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Computational Technologies
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Computational Technologies
by Petr N. Vabishchevich
Computational Technologies
Title Page
Copyright Page
List of contributors
Table of Contents
Preface
Introduction
1 Architecture of parallel computing systems
1.1 History of computers
1.2 Architecture of parallel computers
1.2.1 Flynn’s taxonomy of parallel architecture
1.2.2 Address-space organization
1.3 Modern supercomputers
1.4 Multicore computers
1.5 Operating system processes and threads
1.5.1 Processes
1.5.2 Threads
1.6 Programming multi-threaded applications
1.6.1 Multi-threading: pros and cons
1.6.2 Program models
2 Multi-threaded programming
2.1 POSIX threads
2.2 Creating and terminating threads
2.3 Thread life-cycle
2.4 Multi-threaded matrix summation
2.5 Thread synchronization
2.5.1 Semaphore
2.5.2 Mutex
3 Essentials of OpenMP
3.1 OpenMP parallel programming model
3.2 The parallel construct
3.3 Work-sharing constructs
3.3.1 The for directive
3.3.2 The sections directive
3.3.3 The single directive
3.3.4 Combined work-sharing constructs
3.4 Work-sharing clauses
3.4.1 The shared clause
3.4.2 The private clause
3.4.3 The schedule clause
3.4.4 The reduction clause
3.5 Synchronization
3.5.1 The barrier directive
3.5.2 The critical directive
3.5.3 The atomic directive
3.6 Dirichlet problem for the Poisson equation
3.6.1 Problem formulation
3.6.2 Parallel implementation
4 MPI technology
4.1 Preliminaries
4.1.1 General information
4.1.2 Compiling
4.1.3 Getting started with MPI
4.1.4 Determination of the number of processes and their ranks
4.1.5 The standard MPI timer
4.2 Message-passing operations
4.2.1 Data exchange between two processes
4.2.2 Data types
4.3 Functions of collective interaction
4.3.1 General information
4.3.2 Synchronization function
4.3.3 Broadcast function
4.3.4 Data gathering functions
4.3.5 Data distribution functions
4.3.6 Matrix-vector multiplication
4.3.7 Combined collective operations
4.3.8 Global computational operations
4.3.9 Scalar product of vectors
4.4 Dirichlet problem for the Poisson equation
4.4.1 Problem formulation
4.4.2 Parallel algorithm
5 ParaView: An efficient toolkit for visualizing large datasets
5.1 An overview
5.2 Data file formats
5.2.1 Serial formats
5.2.1.1 Structured points
5.2.1.2 Structured grid
5.2.1.3 Rectilinear grid
5.2.1.4 Polygonal representation
5.2.1.5 Unstructured grid
5.2.2 XML formats
5.3 Preparing data
5.3.1 Structured 2D grid
5.3.2 Structured 3D grid
5.3.3 Unstructured 2D grid
5.4 Working with ParaView
5.4.1 Loading data
5.4.2 Filters
5.4.3 Time series
5.5 Parallel visualization
5.5.1 The architecture of ParaView
5.5.2 Running in parallel mode
6 Tools for developing parallel programs
6.1 Installation of PTP
6.1.1 Prerequisites
6.1.2 Installing Eclipse with PTP
6.1.3 Installing the plug-in
6.2 Program management
6.2.1 Basics of PTP
6.2.2 Creating a connection with a remote computer
6.2.3 Creating projects
6.2.4 Project synchronization
6.2.5 Editing MPI programs
6.2.6 Building programs
6.2.7 Running programs
6.3 Parallel debugging
6.3.1 Debug configuration
6.3.2 Parallel debug perspective
6.3.3 Process managing
6.3.4 Breakpoints
6.4 Performance analysis
6.4.1 Installation
6.4.2 Configuration
6.4.3 Running
7 Applied software
7.1 Numerical simulation
7.1.1 Mathematical modeling
7.1.2 Basic steps of a computational experiment
7.1.3 Mathematical models
7.2 Applied software engineering
7.2.1 Features of applied software
7.2.2 Modular structure
7.3 Software architecture
7.3.1 Basic components
7.3.2 Data preparation
7.3.3 Computational modules
7.3.4 Data processing and visualization
7.4 General purpose applied software
7.4.1 User-friendly interface
7.4.2 Basic features
7.4.3 The Salome platform
7.5 Problem-oriented software
7.5.1 Parametric study
7.5.2 Componet-based implementation of functionalities
7.5.3 Computational components
8 Geometry generation and meshing
8.1 General information
8.1.1 Structured meshes
8.1.2 Unstructured meshes
8.2 The Gmsh workflow
8.2.1 Elementary entities
8.2.2 Commands for working with geometric objects
8.2.3 Physical entities
8.2.4 Building geometry
8.2.5 Tools
8.2.6 Creating a complex geometry
8.2.7 Generating a mesh
8.3 NETGEN first look
8.3.1 Creating a geometry
8.3.2 Generating a mesh
9 PETSc for parallel solving of linear and nonlinear equations
9.1 Preliminaries
9.1.1 Brief description
9.1.2 Installation
9.1.3 Development of programs
9.1.4 Matrices and vectors
9.2 Solvers for systems of linear equations
9.2.1 Problem formulation
9.2.2 Finite difference approximation
9.2.3 Numerical implementation
9.3 Solution of nonlinear equations and systems
9.3.1 Statement of the problem
9.3.2 Solution algorithm
9.3.3 Implementation in PETSc
9.4 Solving unsteady problems
9.4.1 Problem formulation
9.4.2 Approximation
9.4.3 The program
10 The FEniCS project
10.1 Preliminaries
10.1.1 Main features
10.1.2 Installation
10.2 Model problem
10.2.1 Problem formulation
10.2.2 Variational formulation
10.3 Finite element discretization
10.3.1 Discretization
10.3.2 Finite elements
10.4 Program
10.4.1 UFL application
10.4.2 C++ implementation
10.4.3 Linear solvers
10.4.4 Compilation
10.5 Result processing
10.5.1 Visualization
10.5.2 Functionals
10.6 Nonlinear problems
10.6.1 Problem formulation
10.6.2 UFL application
10.6.3 C++ implementation
10.7 Time-dependent problems
10.7.1 Problem description
10.7.2 UFL application
10.7.3 C++ implementation
11 Numerical study of applied problems
11.1 Heat transfer with phase transitions
11.1.1 Mathematical model
11.1.2 Finite element discretization
11.1.3 Numerical implementation
11.1.4 Predictions
11.2 Lid-driven cavity flow
11.2.1 Incompressible Navier-Stokes equations
11.2.2 Variational formulation
11.2.3 Numerical algorithm
11.2.4 Computational experiments
11.3 Steady thermoelasticity problem
11.3.1 Governing equations
11.3.2 Finite element technique
11.3.3 Algorithm of calculations
11.3.4 Numerical results
11.4 Joule heating problem
11.4.1 Problem formulation
11.4.2 Discrete problem
11.4.3 Computational algorithm
11.4.4 Numerical simulations
Bibliography
Index
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