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Neumann Boundary Condition for Poisson Equation solution in Polar Coordinates |
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March 29, 2011, 15:12 |
Neumann Boundary Condition for Poisson Equation solution in Polar Coordinates
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#1 |
Senior Member
Prapanch Nair
Join Date: Mar 2009
Location: Bangalore, India
Posts: 105
Rep Power: 17 |
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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July 29, 2011, 11:55 |
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#2 |
New Member
Amir
Join Date: Oct 2010
Posts: 16
Rep Power: 16 |
Hello,
I have the same problem, any guidance is appreciated. no reply since 2009! |
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July 30, 2011, 20:07 |
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#3 | |
Senior Member
Arjun
Join Date: Mar 2009
Location: Nurenberg, Germany
Posts: 1,285
Rep Power: 34 |
Quote:
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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Tags |
bicgstab, conjugate gradient, poisson equation, polar coordinates, singularity |
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