3D static finite element analysis benchmark?!

[Smartcookie]

Hello,
I've written a 3d finite element code in matlab, generating tetrahedral volume meshes and solving possion equation. I need an example with analyrtical solution to check my program? anyone got a benchmark?

 

[GBor]

For more complicated models that those you might duplicate out of your last engineering textbook, I tend to benchmark against commercially available software packages with which I am very familiar. That way, I know the software is being run properly and I trust the results I'm getting from the package.

Otherwise, I have been known to use books like "Standard Handbook of Engineering Calculations" from McGraw-Hill or various Machine Design handbooks and textbooks.

 

[xerf]

Poisson's equation has analytical solutions for basic geometries, for example a parallelepiped, cylinder etc.

Any decent math textbook discussing PDE should have some solved examples, though it might not include PDE on 3D domains. Maybe a handbook on PDE might have some.

Probably a better bet would be a text on heat transfer (or trasport phenomena), it should have some examples since Poisson's eq. describes steady heat condution (or diffusion) with constant source term.....I think.

 

[EdR]

Start with simple problems from a textbook...If you start with something complex you will never get it checked out...

Ed.R.

 

[corus]

Is it transient or just steady state thermal problems? I have examples that compare results with both theoretical solutions and with other codes that have no easily obtained theoretical solution.

corus

 

[torpen]

Hello,

you can find example solutions of Poisson's equation in 1-d and 2-d at the following link :

http://farside.ph.utexas.edu/teaching/329/lectures/node60.html

Regards,

Torpen