JTB_CODIST 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.
The program produces an approximate (steady-state) solution to a heat equation on a rectangular domain (see 2D_heat_ex.pdf for details). 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 and this line must be visible (i.e. not a commented line).
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.
To run this code begin by opening a matlabpool (assuming one os not running), then issue the command run_spmd. The Command Window should look like this:
>> matlabpool open 'local' 2 Starting matlabpool using the parallel configuration 'local'. Waiting for parallel job to start... Connected to a matlabpool session with 2 labs. >> run_spmd Elapsed time is 1.570656 seconds. gmres(200) converged at outer iteration 1 (inner iteration 70) to a solution with relative residual 7.4e-07 Elapsed time is 2.413968 seconds. >>
run_pmode.m performs the same overall task as run_spmd.m but uses the MATLAB Parallel Computing Toolbox interactive pmode interface. In this case the spmd command in assemb_co.m must be commented out. Problem data are specified as above.
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).
Here we output plots of the steady-state solution, and the state for transient step 1 and transient step 2.
For this run, first 'comment out' the spmd line (62) in assemb_co.m. Then initiate
PMODE (pmode start 2). Check to be sure you're in the correct directory, else use
'cd' appropriately. In the PMODE window type run_pmode
Gene Cliff, Aerospace and Ocean Engineering / Interdisciplinary Center for Applied Mathematics, Virginia Tech.
The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.
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You can go up one level to the MATLAB source codes.