# Introduction
The purpose behind this GitHub project is to showcase materials related to the final project for a graduate course TAM 574, called **Advanced Finite Element Methods**, taught by Professor Robert Haber at UIUC.
# The Project
This GitHub project contains the source code, some post-processing scripts, some videos, and the final report for my submission regarding the final project.
The final project from the course essentially revolved around building a **Space-Time Discontinuous Galerkin** (STDG) Finite Element code for solving a small system of Hyperbolic Partial Differential Equations.
When developing this code, one would aim to validate the code by finding the parabolic limit of the system of hyperbolic equations and comparing the numerical solution of this parabolic limit to the exact solution.
After the validation, the next step would be to gain an idea of the convergence of the STDG method by using some error estimators and plotting their values for various values of refinement and polynomial order within the elements.
### Comments
The report located in the **docs/** directory in the project helps to document and show the results of the analysis done for the above areas, while the source code helps show what I implemented at the time of the project to get the results within the report.
# Software and Visualization
To compile the software, just type `make` at the command line. After compilation takes place, you can then `cd` to the `bin/` directory and run the optimized executable `sim_exec` by typing `./sim_exec`. This executable needs to be run in a location where the files `GaussAbscissa.txt` and `GaussWeights.txt` exist, hence why you could start out by running it in the `bin/` directory.
After running the simulation, some `x_*`,`u_*`,`q_*` data files will be generated in the same location as where the simulation was run. You can use/modify the matlab script in `matlab/scripts/plotSolution.m` to display the final solution for each field and the space-time solution for each field using these output data files.
Note that this software has not been touched since 2013 other than to add comments or rename a couple setup variables in `main.cpp`, so the software is not as flexible as it could be. If future work was to be done, it would be great to make it possible to pass in configuration files that can specify where quadrature data is, the file paths and names for data we want to output, the polynomial basis choice, and more. As of now, things are hard coded in the executable, so one would need to manually change things either in the code or post-execution of the software.
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研究生课程TAM 574-高级有限元方法期末项目中实现的时空不连续代码【国外】.zip
共69个文件
txt:21个
cpp:10个
m:9个
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研究生课程TAM 574-高级有限元方法期末项目中实现的时空不连续代码【国外】.zip (69个子文件)
TAM574_STDG-master
.DS_Store 6KB
Makefile 1KB
movies
trial4.avi 19.6MB
trial2.avi 44.18MB
trial1.avi 42.92MB
trial3.avi 19.9MB
trial_p1.avi 15.51MB
trial_p0.avi 4.86MB
src
calculus.cpp 1KB
grid.cpp 34KB
.DS_Store 6KB
calculus.h 259B
simulation.cpp 1004B
matrix.h 2KB
shapefunctions.h 232B
cell.h 3KB
main.cpp 2KB
cell.cpp 6KB
matrix.cpp 11KB
vector.cpp 2KB
shapefunctions.cpp 837B
simulation.h 642B
vector.h 800B
grid.hpp 5KB
postprocessing.cpp 33B
postprocessing.h 93B
geometry.h 734B
geometry.cpp 318B
matlab
.DS_Store 6KB
data
q_c16.txt 2KB
x_nx100.txt 3KB
u_c4.txt 2KB
u_c2.txt 2KB
x_c16.txt 338B
x_c256.txt 338B
x_c4.txt 338B
u_nx100.txt 16KB
u_c256.txt 2KB
u_c16.txt 2KB
x_c2.txt 338B
q_c2.txt 2KB
q_c4.txt 2KB
q_nx100.txt 16KB
q_c256.txt 2KB
scripts
getSolutionData.m 323B
old_scripts
TAM574.m 534B
FiguresAt1second.m 2KB
PlotSpecificTimes.m 1KB
ConvergenceStudy.m 2KB
PlotData.m 2KB
GetData.m 1KB
ConvergePlots.m 5KB
plotSolution.m 1KB
docs
Tam574_Project Formulation_CHowardv2.pdf 377KB
bin
GaussAbscissa.txt 16KB
GaussWeights.txt 17KB
build
xcode
TAM574_STDG
.DS_Store 6KB
TAM574_STDG.xcodeproj
project.pbxproj 15KB
xcuserdata
christianjhoward.xcuserdatad
xcdebugger
Breakpoints_v2.xcbkptlist 1KB
xcschemes
xcschememanagement.plist 483B
TAM574_STDG.xcscheme 3KB
project.xcworkspace
contents.xcworkspacedata 156B
xcuserdata
christianjhoward.xcuserdatad
UserInterfaceState.xcuserstate 42KB
GaussAbscissa.txt 16KB
TAM574_STDG
GaussAbscissa.txt 16KB
GaussWeights.txt 17KB
GaussWeights.txt 17KB
README.md 3KB
纵向毕业季.bmp 2.79MB
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