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I am trying to solve the 2D laplace equation,

$\frac{\partial^2 T}{\partial x^2} + \frac{\partial^2 T}{\partial y^2} = 0; \qquad 0 \lt x \lt 1, \quad0 \lt y \lt 1$

Subjected to the boundary conditions,

${\frac{d T}{d x}}|_{x=0,y}=0;$

${\frac{d T}{d y}}|_{x,y=0}=0;$

${\frac{d T}{d y}}|_{x,y=1}=0;$

$T|_{x=1,y} = 1; $

I am using Finite Difference method to discretise the differential equation and foward difference in the first two B.Cs and backward difference for the 3rd B.C. The solution which is $T=1$ at all grid points is perfectly coming out in Gauss Seidal as well as Jacobi iterative methods, but using BicgStab algorithm it is not converging even though the same matrices as Jacobi or Gauss Seidal. Any Ideas may help. Thank you.

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    $\begingroup$ What do you mean by not converging? Is it diverging, is it slow, is it stalled? It should converge if properly implemented. $\endgroup$ – EMP Sep 26 '19 at 21:02
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    $\begingroup$ Without additional info, I strongly suspect the implementation of the iterative solver (or the call to it) has a problem. Is it you custom BiCGStab implementation? $\endgroup$ – Anton Menshov Sep 26 '19 at 21:38
  • $\begingroup$ @EMP @ Anton; Thanks for your replyYes the was fluctuating rapidly. Now it is converging. The discretization of the laplace equation results into a Negative Definite Matrix A, so by multiplying the equation by $-1$ made it to a Positive Definite one, (and the RHS zero). The PD matrix with negative off diag terms and positive diagonal term along with the appropriate b.c.s converged rapidly. I think I read somewhere that BiCGSTAB works only for Positive Definite Symmetric or Asymmetric matrices. $\endgroup$ – Ark101 Sep 28 '19 at 16:14

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