Abstract of Venera Khoromskaia

Numerical solution of the Hartree-Fock equation in the multilevel tensor structured format
We describe a novel method for the numerical solution of the self-consistent Hartree-Fock equation using a grid-based tensor approximation of arising functions and operators in 3D. Main computational steps are performed using the numerical ``agglomerated'' tensor-structured evaluation of the three- and six- dimensional integrals involved, with complexity that scales linearly in the one-dimension grid size n. High accuracy is achieved due to the multigrid accelerated canonical-to-Tucker rank optimization algorithm for 3-rd order tensors, which enables computations over huge spatial grids using MATLAB on a SUN station. As a solution method of the discrete nonlinear eigenvalue problem we apply the multilevel tensor-truncated DIIS iteration on a sequence of refined grids. We demonstrate a stable convergence in a moderate number of iterations, illustrated by convincing numerical examples for all electron case of H2O, and pseudopotential case of CH4 and CH3OH molecules.


Lars Grasedyck (MPI Leipzig, Germany)
Wolfgang Hackbusch (MPI Leipzig, Germany)
Boris Khoromskij (MPI Leipzig, Germany)