On Fri, Jun 12, 2009 at 5:39 PM, <span dir="ltr"><<a href="mailto:naromero@alcf.anl.gov">naromero@alcf.anl.gov</a>></span> wrote:<br><div class="gmail_quote"><blockquote class="gmail_quote" style="border-left: 1px solid rgb(204, 204, 204); margin: 0pt 0pt 0pt 0.8ex; padding-left: 1ex;">
Matt,<br>
<br>
Yes, it is a sparse eigenvalue problem. And yes, I have taken a look at SLEPc before. For some of our<br>
very large problems, we may get up to 10,000 (out of 10^7) eigenvalues and then SLEPc might need hooks<br>
into ScaLAPACK for the subspace diagonalization. Last time I checked ScaLAPACK interface in SLEPc<br>
was not available.</blockquote><div><br>Not sure why you would need ScaLAPACK. Everything it has is either in PETSc or SLEPc, or PLAPACK, or<br>you can use it through PETSc (which will download it automatically and build it).<br>
<br> Matt<br> </div><blockquote class="gmail_quote" style="border-left: 1px solid rgb(204, 204, 204); margin: 0pt 0pt 0pt 0.8ex; padding-left: 1ex;"><br>
Nichols A. Romero, Ph.D.<br>
<div class="im">Argonne Leadership Computing Facility<br>
Argonne National Laboratory<br>
Building 360 Room L-146<br>
9700 South Cass Avenue<br>
Argonne, IL 60490<br>
(630) 252-3441<br>
<br>
<br>
</div><div><div></div><div class="h5">----- Original Message -----<br>
From: "Matthew Knepley" <<a href="mailto:knepley@gmail.com">knepley@gmail.com</a>><br>
To: "PETSc users list" <<a href="mailto:petsc-users@mcs.anl.gov">petsc-users@mcs.anl.gov</a>><br>
Sent: Friday, June 12, 2009 11:21:08 AM GMT -06:00 US/Canada Central<br>
Subject: Re: non-linear partial differential equations<br>
<br>
You can solve matrix-free nonlinear equations with PETSc. If you are actually<br>
solving an eigenproblem, I would recommend using SLEPc which has PETSc<br>
underneath.<br>
<br>
Matt<br>
<br>
<br>
On Fri, Jun 12, 2009 at 10:20 AM, < <a href="mailto:naromero@alcf.anl.gov">naromero@alcf.anl.gov</a> > wrote:<br>
<br>
<br>
Hi,<br>
<br>
I would like to understand if the methods in PETSc are applicable to my<br>
problem.<br>
<br>
I work in the area of density functional theory. The KS equation in<br>
real-space (G) is<br>
<br>
[-(1/2) (nabla)^2 + V_local(G) + V_nlocal(G) + V_H[rho(G)] psi_nG = E_n*psi_nG<br>
<br>
rho(G) = \sum_n |psi_nG|^2<br>
<br>
n is the index on eigenvalues which correspond to the electron energy levels.<br>
<br>
This KS equation is sparse in real-space and dense in fourier-space. I think<br>
strictly speaking it is a non-linear partial differential equation. V_nlocal(G)<br>
is an integral operator (short range though), so maybe it is technically a<br>
non-linear integro-partial differential equation.<br>
<br>
I understand that PETSc is a sparse solvers. Does the non-linearity in the<br>
partial differential equation make PETSc less applicable to this problem?<br>
<br>
On one more technical note, we do not store the matrix in sparse format. It is<br>
also matrix*vector based.<br>
<br>
<br>
<br>
Argonne Leadership Computing Facility<br>
Argonne National Laboratory<br>
Building 360 Room L-146<br>
9700 South Cass Avenue<br>
Argonne, IL 60490<br>
(630) 252-3441<br>
<br>
<br>
<br>
<br>
--<br>
What most experimenters take for granted before they begin their experiments is infinitely more interesting than any results to which their experiments lead.<br>
-- Norbert Wiener<br>
</div></div></blockquote></div><br><br clear="all"><br>-- <br>What most experimenters take for granted before they begin their experiments is infinitely more interesting than any results to which their experiments lead.<br>
-- Norbert Wiener<br>