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
