Contents of Dictaat Parallel Rekenen II (A117)

• Introduction to the application TRIWAQ
  • Introduction
    • The continuous mathematical problem
    • The finite difference method
    • Amount of calculations
  • Analysis of the sequential software
  • Approach of the parallelisation
    • Grid partitioning
    • Communication and synchronisation
    • Modifications to the algorithm
      • iterative solution methods
      • integration schemes
      • spatial discretisations
      • alternatives to finite differences
• Introduction to the Parallelisation of DIANA
  • Introduction
    • The FEM solution process
    • The architecture of the DIANA software package
  • Problem analysis
  • A methodology for parallel FEM computations
  • Domain decomposition
  • Block data structures for sparse matrices
  • The depedence graph of the parallel block solution
  • A macro dataflow implementation
  • Results and concluding remarks
• Parallel software design for CFD problems
  • Introduction
  • Abstraction in software
    • Different forms of abstraction
    • Two basic abstraction mechanisms: procedural abstraction and data abstraction
  • Elementary Steps in software development
    • The development steps
    • The development steps in a formal framework
    • Solving a Matrix equation as an illustration
      • Formal specification and realisation of a procedural abstraction
      • Data reification
      • Realisation of procedural abstraction and data reification
  • A glance at software development methods
    • What driven development
    • How-driven development
    • General notations - specification languages
    • A rigorous approach
  • Application of the Approach on a 2D heat transfer problem
    • Introduction
    • Physical and continuous mathematical model
    • Discrete mathematical model
    • Towards arrays, a normalised grid-function
    • A matrix equation
    • Data refinement for parallel computing
  • The impact on the applications TRIWAQ and DIANA
  • Conclusions
• Graph partitioning in parallel processing
  • Introduction
    • Review of graph terminology
    • Graphs in parallel processing
  • Partitioning Graphs
    • Classes of Partitioning Methods
    • Dynamical methods
  • Partitioning Methods for (Internally) Regular grids
  • Partitioning Methods for General Graphs
  • Optimisation Methods
  • Partitioning for TRIWAQ and DIANA
• Mapping and task scheduling
  • Introduction
  • Scheduling without communication cost
    • List scheduling
    • Comparisons
  • Communication are not free
    • Load balancing communication scheduling
    • Scheduling precedence graphs
    • Dynamic task scheduling
• Appendix: Introduction to finite element method
  • A simple example
• References
• Index