# non-linear partial differential equations

naromero at alcf.anl.gov naromero at alcf.anl.gov
Fri Jun 12 17:39:15 CDT 2009

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.

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 experiments lead.
-- Norbert Wiener