non-linear partial differential equations
Matthew Knepley
knepley at gmail.com
Fri Jun 12 11:21:08 CDT 2009
You can solve matrix-free nonlinear equations with PETSc. If you are
actually
solving an eigenproblem, I would recommend using SLEPc which has PETSc
underneath.
Matt
On Fri, Jun 12, 2009 at 10:20 AM, <naromero at alcf.anl.gov> wrote:
> Hi,
>
> I would like to understand if the methods in PETSc are applicable to my
> problem.
>
> I work in the area of density functional theory. The KS equation in
> real-space (G) is
>
> [-(1/2) (nabla)^2 + V_local(G) + V_nlocal(G) + V_H[rho(G)] psi_nG =
> E_n*psi_nG
>
> rho(G) = \sum_n |psi_nG|^2
>
> n is the index on eigenvalues which correspond to the electron energy
> levels.
>
> This KS equation is sparse in real-space and dense in fourier-space. I
> think
> strictly speaking it is a non-linear partial differential equation.
> V_nlocal(G)
> is an integral operator (short range though), so maybe it is technically a
> non-linear integro-partial differential equation.
>
> I understand that PETSc is a sparse solvers. Does the non-linearity in the
> partial differential equation make PETSc less applicable to this problem?
>
> On one more technical note, we do not store the matrix in sparse format. It
> is
> also matrix*vector based.
>
>
>
> Argonne Leadership Computing Facility
> Argonne National Laboratory
> Building 360 Room L-146
> 9700 South Cass Avenue
> Argonne, IL 60490
> (630) 252-3441
>
>
--
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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