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 Phiper December 8, 2010 13:28

Iterative solution to Poissons Equation

Can someone please explain either the SOR iterative solution to Poissons Equation or any other that may be faster? I'm having trouble wrapping my head around the concept of how this equation can be used to create a mass-conserving field. Thanks for any help!!!

**Edit: Or link me to any explanations or previous threads

 dandalf December 8, 2010 14:42

1 Attachment(s)
I have attached a quick derrivation of the pressure poisson equation, I hope this explains how it maintains conservation of mass.

The pressure requirements at physical boundaries can also be derrived useing similar methods,

As for solvers, I have been using a direct itterative Gauss -Seidel method, although I would welcome any sugestions for an alternative.

 quarkz December 9, 2010 16:01

Are you trying to solve the Poisson eqn? You can try multigrid which is very suitable for Poisson eqn. PETSc and hypre can be used together to solve your Poisson eqn.

 Phiper December 9, 2010 19:58

Yes I've heard of multigrid before. I just don't understand how it works. And I've looked at a few explanations online but i havn't really found them satisfactory.

 ignat December 10, 2010 02:58

Quote:
 Originally Posted by Phiper (Post 286568) Can someone please explain either the SOR iterative solution to Poissons Equation or any other that may be faster?
I think conjugate gradient method with preconditioner is faster then SOR.
I recommended to use Saad's SPARSKIT library, see here