HI Dear ALL,

Could anybody be kindly enough to give me an instruction to solve this

2D poisson equation using Fortran language:

=R-x^2-y^2

Any comments will be greatly appreciated. Thanks.

Ziven

> =R-x^2-y^2> > > > Any comments will be greatly appreciated. Thanks.> > > > Ziven

I think the Poisson equation is better written as: (see Wiki)

\Delta \phi = f

or more explicitly in 2 coordinates:

(d/dx)^2 phi(x,y) + (d/dy)^2 phi(x,y) = f(x,y)

To solve it you can discretize and use plain conjugate gradient

as a solver, but you must pre-condition the Laplace operator to

get decent convergence! Use SSOR and keep the operator symmetric,

and you'll be fine. By realizing that the discretized Laplace is

proportional to:

1 + L + U

with L and U the lower and upper triangular part, you can then

use a left and right preconditioner like:

(1 + w*L)^-1 * (1 + L + U) * (1 + w*U)^-1

which is symmetric, has easy matrix-free evaluation, and after

playing with w will give you pretty good convergence.

-- Jos

PS: don't use the Octave example on the Wiki CG page. It

contains an error.. (use the algorithm written above it)

Numerical Recipes has a pretty good description of Poisson

solvers, including a variety of actual programs to use.

(Depending on how much work you want to do, and how fast

you need the solution.)

I would at least start there.

-- glen

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