to about 15e-12.
3. Reduce ERRLIM - as you can see I've done this to about 1e-6
4. I've also played with CHANGELIM, reducing it to 0.25 or 0.1 but this doesn't seem to help consistently.

I'm using the professional version. I wonder if anyone has any idea of what is happening. I apologise in advance if it's really obvious!
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Ji Wang (jjiiwang)
New member
Username: jjiiwang

Post Number: 1
Registered: 10-2005
Posted on Saturday, October 22, 2005 - 06:11 am:   

I need to calculate eigenvalues in a specified interval, like getting the overtones in the vibration problems.

I am wondering if flexPDE will allowe me to do this.
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Robert G. Nelson (rgnelson)
Moderator
Username: rgnelson

Post Number: 478
Registered: 06-2003
Posted on Saturday, October 22, 2005 - 04:28 pm:   

FlexPDE will compute a selected number of eigenvalues of lowest magnitude.
You can shift the window by offsetting the equation. See the example
"Samples | Eigenvalues | Shiftguide.pde".

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