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Koch, Marcel ; Koch, Marcel Dominique: Generating block-structured kernels for low order finite element methods : a high-performance oriented view. 2021
Inhalt
List of Tables
List of Figures
List of Algorithms
Introduction & Outline
Foundational Considerations
Finite Element Methods
Weak Formulation
Discretization
Assembly
Extensions
Iterative Linear System Solvers
Simple Iterative Methods
Krylov Subspace Methods
Software Tools
Dune
UFL
Performance on Modern Hardware
Block-Structured Grids
General Description
Geometry Transformation
Local Data Structure
Global Data Structure
Ensuring Consistency
Efficient Vectorization
Benchmarks
Global Assembly
Efficient Geometry Computation
Efficient Vectorization
Operator Application
Summary
Outlook
Preconditioners for Block-Structured Grids
Domain Decomposition Theory
Non-Overlapping Methods
Neumann-Neumann Method
Two Level Methods
Application to Block-structured Grids
Validation
Outlook
Generating Local Kernels
Code Generation Framework
Intermediate Representation
UFL to Intermediate Representation
Support for Block-Structured Grids
Visitor Specializations
Preconditioner Generation
Optimizations
Vectorization
Loop Invariant Code Motion
Benchmarks
Efficient Vectorization
Efficient Geometry Computation
Operator Application
Outlook
Representation of Local Structure
Performance Evaluation
Theoretical Performance
Measured Performance
Poisson Model
p-Laplacian
Navier-Stokes Model
Concluding Remarks
Summary & Conclusion
Performance Measuring Settings
Hardware
Software
Methodology
Bibliography