Eigensolvers for Large Electronic Structure Calculations

The solution of the single particle Schroedinger equation that arises in electronic structure calculations often requires solving for interior eigenstates of a large Hamiltonian. The states at the top of the valence band and at the bottom of the conduction band determine the band gap that relates to important physical characteristics such as optical or transport properties.

In order to avoid the explicit computation of all eigenstates, a folded spectrum method has been usually employed to compute only the eigenstates near the band gap. In this talk, we compare the conjugate gradient minimization, the optimal block preconditioned conjugate gradient, the implicit restarted Lanzos, and variants of the (Jacobi-)Davidson algorithms applied to the folded spectrum matrix for the computation of eigenstates of interest. We also show results for when some of these algorithms are applied to the unfolded spectrum.

Speaker Bio: Osni Marques is a member of the Scientific Computing Group, High Performance Computing Research Department, at the Lawrence Berkeley National Laboratory (LBNL). He is the PI for the project Advanced CompuTational Software (ACTS) Collection, funded by the Advanced Scientific Computing Research (ASCR) Program of the US Department of Energy (DOE). The ACTS Collection (http://acts.nersc.gov) comprises a set of software tools developed mostly at DOE laboratories and universities, and that can simplify the solution of common and important computational problems. The project aims at improving the usability, accessibility and acceptance of ACTS tools, in particular on DOE's computer facilities, and to make the tools more widely used and more effective in solving DOE's and the nation's scientific problems. Osni's research interests include the study, implementation and testing of algorithms for the solution of problems in numerical linear algebra, in particular eigenvalue problems, and high-end scientific computing. The eigensolvers he has implemented have been used in applications related to protein motions, acoustics problems in automobile design, structural analyses, and also in applications that require the computation of singular values and singular vectors of large, sparse matrices, for the solution of inverse problems in Geophysics (jointly with LBNL's Earth Sciences Division). Osni has been a collaborator in a project funded by DOE for the study of electronic properties of 3D, million-atom semiconductor nanostructures. Osni has also been a collaborator in a project funded by NSF for further development of the LAPACK and ScaLAPACK libraries of algorithms for dense linear algebra calculations. As part of this project he developed an infrastructure for exhaustively testing the tridiagonal eigensolvers implemented in LAPACK.

Presentation Slides: PDF

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