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Neumann Boundary Condition for Poisson Equation solution in Polar Coordinates

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Old   March 29, 2011, 14:12
Default Neumann Boundary Condition for Poisson Equation solution in Polar Coordinates
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Prapanch Nair
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I am attempting to solve the poisson equation in polar coordinates (2D). The problem domain is an annulus. At both 'r' boundaries, neumann homogenous boundary conditions. And theta is periodic.

I am attempting to solve this using BiCGStab solver, that I have written myself. For the above BCs the matrix is singular and hence my solution isn't converging.

To force an additive constant. I made 'nth' row of my matrix the nth row of identity matrix. And changed the correspoding b(n) to 0. Thus I attempted to make '0' the additive constant. When I did that, the solution at the nth position has a sharp peak in the solution. I have used the same strategy with CG solver on a symmetric system and it worked.

It is to be noted that this solution with the peak is a converged solution. When i change the additive constant at n to values other than 0, I am getting a scaled shift in my solutions. Also note that A matrix is nonsymmetric for such a problem in polar coordinates.

My BiCGSTAB is working fine with dirichlet BCs either wholly or partially on the boundary.
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Old   July 29, 2011, 10:55
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Amir
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Hello,
I have the same problem, any guidance is appreciated.
no reply since 2009!
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Old   July 30, 2011, 19:07
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Arjun
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Quote:
Originally Posted by Amir_Ghasemi View Post
Hello,
I have the same problem, any guidance is appreciated.
no reply since 2009!
It is solved just like any other Neumann system is solved. Nothing special.

Not more than that could be said about it. Now it is upto you or user to implement things properly.

I have solved pure neumann equation in 3d and 2d in polor coordinates without any problems of any sort. Can use BicCGstab or multigrid, no probs here.
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bicgstab, conjugate gradient, poisson equation, polar coordinates, singularity

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