# Iterative solution to Poissons Equation

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 December 8, 2010, 13:28 Iterative solution to Poissons Equation #1 New Member   Philip Piper Join Date: Oct 2010 Posts: 12 Rep Power: 6 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

December 8, 2010, 14:42
#2
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Dan
Join Date: Oct 2010
Location: UK
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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.
Attached Files
 PressureShort.pdf (88.7 KB, 31 views)

 December 9, 2010, 16:01 #3 Senior Member   TWB Join Date: Mar 2009 Posts: 105 Rep Power: 8 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.

 December 9, 2010, 19:58 #4 New Member   Philip Piper Join Date: Oct 2010 Posts: 12 Rep Power: 6 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.

December 10, 2010, 02:58
#5
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Alexey
Join Date: May 2009
Location: St.Petersburg, Russia
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Quote:
 Originally Posted by Phiper 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