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
- 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
- Linear Algebra Basics and Definitions
- Ab-Initio Molecular Dynamics and Electronic Structure Calculations
- Molecular Dynamics Simulations
- Density Functional Theory
- 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
- 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
- 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
- Summary of Findings
- Hardware Acceleration of Submatrix Operations
- GPU Acceleration Using Tensor Cores
- FPGA Acceleration of Matrix Multiplications
- FPGA Accelerator for Iteration Schemes
- Summary of Findings
- Conclusion
- 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