Setup comparison notebook and geo file

mlmc/conf/geo/ComparisonSquare.geo

+POINTS:
+0 0
+3 0
+3 3
+0 3
+CELLS:
+3 1 0 1 3
+3 1 1 2 3
+FACES:
+2 1 0 1
+2 1 1 2
+2 1 2 3
+2 1 3 0

notebooks/Comparison MLMC and SG.ipynb

 %% Cell type:markdown id: tags:
 
 # Comparison MLMC and SG
 
 %% Cell type:markdown id: tags:
 
 The aim of this project is to compare Multilevel MC methods with intrusive methods. We investigate an uncertain advection equation
 
 \begin{align}
 \partial_t u + \Omega \cdot \nabla u = 0
 \end{align}
 
 Here, $\Omega=\frac{1}{\sqrt{2}}(1,1)^T$, i.e. $\Omega$ is the unit vector into the upper right direction. The initial condition is
 
 \begin{align}
 u(t=0, x, \xi) = \frac{1}{4 \pi \cdot 0.01} \exp \left( - \frac{\Vert x - x_C(\xi) \Vert^2}{4 \cdot 0.01} \right)
 \end{align}
 
 The center point $x_C$ is unvertain and has the form
 
 \begin{align}
 x_c(\xi) = \begin{pmatrix} 0.75 \\ 0.75 \end{pmatrix} + \sigma \xi \cdot \begin{pmatrix} 1 \\ 1 \end{pmatrix}
 \end{align}
 
 We choose $\sigma = 0.1$ and the random variable $\xi$ is uniformly distributed in $[−1, 1]$. The final time at which we investigate the solution is $t_{\text{end}} = 2.0$ and the spatial domain $D$ is given by $D = [0, 3] \times [0, 3]$.
 
 %% Cell type:markdown id: tags:
 
 ### First SG Results
 
 %% Cell type:markdown id: tags:
 
 Figures 1 and 2 show first results and give a first impression of the solution.
-The results have been computed with stochastic-Galerkin (SG) using 6 moments. Note that since
+The results have been computed with stochastic-Galerkin (SG) on 92544 triangular cells using 6 moments. Note that since
 the equation is linear, the SG solution will be equivalent to the stochastic-Collocation solution.
 
-92544 Zellen
-
 %% Cell type:markdown id: tags:
 
 <img src="SG Expectation.png" alt="drawing" width="300"/> <img src="SG Variance.png" alt="drawing" width="300"/>
 
 %% Cell type:markdown id: tags:
 
 ### First MLMC Results
 
 %% Cell type:code id: tags:
 
 ``` python
 import sys
 sys.path.append('..')
 
 from python.mlmc_mppy import mpp
 from mpp.python.vtk_utilities import *
 
 import pandas as pd
 
 mpp.mute = False
 mpp.build()
 mpp.executable = "MLMC-M++"
 ```
 
+%%%% Output: stream
+
+    
+    ================ build  sprng5 ================
+    
+    -- libsprng.a found.
+    
+    ================ running cmake ================
+    
+    -- Setting prepare commit message hook to mpp
+       file: /home/niklas/CLionProjects/mlmc/mpp/doc/../../.git/modules/mpp/hooks/prepare-commit-msg
+    -- C++ version= 17
+    -- Compiler version= c++
+    -- Compiler optimization= -O0
+    -- A library with LAPACK API found.
+    -- Using SuperLU 4.0
+    -- Time independent problem
+    -- 2 dimensional problem
+    -- Only affine linear transformations
+    -- Geometric tolerance= 1e-10
+    -- is near zero= 1e-15
+    -- very large= 1e30
+    -- infinity= 1e100
+    -- Configuring done
+    -- Generating done
+    -- Build files have been written to: /home/niklas/CLionProjects/mlmc/build
+    
+    ================ running  make ================
+    
+    [  3%] Built target LIB_PS
+    [  5%] Built target gtest
+    [  7%] Built target gtest_main
+    Scanning dependencies of target MLMC
+    [  9%] Built target gmock
+    [  9%] Building CXX object mlmc/src/CMakeFiles/MLMC.dir/main/MainProgram.cpp.o
+    [ 77%] Built target SRC
+    [ 78%] Built target gmock_main
+    [ 78%] Linking CXX static library libMLMC.a
+    [ 92%] Built target MLMC
+    [ 93%] Linking CXX executable MLMC-M++
+    [ 94%] Linking CXX executable BenchmarkTransportResults
+    [ 96%] Linking CXX executable BenchmarkEllipticResults
+    [ 96%] Linking CXX executable TestMainProgram
+    [ 97%] Built target BenchmarkTransportResults
+    [ 98%] Linking CXX executable TestMultilevelPlotter
+    [ 98%] Built target TestMultilevelPlotter
+    [ 99%] Built target MLMC-M++
+    [100%] Built target TestMainProgram
+    [100%] Built target BenchmarkEllipticResults
+
 %% Cell type:code id: tags:
 
 ``` python
 mpp.reset_data()
 mpp.clean_data()
 
 mpp.run(4, config="mlmc_vs_sg")
 ```
 
+%%%% Output: stream
+
+    
+    ================ running  mpp ================
+    
+    
+    Error:
+    Assembling for Problem=StochasticInitialConditions2D with Model=DGTransport not implemented
+    
+           on proc 3
+           in /home/niklas/CLionProjects/mlmc/mlmc/src/main/MainProgram.cpp
+           on line 199
+    
+    
+    Error:
+    Assembling for Problem=StochasticInitialConditions2D with Model=DGTransport not implemented
+    
+           on proc 0
+           in /home/niklas/CLionProjects/mlmc/mlmc/src/main/MainProgram.cpp
+           on line 199
+    
+    
+    Error:
+    Assembling for Problem=StochasticInitialConditions2D with Model=DGTransport not implemented
+    
+           on proc 1
+           in /home/niklas/CLionProjects/mlmc/mlmc/src/main/MainProgram.cpp
+           on line 199
+    
+    
+    Error:
+    Assembling for Problem=StochasticInitialConditions2D with Model=DGTransport not implemented
+    
+           on proc 2
+           in /home/niklas/CLionProjects/mlmc/mlmc/src/main/MainProgram.cpp
+           on line 199
+    
+    --------------------------------------------------------------------------
+    Primary job  terminated normally, but 1 process returned
+    a non-zero exit code. Per user-direction, the job has been aborted.
+    --------------------------------------------------------------------------
+    --------------------------------------------------------------------------
+    mpirun detected that one or more processes exited with non-zero status, thus causing
+    the job to be terminated. The first process to do so was:
+    
+      Process name: [[6777,1],0]
+      Exit code:    1
+    --------------------------------------------------------------------------
+
+%%%% Output: execute_result
+
+    1
+
 %% Cell type:code id: tags:
 
 ``` python
 mpp.parse_log()
 mpp.show_convergence_results()
 mpp.show_mlmc_results()
 ```