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Converges to wrong solution for coupled PDEs?

Posted 26 mai 2011, 13:55 UTC−4 Modeling Tools & Definitions, Parameters, Variables, & Functions, Studies & Solvers Version 4.1 2 Replies

cchriste
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Hello all.

I have have two first-order coupled differential equations:

u1x = -i*kappa*u2
u2x= -i*kappa*u1

Given the boundary conditions that u1(0)=1 and u2(0)=0, the solution for is u2(x) = sin(kappa*x). However, when I run through these equations using general PDE physics, it finds a solution that appears to be exactly u2(x)=sin(kappa*x/3).

My actual simulation is more complicated but this seems to be one of the problems. I have attached a model that shows this effect. Can anyone think of reason it might be converging an apparently wrong solution? I have tried changing the mesh and the discretization, but that does not help.

Thanks.

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2 Replies Last Post 31 mai 2011, 14:45 UTC−4
Nagi Elabbasi Facebook Reality Labs
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Posted: 1 decade ago 29 mai 2011, 09:26 UTC−4
Use the Coefficient form PDE with a=i*kappa and beta=-1. I tried it and it works. Even though the final PDE is the same as yours it will be handled differently by COMSOL since it expects a conservative flux term in the general form PDE.

Also, are you sure of the equations? It looks to me that you can use one variable instead and set the equation to u1x = -i*kappa*u1 where u1 is a complex variable.

Nagi Elabbasi
Veryst Engineering
Use the Coefficient form PDE with a=i*kappa and beta=-1. I tried it and it works. Even though the final PDE is the same as yours it will be handled differently by COMSOL since it expects a conservative flux term in the general form PDE. Also, are you sure of the equations? It looks to me that you can use one variable instead and set the equation to u1x = -i*kappa*u1 where u1 is a complex variable. Nagi Elabbasi Veryst Engineering
cchriste
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Posted: 1 decade ago 31 mai 2011, 14:45 UTC−4
Thank you very much, it is working much better now. I wonder what internally causes COMSOL to give this extra factor?

You are also right about the equations, the real part of the solution to your equation will be same as the full solution to mine. The form of mine makes the physics a little easier to understand when it starts to get more complicated, though perhaps COMSOL can handle one better than the other.

Cory
Thank you very much, it is working much better now. I wonder what internally causes COMSOL to give this extra factor? You are also right about the equations, the real part of the solution to your equation will be same as the full solution to mine. The form of mine makes the physics a little easier to understand when it starts to get more complicated, though perhaps COMSOL can handle one better than the other. Cory

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