Commit 6312d7fa authored by niklas.baumgarten's avatar niklas.baumgarten
Browse files

Setup comparison notebook and geo file

parent 5d272a9f
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%% 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()
```
......
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