Ph.D. Thesis Defense Announcement

Towards electronic structure calculations at the Exascale

By

Phanisri Pradeep Pratapa

Advisor:

Dr. Phanish Suryanarayana (CEE)

Committee Members:

Dr. Glaucio H. Paulino (CEE), Dr. Arash Yavari (CEE),

Dr. Edmond Chow (CSE), Dr. John E. Pask (Lawrence Livermore National Laboratory)

Date & Time: Thursday, July 7, 2016, at 2.00 PM

Location: Sustainable Education Building, 122

Development of new materials need better understanding of the behavior of materials at nanoscale which involves accurate simulation of

atomic and electronic interactions. Electronic structure is especially important when the atomic interactions involve breaking or formation of

chemical bonds. When such interactions are present, first principles based ab-initio electronic structure calculations of atoms, which do not

involve any empirical potentials, would be a suitable choice to study the behavior of materials at nanoscale. Such simulations involving many

thousands of atoms are intractable by current software (especially for metals) due to their cubic scaling with respect to the system size. In this

dissertation, the cubic scaling bottleneck is overcome by developing a linear scaling method amenable to massive parallelization.

A linear scaling Density Functional Theory (DFT) framework has been developed using Clenshaw-Curtis Spectral Quadrature (SQ) method

and implemented on massively parallel computers to simulate the electronic structure of hundreds of thousands of atoms. Finite difference

representation has been employed in order to exploit the locality of electronic interactions in real space, enable systematic convergence and

facilitate large-scale parallel implementation. In combination with linear scaling electrostatics, the electron density, energy and atomic forces

can be calculated with effort that scales linearly with the number of atoms for both insulating and metallic systems.

The method is validated and systematic convergence of energy and forces to the exact diagonalization result is demonstrated. The efficiency

and suitability of the method for high temperature calculations is also discussed. The parallel scaling of the method to more than hundred

thousand processors involving many thousands of atoms has been studied. The extreme parallelizability demonstrated by the method

promises the potential to make use of the next generation exascale computer architectures for scientific simulations. In the spirit of massive

parallelizability and efficiency, new extrapolation techniques have been developed to accelerate the convergence of fixed point iterations.

These techniques when applied to basic iterative methods give rise to efficient solvers for linear systems of equations. Robust and efficient

performance of these methods is demonstrated in acceleration of the non-linear fixed point iteration that is used to solve the electronic

structure problem.