non-linear partial differential equations

Matthew Knepley knepley at gmail.com
Fri Jun 12 18:01:20 CDT 2009

On Fri, Jun 12, 2009 at 5:39 PM, <naromero at alcf.anl.gov> wrote:

> Matt,
>
> Yes, it is a sparse eigenvalue problem. And yes, I have taken a look at
> SLEPc before. For some of our
> very large problems, we may get up to 10,000 (out of 10^7) eigenvalues and
> then SLEPc might need hooks
> into ScaLAPACK for the subspace diagonalization. Last time I checked
> ScaLAPACK interface in SLEPc
> was not available.

Not sure why you would need ScaLAPACK. Everything it has is either in PETSc
or SLEPc, or PLAPACK, or
you can use it through PETSc (which will download it automatically and build
it).

Matt

>
> Nichols A. Romero, Ph.D.
> Argonne National Laboratory
> Building 360 Room L-146
> 9700 South Cass Avenue
> Argonne, IL 60490
> (630) 252-3441
>
>
> ----- Original Message -----
> From: "Matthew Knepley" <knepley at gmail.com>
> To: "PETSc users list" <petsc-users at mcs.anl.gov>
> Sent: Friday, June 12, 2009 11:21:08 AM GMT -06:00 US/Canada Central
> Subject: Re: non-linear partial differential equations
>
> 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 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
> -- Norbert Wiener
>

--
What most experimenters take for granted before they begin their experiments
is infinitely more interesting than any results to which their experiments