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Document Type

Open Access Dissertation

Degree Name

Doctor of Philosophy (PhD)

Degree Program

Electrical and Computer Engineering

Year Degree Awarded

2018

Month Degree Awarded

September

First Advisor

Dr. Eric Polizzi

Subject Categories

Atomic, Molecular and Optical Physics | Electronic Devices and Semiconductor Manufacturing | Nanoscience and Nanotechnology | Nanotechnology Fabrication | Numerical Analysis and Scientific Computing | Quantum Physics | Semiconductor and Optical Materials

Abstract

Density functional theory (DFT) and time dependent density functional theory (TDDFT) have had great success solving for ground state and excited states properties of molecules, solids and nanostructures. However, these problems are particularly hard to scale. Both the size of the discrete system and the number of needed eigenstates increase with the number of electrons. A complete parallel framework for DFT and TDDFT calculations applied to molecules and nanostructures is presented in this dissertation. This includes the development of custom numerical algorithms for eigenvalue problems and linear systems. New functionality in the FEAST eigenvalue solver presents an additional level of distributed memory parallelism and is used for the ground state DFT calculation, allowing larger molecules to be simulated. A parallel domain decomposition linear system solver has also been implemented. This approach uses a Schur complement technique and a combination of direct sparse solvers to outperform black box distributed memory solvers in both performance and scalability. All other aspects of the code have been rewritten to operate in the domain decomposition framework and have been parallelized using both MPI and OpenMP. Numerical experiments demonstrate that our all-electron code can be applied to systems containing up to a few thousand atoms.

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