Poisson Equation

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Poisson Equation

Postby Creator » Mon Oct 05, 2009, 16:03

Currently I work on the new approach to multigrids methods for Poisson equation resolving. It continues my recent work, described in paper Accurate RT Disparity Estimation with Variational Metod.
A pretty interesting result, that I would like to publish here is the residual r(x,y) = f(x,y) + L[u(x,y)] scaled by factor of 1024. The problem is formulated as follows: constant boundary conditions (u(x,y) = 128 on boundaries) and two knots inside the area - a sink (left) and a source (right) (f(width/4, height/2) = -128 and f(3*width/4, height/2) = 128).
Both residual clouds look like a random Gaussian distributions, but nevertheless there are a pretty large difference in distributions for the positive and negative peculiarities. (The absolute value of the residual is shown).
The solution
The residual

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