[petsc-users] Blocked matrix storage

Matthew Knepley knepley at gmail.com
Fri Feb 26 11:13:10 CST 2016

On Fri, Feb 26, 2016 at 11:01 AM, Manav Bhatia <bhatiamanav at gmail.com>

> Hi,
>   I am working on a problem with system of equations in complex numbers,
> and am splitting it up to solve it with petsc compiled for real number
> support:
> (J_R + i J_I) (x_R + i x_I) + (r_R + i r_I) = 0
> is then defined as
> [ J_R   -J_I] {x_R}  +  {r_R}  = {0}
> [ J_I    J_R] {x_I}  +  {r_I}  = {0}
> I have tried block-Schur solver with the Jacobian defined using the nested
> matrix format with a separate matrix for each quadrant of the Jacobian.
> This works well for diagonally dominant cases, but for high-frequency
> problems (J_I scales with frequency), the solver convergence is very slow.
> Now, I am attempting to create a single matrix so that I can use the other
> ksp+pc combinations for this system of equations.
> I am wondering if there is a natural way to create an mpiaij or an mpibaij
> matrix from the nested matrix defined above.

You can use this


to have the same assembly code insert into a global matrix. That way you
can use Fieldsplit or other preconditioners.
Also, a full Schur complement would converge in 1 iteration with exact
solves. I always start there and then back off.


> I would appreciate any guidance on this.
> Regards,
> Manav

What most experimenters take for granted before they begin their
experiments is infinitely more interesting than any results to which their
experiments lead.
-- Norbert Wiener
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