[petsc-users] Need help: Poisson's equation with complex number

[Barry Smith]

  I would start with -pc_type gamg and -ksp_type gmres see how many iterations it requires and how the number of iterations grows when you  refine the mesh (if life is good then the iterations will grow only moderately as you refine the mesh).  If these options result in very bad convergence then send us the output with -ksp_monitor_true_residual and we'll have to consider other options.

  Barry



> On Jul 8, 2016, at 6:59 PM, Yaoyu Hu <huyaoyu1986 at gmail.com> wrote:
> 
> Hi everyone,
> 
> I am now trying to solve a partial differential equation which is
> similar to the three dimensional Poisson’s equation but with complex
> numbers. The equation is the result of the transformation of a set of
> fluid dynamic equations from time domain to frequency domain. I have
> Dirichlet boundary conditions all over the boundaries. The coefficient
> matrix that obtained by finite volume method (with collocated grid) is
> made of complex numbers. I would like to know that, for my discretized
> equation which solver and PC are the most suitable to work with. And
> BTW, the solution should be done in parallel with about 10^4 - 10^6
> unknowns.
> 
> It is the first time for me to solve equations with complex numbers,
> however, I am not so good at mathematics involving complex number. I
> would like to know want should I bear in mind throughout the whole
> process? Any suggestions or comments are appreciated.
> 
> Thanks!
> 
> HU Yaoyu