README.md

stochasticPoisson : based on the article "Multilevel Scalable Solvers for Stochastic Linear and Nonlinear Problems" (https://arxiv.org/abs/2310.14649)

Linear and Nonlinear Poisson problems with diffusion coefficient modelled as random process solved using multilevel domain decomposition-based methods.

Folder Structure

1. poisson/NLPoisson : Codes and files related to stochastic linear Poisson problem
2. poisson/kledata : Multiplication tensors required for running the stochastic code
3. poisson/macro_0X_DX : pre generated macros to run the main code for different number random variables and order of expansion. can be copied over to macros folder while running.
4. poisson/macros : current generated macros for the problem
5. poisson/output : outputs with .vtu files
6. poisson/cluster : files required for running the code in cluster

Software needed

1. FreeFEM : Installation instructions for FreeFEM in Digital Alliance of Canada clusters is given in ./cluster/install_FreeFEM.txt
2. Paraview
3. g++
4. MATLAB

Instructions to run stochastic Poisson in cluster

1. Install the FreeFEM package as detailed in : ./cluster/install_FreeFEM.txt

2. Use the instructions inside ./cluster/instructions_parallel.txt for compiling the code interactively or by submitting a batch script.

3. A batch script is provided inside ./cluster/runff_beluga_withparam.sh. Note that, you need to change the path to your installation and filename accordingly.

Instructions to run stochastic Poisson in user machine

1. run the preprocessing step first, sequentially - single core.

    1.1 FreeFem++ generate.edp -nRV 2 -ordOUT 3
   
    output files are created inside ./macro/
               ssinit.edp
      ssolution.edp
      ssweakform1.edp
      ssweakform2.edp
   
      1.2 Change the values of random parameters inside "weakformL.cpp/weakformNL.cpp" according to the "ssinit.edp" values.
   
    	int ordIN = 2;
    	int nRV = 3;
    		int ordOUT = 3;
   
    
    1.3 g++ weakformNL.cpp
    1.4 ./a.out
   
    output :
        td has 730 elements
        finished initial part of ssweakcomp.edp
         j 0 k 0 l 0
         j 1 k 0 l 0
         j 2 k 0 l 0
         j 3 k 0 l 0
         j 4 k 0 l 0
         j 5 k 0 l 0
         j 0 k 1 l 0
         j 1 k 1 l 0
         j 2 k 1 l 0
         .........
         ........
         ........
   
    1.5 cd -
   

2. run the main code

       2.1 ff-mpirun -n 4 poissonNL_process2L.edp -m 50 -n 50
   
   
     output :
   
   
        Number of Vertices for coarse grid  2601
        Number of Vertices for fine mesh is  10201
        3
            -111111   2   3
        number of random variable  2
        order of input  2
        order of output  3
        Number of input PC   6
        Number of output PC  10
        Mean of Gaussian  0
        Sd of Gaussian  0.1
        Size of linear System  102010
        sindex is 25 2
               1   1
               1   2
               2   1
               2   2
               1   3
               3   1
   

3. .vtu files inside ./output folder.

Please cite the article and the repository if you use this code