enhancementgood first issue
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Description
AMGX ships with many nice sample programs, including simple implementation of Poisson-like equations. Currently, the charge function (e.g. in A x = b, the array b) is set to 1.d0 everywhere.
This is a poor choice, since integrating a constant over larger and large volumes gives you an exponentially growing solution. As a consequence, the sample cases have terrible convergence rates and do not scale as the problem size is increased.
I suggest a better choice: set b = sin( 2 * pi * x / Lx ) * sin( 2 * pi * y / Ly ) * sin( 2 * pi * z / Lz ), which satisfies either periodic or Dirichlet boundary conditions. This is more representative of the use of a Poisson solver.