FEM2D_HEAT_RECTANGLE_STEADY_SPMD
Codistributed Array Example for Parallel Computing Toolbox


FEM2D_HEAT_RECTANGLE_STEADY_SPMD is a MATLAB program which demonstrates how the linear system associated with a finite element problem can be treated as a codistributed array whose entries are assigned to different MATLAB workers, so that the matrix is assembled in parallel, by Gene Cliff.

The program produces an approximate (steady-state) solution to a heat equation on a rectangular domain. The code uses the MATLAB Parallel Computing Toolbox's Single Program Multiple Data (spmd) mode. A matrix assembly step is carried out by the assemb_co.m code. It contains a line that invokes the spmd mode.

Problem data are given in p_data.m. In particular, the grid parameters are given by:

        param.nodesx =   51; % (=nx)
        param.nodesy =   51; % (=ny)
      
There will be nx*ny unknowns, and (nx-1)*(ny-1)/2 triangular elements.

This code uses the ILU preconditioner and the GMRES solver to solve the linear system. These routines are currently not 'overloaded' for codistributed arrays, so we 'gather' the required arrays on lab #1. We expect that GMRES (at least) will be overloaded to handle codistributed arrays in upcoming releases of the software.

The code produces a collection of ASCII text files (outj, one for each lab). These files contain brief information about the columns of an FEM matrix assembled on that lab, and on what fraction of the elements were evaluated.

This code uses the 'backslash' operator \ (mldivide or matrix-left-divide) on codistributed array(s). Unfortunately, while mldivide has been overloaded for codistributed arrays, it is not (yet ?) available for arrays with the 'sparse' attribute. Thus, the arrays are converted to 'full' before the solve step(s).

The function has the form:

function zz_ss = fem2d_fun ( param )
where

Depending on the situation, the function could be executed in parallel:

Licensing:

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

Languages:

FEM2D_HEAT_RECTANGLE_STEADY_SPMD is available in a MATLAB version.

Related Data and Programs:

CELL_DETECTION_TASKS, a MATLAB program which creates modified versions of a sequence of gray-scale TIF files containing images of cells; the process of each file is carried out independently, using the "task" feature of MATLAB's parallel computing toolbox.

CG_DISTRIBUTED, a MATLAB program which implements a version of the NAS CG conjugate gradient benchmark, using distributed memory.

COLLATZ_PARFOR, a MATLAB program which seeks the maximum Collatz sequence between 1 and N, running in parallel using MATLAB's "PARFOR" feature.

CONTRAST_SPMD, a MATLAB program which demonstrates the SPMD parallel programming feature for image operations; the client reads an image, the workers increase contrast over separate portions, and the client assembles and displays the results.

CONTRAST2_SPMD, a MATLAB program which demonstrates the SPMD parallel programming feature for image operations; this improves the contrast_spmd program by allowing the workers to share some data; this makes it possible to eliminate artificial "seams" in the processed image.

DIJKSTRA_SPMD, a MATLAB program which uses the SPMD feature to parallelize a simple example of Dijkstra's minimum distance algorithm for graphs.

FACE_SPMD, a MATLAB program which demonstrates the SPMD parallel programming feature; the client has a 3D box that has been dissected into tetrahedrons. Multiple workers cooperate to construct a list of the triangular faces that lie on the boundaries of the box.

FD2D_HEAT_EXPLICIT_SPMD, a MATLAB program which uses the finite difference method and explicit time stepping to solve the time dependent heat equation in 2D. A black and white image is used as the "initial condition". MATLAB's SPMD facility is used to carry out the computation in parallel.

FMINCON_PARALLEL, a MATLAB program which demonstrates the use of MATLAB's FMINCON constrained minimization function, taking advantage of MATLAB's Parallel Computing Toolbox for faster execution.

IMAGE_DENOISE_SPMD, a MATLAB program which demonstrates the SPMD parallel programming feature for image operations; the client reads an image, the workers process portions of it, and the client assembles and displays the results.

LINEAR_SOLVE_DISTRIBUTED, a MATLAB program which solves a linear system A*x=b using MATLAB's spmd facility, so that the matrix A is "distributed" across multiple MATLAB workers.

MATLAB_PARALLEL, MATLAB programs which illustrate "local" parallel programming on a single computer with MATLAB's Parallel Computing Toolbox.

MATRIX_ASSEMBLE_SPMD, a MATLAB program which demonstrates the SPMD parallel programming feature by having each worker assemble part of the Hilbert matrix, which is then combined into one array by the client program.

MD_PARFOR, a MATLAB program which carries out a molecular dynamics simulation, running in parallel using MATLAB's "PARFOR" feature.

ODE_SWEEP_PARFOR, a MATLAB program which demonstrates how the PARFOR command can be used to parallelize the computation of a grid of solutions to a parameterized system of ODE's.

ONED, a MATLAB library which contains functions useful for 1D finite element calculations.

PLOT_SPMD, a MATLAB library which demonstrates the SPMD parallel programming feature, by having a number of labs compute parts of a sine plot, which is then displayed by the client process.

PRIME_PARFOR, a MATLAB program which counts the number of primes between 1 and N; running in parallel using MATLAB's "PARFOR" feature.

PRIME_SPMD, a MATLAB program which counts the number of primes between 1 and N; running in parallel using MATLAB's "SPMD" feature.

QUAD_PARFOR, a MATLAB program which estimates an integral using quadrature; running in parallel using MATLAB's "PARFOR" feature.

QUAD_SPMD, a MATLAB program which estimates an integral using quadrature; running in parallel using MATLAB's "SPMD" feature.

QUAD_TASKS, a MATLAB program which estimates an integral using quadrature; running in parallel using MATLAB's "TASK" feature.

RANDOM_WALK_2D_AVOID_TASKS, a MATLAB program which computes many self avoiding random walks in 2D by creating a job which defines each walk as a task, and then computes these independently using MATLAB's Parallel Computing Toolbox task computing capability.

SATISFY_PARFOR, a MATLAB program which demonstrates, for a particular circuit, an exhaustive search for solutions of the circuit satisfiability problem, running in parallel using MATLAB's "PARFOR" feature.

SUBSET_SUM_TASKS, a MATLAB program which solves a subset sum problem by exhaustive search, subdividing the search range among separate tasks.

TWOD, a MATLAB library which contains functions useful for 2D finite element calculations.

Author:

Gene Cliff
Aerospace and Ocean Engineering / Interdisciplinary Center for Applied Mathematics,
Virginia Tech.

Reference:

The User's Guide for the Parallel Computing Toolbox is available at http://www.mathworks.com/access/helpdesk/help/pdf_doc/distcomp/distcomp.pdf

  1. Gene Cliff,
    Notes on a 2D Thermal Model: an Example for MATLAB's Parallel Computing Toolbox.,
    fem2d_heat_steady_spmd.pdf.
  2. Gaurav Sharma, Jos Martin,
    MATLAB: A Language for Parallel Computing,
    International Journal of Parallel Programming,
    Volume 37, Number 1, pages 3-36, February 2009.

Source Code:

MATLAB codes:

Other files:

You can go up one level to the MATLAB source codes.


Last revised on 29 March 2010.