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Bringing Massive Parallelism and Hardware Acceleration to Linear Scaling Density Functional Theory Through Targeted Approximations / by Michael Laß. Paderborn, 2022
Inhalt
Acknowledgements
Abstract
Zusammenfassung
Table of Contents
Introduction
Contributions
Thesis Structure
Foundations
High-Performance Computing Systems and Applications
HPC Clusters Used in This Work
GPUs as Accelerator Platform in HPC
FPGAs as Accelerator Platform in HPC
Approximate Computing
Goals and Restrictions
Applications
Levels of and Techniques for Approximation
Linear Algebra Basics and Definitions
Fundamental Terms
Matrix Powers and (Inverse) p-th Roots
Matrix Sign Function
Ab-Initio Molecular Dynamics and Electronic Structure Calculations
Molecular Dynamics Simulations
Computation and Integration of Forces
Statistical Ensembles
Density Functional Theory
SCF Cycle
Density Matrix Based DFT
Linear Scaling DFT
LSDFT in the Quantum Chemistry Code CP2K
Distributed Block Compressed Sparse Row (DBCSR) Matrix Library
Basis Sets Relevant for This Work
Computational Hotspots in AIMD Simulations
Motivating Approximations in DFT Computations
Iterative Methods as Target for Approximations
Computation of Inverse p-th Roots
Problem and Data Set
Methodology
Results
Iterative Computation of the Sign Function
Rate of Convergence
Error Accumulation
Summary of Findings
Submatrix Method: Algorithmic Approximation of Matrix Functions
Algorithm Description
Building the Submatrices
Performing Submatrix Operations
Assembling the Result Matrix
Implementation Notes
Applicability and Approximation Error
Computation of Inverse p-th Roots
Computation of the Matrix Sign Function
Controlling the Approximation Error
Complexity and Scalibility
Single-Threaded Scenario
Parallel Execution of Submatrix Operations
Application to Electronic Structure Methods
Performance Evaluation
Implementation Details
Results
Summary of Findings
Integration of the Submatrix Method into CP2K
Extension of the Matrix Sign Function Definition in CP2K
Implementation of the Submatrix Method Within CP2K
Overview
Data Transfers
Minimization of Floating-Point Operations
Shared-Memory Parallelism
Load Balancing
Sign Calculation Based on Diagonalization
Adaptation of the Method to Canonical Ensembles
Availability
Evaluation
Performance and Error for Various filter Thresholds
Scaling
Larger Basis Sets
Summary of Findings
Hardware Acceleration of Submatrix Operations
GPU Acceleration Using Tensor Cores
FPGA Acceleration of Matrix Multiplications
FPGA Accelerator for Iteration Schemes
Required Kernels
Host Code Design
Evaluation
Summary of Findings
Conclusion
Summary
Outlook and Future Work
List of Figures
List of Tables
List of Algorithms
List of Listings
Acronyms
Author's Peer-Reviewed Publications
Author's Preprints, Presentations, Software and Artifacts
Bibliography
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