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  • Artemov, Anton G., 1990- (författare)
  • Parallelization of dynamic algorithms for electronic structure calculations
  • 2021
  • Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
    • The aim of electronic structure calculations is to simulate behavior of complex materials by resolving interactions between electrons and nuclei in atoms at the level of quantum mechanics. Progress in the field allows to reduce the computational complexity of the solution methods to linear so that the computational time scales proportionally to the size of the physical system. To solve large scale problems one uses parallel computers and scalable codes. Often the scalability is limited by the data distribution.This thesis focuses on a number of problems arising in electronic structure calculations, such as inverse factorization of Hermitian positive definite matrices, approximate sparse matrix multiplication, and density matrix purification methods. No assumptions are made about the data distribution, instead, it is explored dynamically.The thesis consists of an introduction and five papers. Particularly, in Paper I we present a new theoretical framework for localized matrices with exponential decay of elements. We describe a new localized method for inverse factorization of Hermitian positive definite matrices. We show that it has reduced communication costs compared to other widely used parallel methods. In Paper II we present a parallel implementation of the method within the Chunks and Tasks programming model and do a scalability analysis based on critical path length estimation.We focus on the density matrix purification technique and its core operation, sparse matrix-matrix multiplication, in Papers III and IV. We analyze the sparse approximate matrix multiplication algorithm with the proposed localization framework, add a prior truncation step, and derive the asymptotic behavior of the Frobenius norm of the error. We employ the sparse approximate multiplication algorithm in the density matrix purification process and propose a method to control the error norm by choosing the right truncation threshold value. We present a new version of the Chunks and Tasks matrix library in Paper V. The library functionality and architecture are described and discussed. The efficiency of the library is demonstrated in a few computational experiments.
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