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How to impose dirichlet conditions in a crank-nicholson scheme ?

How to impose dirichlet conditions in a crank-nicholson scheme ?

How to impose dirichlet conditions in a crank-nicholson scheme ?

(OP)
Hi all,

I am a beginner in the finite element method. I am writing my first program to solve the transient heat conduction equation.

I use the Crank-Nicholson scheme. I can construct the mass and stiffness matrix (MM and SM), and assemble them to have my linear system of equations Ax=B, with :

A= (MM+(Deltat/2)*SM);
B= (MM-(Deltat/2)*SM)*OLDT; OLDT is the temperature vector at the previous step.

Then I want to impose Dirichlet conditions at the surface of the domain, but I don't know how to do this. I know the different methods in static problem (penalty method,...) but not in transient.

Can you help me?

Thanks a lot for your help,

Best regards.

RE: How to impose dirichlet conditions in a crank-nicholson scheme ?

sebastienj,

This is a question for the software developers. I do not know if we have any on this forum. Most of us are users of software.

Gurmeet

RE: How to impose dirichlet conditions in a crank-nicholson scheme ?

This might help, it might not. Numerical Recipes, Chapter 19.2, has a short algorithm (Eq. 19.2.9) that you can easily program. I think if you write out the equations for a number of points, assemble in a matrix, I think you can see where you have to enforce the Dirichlet B.C.

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