non-linear partial differential equations
naromero at alcf.anl.gov
naromero at alcf.anl.gov
Fri Jun 12 10:20:15 CDT 2009
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.
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