[petsc-users] reuse a real matrix for a second linear system with complex numbers

[Matthew Knepley]

On Fri, May 14, 2021 at 10:36 AM feng wang <snailsoar at hotmail.com> wrote:

> Thanks for your comments. It is very helpful!
>
> I might try the 1st approach first.   For the 2nd approach which uses an
> equivalent real-number system, I see potential issues when running in
> parallel. I have re-ordered my cells to allow each rank hold continuous
> rows in the first real system Ax=B. For the equivalent real-number system,
> each rank now holds (or can assign values to) two patches of continuous
> rows, which are separated by N rows, N is the size of square matrix A. I
> can't see a straightforward way to allow each rank hold continuous rows in
> this case. or petsc can handle these two patches of continuous rows with
> fixed row index difference in this case?
>

I just wrote it that way for ease of typing. You can imagine permuting into
2x2 blocks with

  /a  w\
  \-w a/

for each entry.

  Thanks,

     Matt


> By the way, could I still re-use my KSP object in my second system by
> simply changing the operators and setting new parameters?
>
> Thanks,
> Feng
>
> ------------------------------
> *From:* Matthew Knepley <knepley at gmail.com>
> *Sent:* 14 May 2021 10:00
> *To:* feng wang <snailsoar at hotmail.com>
> *Cc:* petsc-users at mcs.anl.gov <petsc-users at mcs.anl.gov>
> *Subject:* Re: [petsc-users] reuse a real matrix for a second linear
> system with complex numbers
>
> On Fri, May 14, 2021 at 4:23 AM feng wang <snailsoar at hotmail.com> wrote:
>
> Dear All,
>
> I am solving a coupled system. One system is AX=B. A, X and B are all real
> numbers and it is solved with GMRES in petsc. Now I need to solve a second
> linear system, it can be represented as (A+i*w)*Z=C. i is the imaginary
> unit.  Z and C are also complex numbers.
>
> So the Jacobian matrix of the second system is just A plus a diagonal
> contribution i*w.  I would like solve the second system with GMRES, could
> petsc handle this? any comments are welcome.
>
>
> Mixing real and complex numbers in the same code is somewhat difficult
> now. You have two obvious choices:
>
> 1) Configure for complex numbers and solve your first system as complex
> but with 0 imaginary part. This will work fine, but uses more memory for
> that system. However, since you will already
>      use that much memory for the second system, it does not seem like a
> big deal to me.
>
> 2) You could solve the second system in its equivalent real form
>
>   / A  w \ /Zr\ = /Cr\
>  \ -w  A / \Zi/     \Ci/
>
>    This uses more memory for the second system, but does not require
> reconfiguring.
>
>   THanks,
>
>      Matt
>
> Thanks,
> Feng
>
> --
> 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
>
> https://www.cse.buffalo.edu/~knepley/
> <http://www.cse.buffalo.edu/~knepley/>
>


-- 
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

https://www.cse.buffalo.edu/~knepley/ <http://www.cse.buffalo.edu/~knepley/>
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