Hierarchical Matrices in Computations of Electron Dynamics

Authors:
Othmar Koch;Christopher Ede;Gerald Jordan;Armin Scrinzi
Affiliations:
Institute for Analysis and Scientific Computing (E101), Vienna University of Technology, Vienna, Austria 1040;Photonics Institute (E387), Vienna University of Technology, Vienna, Austria 1040;Photonics Institute (E387), Vienna University of Technology, Vienna, Austria 1040;Photonics Institute (E387), Vienna University of Technology, Vienna, Austria 1040
Venue:
Journal of Scientific Computing
Year:
2010

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Abstract

We discuss the approximation of the meanfield terms appearing in computations of the multi-configuration time-dependent Hartree---Fock method for the solution of the time-dependent multi-particle (electronic) Schrödinger equation by hierarchical matrices. We give theoretical error bounds for the cross approximation defined by low rank approximations of admissible matrix sub-blocks, and illustrate the gain in performance by numerical experiments.