NPDECODES

General Remarks

• Below, the directory . refers to the top level directory of the repository.
• Developers only work in ./developers/<ProblemName>/. From this, a corresponding directory ./homeworks/<ProblemName>/ for the students can be created automatically using ./scripts/deploy_npde.py.
• Not only the solutions, but also the corresponding templates need to compile and run without crash. So be careful when setting the solution/template tags in developers/mastersolution/.
• The bullets below are only a selection. If you spot additional issues, e.g. ugly or too complicated code, fix it.
• Names of .cc and .h files: For example the files in the folder ./developers/MyHomeworkProblem/mastersolution/ should be called myhomeworkproblem_main.cc, myhomeworkproblem_foo.cc, myhomeworkproblem_foo.h, where foo is a placeholder for any name (summarized: lowercase, split words by _).
• Only in Lehrfem exercises: Use nostd::span (C++20) instead of ForwardIteraters for iterating over objects contiguous in memory (used e.g. in Mesh::Entities(), SubEntities(), DofHandler).

Polishing

• Add comments if necessary.
• Use #include <cmath> instead of #include <math.h>.
• Only use the #includes "..." you need, e.g. for Eigen::MatrixXd, #include <Eigen/Core> is sufficient (no #include <Eigen/Dense> needed). Likewise for the dependencies.cmake. However, every file (.h and .cc) should contain all the #includes it needs, not relying on other headers to provide them silently.
• Use forward declarations to avoid #includes whenever possible.
• Make the code follow the Google style (see https://google.github.io/styleguide/cppguide.html). In particular, respect the include order (https://google.github.io/styleguide/cppguide.html#Names_and_Order_of_Includes).
• Never store data in the remote repository that is generated by the code anyway (e.g. figures). The repo should only contain source files (and maybe some mesh files).
• Provide unit tests for all functions that the students have to change.
• Plotting is done as follows: The C++ code only stores the data in a .csv file (using std::ofstream). The plotting is then done by a python script that reads this .csv file. The python script is called within the C++ code via the std::system(...) function. See e.g. BurgersEquation.

Homework Problems

Setting Up a Homework Problem

Only work in ./developers/<ProblemName>/. This folder needs to contain at least:

• CMakeLists.txt (same for every problem, so just copy-paste it from another problem)
• mastersolution/ (contains you code, with tags as described below)
• mastersolution/dependencies.cmake (contains the info needed by the build system, just mimic the ones from other problems) Every problem should contain unit test in the directory mastersolution/test/ containing the following two files:
• problemname_test.cc (contains the unit tests for your code)
• dependencies.cmake (contains the info needed by the build system, just mimic the ones from other test directories) In addition, if a problem needs to load meshes, we put them in the folder ./developers/<ProblemName>/meshes/. Finally, the line add_subdirectory(<ProblemName>) has to be added in ./developers/CMakeLists.txt.

Solution Tags

In the files of ./developers/mastersolution/ we put the following tags

#if SOLUTION
  <only in mastersolution>
#else
  <only in template>
#endif

to indicate what belongs to mastersolution and/or template. Based on these tags, the file ./scripts/deploy_npde.py generates a directory ./homeworks/<ProblemName>/ containg the directories mastersolution, mysolution, temaplates with the corresponding content. The students work exclusively in ./homeworks/<ProblemName>/.

TODO

• BoundaryWave: mysolution has core dump
• CoupledSecondOrderBVP: needs solution tags
• LaxWendroffScheme: unit test of mastersolution takes too long (Oliver)
• PointEvaluationRhs: bad includes (Liaowang)
• RadauThreeTimestepping: mysolution has core dump and mastersolution not returning same sol anymore?
• SDIRKMethodOfLines: mysolution has core dump
• SimpleLinearFiniteElements: bad includes (Amélie)

New Problems

Problems PDF: https://www.sam.math.ethz.ch/~grsam/NUMPDE/HOMEWORK/NPDEProblems.pdf

• Problem 4.1: Finite Volumes with Robin Boundary Conditions (Philippe)
• Problem 5.6: Parametric Finite Elements
• Problem 5.7: Stable Evaluation at a Point
• Problem 5.8: Trace Error Estimates (done already?)
• Problem 6.6: Non-linear Schrödinger Equation with Cubic Non-Linearity (Oliver)
• Problem 7.3: Upwind Quadrature
• Problem 7.4: Exponentially fitted upwind scheme
• Problem 7.5: Transport Problem
• Problem 7.6: Upwind Finite Volume Method