Computational challenges in materials science
Winkelmann, Jan; Bientinesi, Paolo (Thesis advisor); Naumann, Uwe (Thesis advisor); Lang, Bruno (Thesis advisor)
Aachen : RWTH Aachen University (2020, 2021)
Dissertation / PhD Thesis
Dissertation, RWTH Aachen University, 2020
This dissertation sets out to improve performance—in terms of runtime as well as accuracy—of Materials Science simulations by means of custom kernels. The approach for each of our use-cases can be summarized as follows: We present some insight into the numerical properties of the simulation method under consideration. Then, we craft a custom numerical kernel that converts our insight into superior performance on high-performance computing systems. Throughout the dissertation we present three numerical kernels: For the simulation of strongly interacting systems, we derive a new adaptivity criterion for numerical integrals arising within the TUfRG code. We discuss PAID, a high-performance numerical kernel that implements our adaptivity criterion and significantly reduces time-to-solution for the integrals within the TUfRG code. Some Density Functional Theory simulations require the solution of sequence of Hermitian eigenvalue problems. Subspace Iteration can leverage a kind of correlation present in these sequences into improved convergence. We present ChASE, a high-performance solver for Hermitian eigenvalue problems based on Subspace Iteration equipped with polynomial filtering to further improve convergence. ChASE implements a number of significant improvements to the polynomial filter, resulting in a kernel that excels at solving the Hermitian eigenproblems arising in Density Functional Theory simulations. Further, we discuss an optimization framework for the rational filters used in the FEAST solver. Our optimization framework, SLiSe, allows for robust and fast generation of rational filters with very specific properties, resulting in convergence improvements to FEAST. What is more, we present an initial concept for the generation of problem-specific rational filters that leverage existing information about the problem at hand.