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I have to solve a linear equation as a part of a more global simulation. The equation is :

[tex]\mathbf{B} - \mu\Delta \mathbf{B} = \mathbf{S}[/tex]

Where both [tex]\mathbf{B}[/tex] and [tex]\mathbf{S}[/tex] are 3 component vectors fields, depending on x and y (2D fields).

My grid is regular, and has a typical size of [tex]n_x=n_y=512[/tex] (nx can be different from ny).

Boundary conditions are periodic on x borders, but dirichlet or neuman on y borders (but are the same for both y borders). The choice of Dirichlet or Neumann depends on the Field component that is solved.

There are then 3 equations (one for each field component) that have to be solved 4 times per time step of the simulation.

Typical simulation is about 30000 time steps, thus the 3 equations must be solved 120000 times. I need an efficient and parallel method.

I've begun to learn the PETSC library, which is a high level and parallel library for this kind of problem. But I'm not mathematician, and a bit lost with all the non stationnary iterative methods.

I have made a sum up of my problem on the pdf here : http://nau.cetp.ipsl.fr/matrixinertia.pdf [Broken]

Can someone first tell me if the matrices I've calculated and written in this document are ok ? (I'm not used to do this...)

Then, I observe that, because of the boundary conditions, these two matrices are not symmetric... could someone tell me which method in Petsc should be the best for my problem ? (methods are presented here : http://www.mcs.anl.gov/petsc/petsc-as/documentation/linearsolvertable.html [Broken])

Thanks a lot

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# [PETSC] which method ?

Can you offer guidance or do you also need help?

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