Computational Technologies : Advanced Topics

This book discusses questions of numerical solutions of applied problems on parallel computing systems. Nowadays, engineering and scientific computations are carried out on parallel computing systems, which provide parallel data processing on a few computing nodes. In the development of up-to-date applied software, this feature of computers must be taken into account for the maximum efficient usage of their resources. In constructing computational algorithms, we should separate relatively independent subproblems in order to solve them on a single computing node. * State-of-the-art numerical methods and programming techniques * Guide to efficient use of computing systems * Typical problems of computational mathematics serve as examples List of contributors Contents Preface Introduction 1 Architecture of parallel computing systems 1.1 History of computers 1.2 Architecture of parallel computers 1.3 Modern supercomputers 1.4 Multicore computers 1.5 Operating system processes and threads 1.6 Programming multi-threaded applications 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 3 Essentials of OpenMP 3.1 OpenMP parallel programming model 3.2 The parallel construct 3.3 Work-sharing constructs 3.4 Work-sharing clauses 3.5 Synchronization 3.6 Dirichlet problem for the Poisson equation 4 MPI technology 4.1 Preliminaries 4.2 Message-passing operations 4.3 Functions of collective interaction 4.4 Dirichlet problem for the Poisson equation 5 ParaView: An efficient toolkit for visualizing large datasets 5.1 An overview 5.2 Data file formats 5.3 Preparing data 5.4 Working with ParaView 5.5 Parallel visualization 6 Tools for developing parallel programs 6.1 Installation of PTP 6.2 Program management 6.3 Parallel debugging 6.4 Performance analysis 7 Applied software 7.1 Numerical simulation 7.2 Applied software engineering 7.3 Software architecture 7.4 General purpose applied software 7.5 Problem-oriented software 8 Geometry generation and meshing 8.1 General information 8.2 The Gmsh workflow 8.3 NETGEN first look 9 PETSc for parallel solving of linear and nonlinear equations 9.1 Preliminaries 9.2 Solvers for systems of linear equations 9.3 Solution of nonlinear equations and systems 9.4 Solving unsteady problems 10 The FEniCS project 10.1 Preliminaries 10.2 Model problem 10.3 Finite element discretization 10.4 Program 10.5 Result processing 10.6 Nonlinear problems 10.7 Time-dependent problems 11 Numerical study of applied problems 11.1 Heat transfer with phase transitions 11.2 Lid-driven cavity flow 11.3 Steady thermoelasticity problem 11.4 Joule heating problem Bibliography Index

This book discusses questions of numerical solutions of applied problems on parallel computing systems.

Nowadays, engineering and scientific computations are carried out on parallel computing systems, which provide parallel data processing on a few computing nodes. In the development of up-to-date applied software, this feature of computers must be taken into account for the maximum efficient usage of their resources. In constructing computational algorithms, we should separate relatively independent subproblems in order to solve them on a single computing node.

This book discusses questions of numerical solutions of applied problems on parallel computing systems. Nowadays, engineering and scientific computations are carried out on parallel computing systems, which provide parallel data processing on a few computing nodes. In constructing computational algorithms, mathematical problems are separated in relatively independent subproblems in order to solve them on a single computing node In this book we describe the basic elements of present computational technologies that use the algorithmic languages C/C++. The emphasis is on GNU compilers and libraries, FOSS for the solution of computational mathematics problems and visualization of the obtained data.Many examples illustrate the basic features of computational technologies.