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 -------------- next part -------------- An HTML attachment was scrubbed... URL: <http://lists.mcs.anl.gov/pipermail/petsc-users/attachments/20090612/fe104a4a/attachment.htm>
