jacobi_openmp


jacobi_openmp, a C code which illustrates the use of the OpenMP application program interface to parallelize a Jacobi iteration solving A*x=b.

Each step of the Jacobi iteration produces a vector xnew. The i-th entry of xnew is found by ``solving'' the i-th linear equation for the i-th variable. This operation can be done in parallel. It is a little more complicated to compute the maximum difference between the old and new x values, and to compute the maximum residual, but these can be done.

The example uses a standard -1,2,-1 matrix which has very slow convergence. Here, the point is not so much to get the answer, but to show that the process can be speeded up by employing OpenMP.

Licensing:

The computer code and data files described and made available on this web page are distributed under the MIT license

Languages:

jacobi_openmp is available in a C version and a C++ version and a FORTRAN90 version.

Related Data and Programs:

DIJKSTRA_OPENMP, a C code which uses OpenMP to parallelize a simple example of Dijkstra's minimum distance algorithm for graphs.

FFT_OPENMP, a C code which demonstrates the computation of a Fast Fourier Transform in parallel, using OpenMP.

FUNCTIONS_OPENMP, a C code which demonstrates the behavior of a few of the OpenMP library functions.

HEATED_PLATE_OPENMP, a C code which solves the steady (time independent) heat equation in a 2D rectangular region, using OpenMP to run in parallel.

HELLO_OPENMP, a C code which prints out "Hello, world!" from each OpenMP thread.

IMAGE_DENOISE_OPENMP, a C code which applies simple filtering techniques to remove noise from an image, carrying out the operation in parallel using OpenMP.

JACOBI, a C code which implements the Jacobi iteration for solving symmetric positive definite (SPD) systems of linear equations.

jacobi_openmp_test

julia_set_openmp, a C code which produces an image of a Julia set, using OpenMP to carry out the computation in parallel.

MANDELBROT_OPENMP, a C code which generates an ASCII Portable Pixel Map (PPM) image of the Mandelbrot fractal set, using OpenMP for parallel execution.

MD_OPENMP, a C code which carries out a molecular dynamics simulation using OpenMP.

MULTITASK_OPENMP, a C code which demonstrates how to "multitask", that is, to execute several unrelated and distinct tasks simultaneously, using OpenMP for parallel execution.

MXM_OPENMP, a C code which computes a dense matrix product C=A*B, using OpenMP for parallel execution.

openmp_test, C codes which use the OpenMP application program interface for carrying out parallel computations in a shared memory environment.

POISSON_OPENMP, a C code which computes an approximate solution to the Poisson equation in a rectangle, using the Jacobi iteration to solve the linear system, and OpenMP to carry out the Jacobi iteration in parallel.

PRIME_OPENMP, a C code which counts the number of primes between 1 and N, using OpenMP for parallel execution.

QUAD_OPENMP, a C code which approximates an integral using a quadrature rule, and carries out the computation in parallel using OpenMP.

QUAD2D_OPENMP, a C code which applies a product quadrature rule to estimate an integral over a 2D rectangle, using OpenMP for parallel execution.

RANDOM_OPENMP, a C code which illustrates how a parallel program using OpenMP can generate multiple distinct streams of random numbers.

SATISFY_OPENMP, a C code which demonstrates, for a particular circuit, an exhaustive search for solutions of the circuit satisfiability problem, using OpenMP for parallel execution.

SCHEDULE_OPENMP, a C code which demonstrates the default, static, and dynamic methods of "scheduling" loop iterations in OpenMP to avoid work imbalance.

SGEFA_OPENMP, a C code which reimplements the SGEFA/SGESL linear algebra routines from LINPACK for use with OpenMP.

SUPERLU_OPENMP, C codes which illustrate how to use the SUPERLU library with the OpenMP parallel programming interface, which applies a fast direct solution method to solve sparse linear systems, by James Demmel, John Gilbert, and Xiaoye Li.

ZIGGURAT_OPENMP, a C code which demonstrates how the ZIGGURAT library can be used to generate random numbers in an OpenMP parallel program.

Reference:

  1. Peter Arbenz, Wesley Petersen,
    Introduction to Parallel Computing - A practical guide with examples in C,
    Oxford University Press,
    ISBN: 0-19-851576-6,
    LC: QA76.58.P47.
  2. Rohit Chandra, Leonardo Dagum, Dave Kohr, Dror Maydan, Jeff McDonald, Ramesh Menon,
    Parallel Programming in OpenMP,
    Morgan Kaufmann, 2001,
    ISBN: 1-55860-671-8,
    LC: QA76.642.P32.
  3. Barbara Chapman, Gabriele Jost, Ruud vanderPas, David Kuck,
    Using OpenMP: Portable Shared Memory Parallel Processing,
    MIT Press, 2007,
    ISBN13: 978-0262533027,
    LC: QA76.642.C49.
  4. OpenMP Architecture Review Board,
    OpenMP Application Program Interface,
    Version 3.0,
    May 2008.

Source code:


Last revised on 01 August 2020.