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 Kémelli July 14, 2006 06:53

NEUMANN BOUNDARY CONDITION IN MESHLESS METHODS

Hi, dear friends,

I am trying to solve the Poisson equation on a retangular by using Neumann and Dirichlet boundary conditions. In the numerical method there is no mesh. We work with points distributed in the geometry. My question is this: "How to apply the Neumann boundary condition?"

Thank you a lot, Kemelli

 Mani July 14, 2006 09:19

Re: NEUMANN BOUNDARY CONDITION IN MESHLESS METHODS

How do you discretize the Poisson equation, i.e. how do you describe derivatives using the control points? You must know that,... and your question should answer itself.

 Praveen C July 15, 2006 01:41

Re: NEUMANN BOUNDARY CONDITION IN MESHLESS METHODS

I can think of two approaches, which may be called strong and weak implementations.

Strong 1 You already have a formula for the derivatives. Plug them into the Neumann condition and solve for the boundary value.

Strong 2 If you are using least squares for approximating derivatives, use a Lagrange multiplier to include the Neumann condition.

Weak If you are using least squares, square the Neumann condition and add it to the quantity you are minimizing.

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