[petsc-users] trying to solve a lot of ksp problems quickly

[Francis Poulin]

Hello,

I am trying to figure out a faster way of doing in petsc4py and thought I would ask to see how this should be done in petsc.  If I can figure that out then I think I can figure out how to translate it but I am having issues with the basic algorithm I should be using.

I am solving a linear system of ODEs of the form

B du/dt = A u

using Crank-Nicholson.  So the update equation can be written as

(B - dt/2*A)*u^(n+1) = (B + dt/2*A)*u^n

or, if you don't mind using the backslash operator,

u^(n+1) = (B - dt/2*A)\(B + dt/2*A)*u^n

The integration is faster of course after I build the matrix

C = (B - dt/2*A)\(B + dt/2*A)

however building this is very slow and I am not sure how to build it efficiently.  At the moment the majority of my code is just doing that.

In petsc4py I do the following:

(you can find the full code at https://github.com/francispoulin/qg_1L_ts/blob/master/qg_1L_ts.py)

        AeT = PETSc.Mat().createAIJ([Ny-1,Ny-1])
        AeT.setUp(); AeT.assemble()
        ksp = PETSc.KSP().create(PETSc.COMM_WORLD)
        ksp.setOperators(B-dto2*A)
        ksp.setTolerances(1e-16)
        pc = ksp.getPC()
        pc.setType('none')
        ksp.setFromOptions()

        btemp = B+dto2*A
        btemp.assemble()

        bcol = PETSc.Vec().createMPI(Ny-1)
        xcol = PETSc.Vec().createMPI(Ny-1)
        bcol.setUp(); xcol.setUp()

        sc,ec = bcol.getOwnershipRange()
        for i in range(0,Ny-1):
            bcol[sc:ec] = btemp[sc:ec,i]
            bcol.assemble(); xcol.assemble()
            ksp.solve(bcol,xcol)
            AeT[sc:ec,i] = xcol[sc:ec]

       AeT.assemble()

We are building the matrix one row at a time and, as accurate as that maybe, it is very slow.  Is there perhaps a fast way of doing this kind of operation in petsc?

Sorry for the bother but any advice would be greatly appreciated.

Cheers, Francis

------------------
Francis Poulin
Associate Professor
Associate Chair, Undergraduate Studies
Department of Applied Mathematics
University of Waterloo

email:           fpoulin at uwaterloo.ca
Web:            https://uwaterloo.ca/poulin-research-group/
Telephone:  +1 519 888 4567 x32637

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