[Dune] Linear solve with transposed matrix

[Tobias Kasper Skovborg Ritschel]

Thanks for the clarification. I think I will follow your suggestion and evaluate the transposed matrix. I believe that my matrix pattern is symmetric, and currently I would re-evaluate A when solving A^T x = b, anyway.

Thank you for the swift help.

-----Original Message-----
From: Christian Engwer [mailto:christian.engwer at uni-muenster.de] 
Sent: 29. marts 2017 14:52
To: Tobias Kasper Skovborg Ritschel
Cc: dune at dune-project.org
Subject: Re: [Dune] Linear solve with transposed matrix

Hi Tobias,

> I am currently solving linear systems of equations in the form
> 
> A x = b,
> 
> with a preconditioned iterative method in Dune. I would also like to 
> solve linear systems with the same system matrix but transposed
> 
> A^T x = b.
> 
> As far as I can see, the iterative methods and preconditioners in Dune ISTL don't have an option to do so, and I have read<http://lists.dune-project.org/pipermail/dune/2015-August/013856.html> that there isn't an option to directly transpose a matrix (which is also not exactly what I want).

this is true, you can not apply the solver on the transposed matrix. Actually it might work, if you don't want to have a fast solver, you could copy the MatrixAdapter class, which implements the operator interface and just call .mtv(...) instead of .mv(...).  But this would not fast, as the apply-transposed is slower and (more
important) you can't use preconditioners.

Actually I suggest something different...

> The matrix, A, is of the type BCRSMatrix<FieldMatrix<double, 3, 3>>.
>
> What is the easiest way to solve such a system in Dune?

I suggest (and have done this myself) to actually assemble both matrices. You can write a simple adapter around you local local operator to swap row and column idex when writing to the local stiffness matrix (remember that you also have to swap the offsiagonal matrices if you have skeleton terms). This works, as long as your matrix mattern is symmetric. Obviously you could also transpose te matrix afterwards is this particular case...

If you want to follow tis route you should ask for details on the dedicated mailing list for your discretization module.

Ciao
Christian

--
Prof. Dr. Christian Engwer
Institut für Numerische und Angewandte Mathematik Fachbereich Mathematik und Informatik der Universität Münster Einsteinstrasse 62
48149 Münster

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