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<html>
<head>
<title>
FEM2D_HEAT_RECTANGLE_STEADY_SPMD - Codistributed Array Example for Parallel Computing Toolbox
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
FEM2D_HEAT_RECTANGLE_STEADY_SPMD <br> Codistributed Array Example for Parallel Computing Toolbox
</h1>
<hr>
<p>
<b>FEM2D_HEAT_RECTANGLE_STEADY_SPMD</b>
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.
</p>
<p>
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 <i>assemb_co.m</i> code. It contains
a line that invokes the spmd mode.
</p>
<p>
Problem data are given in <i>p_data.m</i>. In particular, the grid parameters are given by:
<pre>
param.nodesx = 51; % (=nx)
param.nodesy = 51; % (=ny)
</pre>
There will be nx*ny unknowns, and (nx-1)*(ny-1)/2 triangular elements.
</p>
<p>
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.
</p>
<p>
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.
</p>
<p>
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).
<p>
<p>
The function has the form:
<blockquote>
function zz_ss = fem2d_fun ( param )
</blockquote>
where
<ul>
<li>
param is a structure containing problem parameters;
</li>
<li>
zz_ss is a vector containing the solution; it must be reshaped
to a 2D array before plotting.
</li>
</ul>
</p>
<p>
Depending on the situation, the function could be executed in parallel:
<ul>
<li>
interactively, and locally, using the <b>matlabpool</b> command;
</li>
<li>
indirectly, and locally, using the <b>batch</b> command;
</li>
<li>
indirectly, and on the Ithaca cluster, using the <b>batch</b> command;
</li>
<li>
indirectly, and on the FSU HPC cluster, using the <b>fsuClusterMatlab</b> command;
</li>
</ul>
</p>
<h3 align = "center">
Licensing:
</h3>
<p>
The computer code and data files described and made available on this web page
are distributed under
<a href = "../../txt/gnu_lgpl.txt">the GNU LGPL license.</a>
</p>
<h3 align = "center">
Languages:
</h3>
<p>
<b>FEM2D_HEAT_RECTANGLE_STEADY_SPMD</b> is available in
<a href = "../../m_src/fem2d_heat_rectangle_steady_spmd/fem2d_heat_rectangle_steady_spmd.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../m_src/cell_detection_tasks/cell_detection_tasks.html">
CELL_DETECTION_TASKS</a>,
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.
</p>
<p>
<a href = "../../m_src/cg_distributed/cg_distributed.html">
CG_DISTRIBUTED</a>,
a MATLAB program which
implements a version of the NAS CG conjugate gradient benchmark,
using distributed memory.
</p>
<p>
<a href = "../../m_src/collatz_parfor/collatz_parfor.html">
COLLATZ_PARFOR</a>,
a MATLAB program which
seeks the maximum Collatz sequence between 1 and N,
running in parallel using MATLAB's "PARFOR" feature.
</p>
<p>
<a href = "../../m_src/contrast_spmd/contrast_spmd.html">
CONTRAST_SPMD</a>,
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.
</p>
<p>
<a href = "../../m_src/contrast2_spmd/contrast2_spmd.html">
CONTRAST2_SPMD</a>,
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.
</p>
<p>
<a href = "../../m_src/dijkstra_spmd/dijkstra_spmd.html">
DIJKSTRA_SPMD</a>,
a MATLAB program which
uses the SPMD feature to parallelize a simple example of Dijkstra's
minimum distance algorithm for graphs.
</p>
<p>
<a href = "../../m_src/face_spmd/face_spmd.html">
FACE_SPMD</a>,
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.
</p>
<p>
<a href = "../../m_src/fd2d_heat_explicit_spmd/fd2d_heat_explicit_spmd.html">
FD2D_HEAT_EXPLICIT_SPMD</a>,
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.
</p>
<p>
<a href = "../../m_src/fmincon_parallel/fmincon_parallel.html">
FMINCON_PARALLEL</a>,
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.
</p>
<p>
<a href = "../../m_src/image_denoise_spmd/image_denoise_spmd.html">
IMAGE_DENOISE_SPMD</a>,
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.
</p>
<p>
<a href = "../../m_src/linear_solve_distributed/linear_solve_distributed.html">
LINEAR_SOLVE_DISTRIBUTED</a>,
a MATLAB program which
solves a linear system <b>A*x=b</b> using MATLAB's <b>spmd</b> facility,
so that the matrix <b>A</b> is "distributed" across multiple MATLAB workers.
</p>
<p>
<a href = "../../m_src/matlab_parallel/matlab_parallel.html">
MATLAB_PARALLEL</a>,
MATLAB programs which
illustrate "local" parallel programming on a single computer
with MATLAB's Parallel Computing Toolbox.
</p>
<p>
<a href = "../../m_src/matrix_assemble_spmd/matrix_assemble_spmd.html">
MATRIX_ASSEMBLE_SPMD</a>,
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.
</p>
<p>
<a href = "../../m_src/md_parfor/md_parfor.html">
MD_PARFOR</a>,
a MATLAB program which
carries out a molecular dynamics simulation,
running in parallel using MATLAB's "PARFOR" feature.
</p>
<p>
<a href = "../../m_src/ode_sweep_parfor/ode_sweep_parfor.html">
ODE_SWEEP_PARFOR</a>,
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.
</p>
<p>
<a href = "../../m_src/oned/oned.html">
ONED</a>,
a MATLAB library which
contains functions useful for 1D finite element calculations.
</p>
<p>
<a href = "../../m_src/plot_spmd/plot_spmd.html">
PLOT_SPMD</a>,
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.
</p>
<p>
<a href = "../../m_src/prime_parfor/prime_parfor.html">
PRIME_PARFOR</a>,
a MATLAB program which
counts the number of primes between 1 and N;
running in parallel using MATLAB's "PARFOR" feature.
</p>
<p>
<a href = "../../m_src/prime_spmd/prime_spmd.html">
PRIME_SPMD</a>,
a MATLAB program which
counts the number of primes between 1 and N;
running in parallel using MATLAB's "SPMD" feature.
</p>
<p>
<a href = "../../m_src/quad_parfor/quad_parfor.html">
QUAD_PARFOR</a>,
a MATLAB program which
estimates an integral using quadrature;
running in parallel using MATLAB's "PARFOR" feature.
</p>
<p>
<a href = "../../m_src/quad_spmd/quad_spmd.html">
QUAD_SPMD</a>,
a MATLAB program which
estimates an integral using quadrature;
running in parallel using MATLAB's "SPMD" feature.
</p>
<p>
<a href = "../../m_src/quad_tasks/quad_tasks.html">
QUAD_TASKS</a>,
a MATLAB program which
estimates an integral using quadrature;
running in parallel using MATLAB's "TASK" feature.
</p>
<p>
<a href = "../../m_src/random_walk_2d_avoid_tasks/random_walk_2d_avoid_tasks.html">
RANDOM_WALK_2D_AVOID_TASKS</a>,
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.
</p>
<p>
<a href = "../../m_src/satisfy_parfor/satisfy_parfor.html">
SATISFY_PARFOR</a>,
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.
</p>
<p>
<a href = "../../m_src/subset_sum_tasks/subset_sum_tasks.html">
SUBSET_SUM_TASKS</a>,
a MATLAB program which
solves a subset sum problem by exhaustive search,
subdividing the search range among separate tasks.
</p>
<p>
<a href = "../../m_src/twod/twod.html">
TWOD</a>,
a MATLAB library which
contains functions useful for 2D finite element calculations.
</p>
<h3 align = "center">
Author:
</h3>
<p>
Gene Cliff<br>
Aerospace and Ocean Engineering / Interdisciplinary Center for Applied Mathematics,<br>
Virginia Tech.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
The User's Guide for the Parallel Computing Toolbox is available at
<a href = "http://www.mathworks.com/access/helpdesk/help/pdf_doc/distcomp/distcomp.pdf">
http://www.mathworks.com/access/helpdesk/help/pdf_doc/distcomp/distcomp.pdf</a>
</p>
<p>
<ol>
<li>
Gene Cliff,<br>
Notes on a 2D Thermal Model: an Example for MATLAB's Parallel Computing Toolbox.,<br>
<a href = "../../presentations/fem2d_heat_steady_spmd.pdf">fem2d_heat_steady_spmd.pdf</a>.
</li>
<li>
Gaurav Sharma, Jos Martin,<br>
MATLAB: A Language for Parallel Computing,<br>
International Journal of Parallel Programming,<br>
Volume 37, Number 1, pages 3-36, February 2009.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "fem2d_fun.m">fem2d_fun.m</a>,
a function which sets up the problem and returns the solution.
</li>
<li>
<a href = "fem2d_script.m">fem2d_script.m</a>,
a script which runs fem2d_fun.
</li>
<li>
<a href = "fem2d_pool.m">fem2d_pool.m</a>
runs fem2d_script interactively and locally.
</li>
<li>
<a href = "fem2d_batch_local.m">fem2d_batch_local.m</a>
runs fem2d_script indirectly and locally.
</li>
<li>
<a href = "fem2d_batch_ithaca.m">fem2d_batch_ithaca.m</a>
runs fem2d_script indirectly and on the Ithaca cluster
</li>
<li>
<a href = "fem2d_fsu.m">fem2d_fsu.m</a>
runs fem2d_fun on the FSU cluster.
</li>
</ul>
</p>
<p>
MATLAB codes:
<ul>
<li>
<a href = "assemb_co.m">assemb_co.m</a>
assemble the finite element system matrix as a codistributed array.
</li>
<li>
<a href = "boundary.m">boundary.m</a>
compute values of 2d quadratic basis functions at 1D Gauss points
along the boundary.
</li>
<li>
<a href = "extract.m">extract.m</a>
a routine for locating the nodes in node_local that correspond to
columns on the lab.
</li>
<li>
<a href = "oned_f_int.m">oned_f_int.m</a>
computes the integral of f(x) times a test function.
</li>
<li>
<a href = "oned_gauss.m">oned_gauss.m</a>
Gauss quadrature rules for 1D intervals.
</li>
<li>
<a href = "p_data.m">p_data.m</a>
sets problem parameters.
</li>
<li>
<a href = "source.m">source.m</a>
evaluates source terms.
</li>
<li>
<a href = "steps.m">steps.m</a>
evaluates a step function.
</li>
<li>
<a href = "twod_bilinear.m">twod_bilinear.m</a>
evaluates the 2D finite element integral.
</li>
<li>
<a href = "twod_f_int.m">twod_f_int.m</a>
computes the integral of f(x,y) times a test function.
</li>
<li>
<a href = "twod_gauss.m">twod_gauss.m</a>
Gauss quadrature rules for 2D regions.
</li>
<li>
<a href = "twod_shape.m">twod_shape.m</a>
evaluates test functions in 2D.
</li>
</ul>
</p>
<p>
Other files:
<ul>
<li>
<a href = "fig_ss.png">fig_ss.png</a>, an image of the steady-state solution;
</li>
<li>
<a href = "fig_1.png">fig_1.png</a>, an image of transient step 1;
</li>
<li>
<a href = "fig_2.png">fig_2.png</a>, an image of transient step 2;
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../m_src.html">
the MATLAB source codes</a>.
</p>
<hr>
<i>
Last revised on 29 March 2010.
</i>
<!-- John Burkardt -->
</body>
</html>