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This repository contains the codes for the homework problems of the recurring courseNumerical Methods for Partial Differential Equations atETH Zurich. The course treats finite element methods (FEMs) using the C++ libraryLehrFEM++ and relies on the following material:

• lecture notes
• homework problems

Moreover, enrolled students can access themoodle page of the course.

Currently, only UNIX based operating systems are supported. Moreover, you need to have the following installed on your machine:

• C++17 compiler (e.g. gcc, clang)
• CMake (at least VERSION 3.10)
• python3
• A reader for .vtk files (e.g. paraview)
• git (not strictly needed, you could also download the repo as .zip file)

This section is suited only for your own computer. To build the codes on the student computers of ETH see below. Open a terminal and type

git clone git@github.com:erickschulz/NPDECODES.gitcd NPDECODES/mkdir buildcd build/cmake ..

This will install LehrFEM++ and its dependencies into a folder~/.hunter/. To build a specific problem, sayTestQuadratureRules, proceed as follows:

cd homeworks/TestQuadratureRules/make

This will build from the source files inNPDECODES/homeworks/TestQuadratureRules/, where the subfoldermysolution/ contains templates to be changed by the students. Recompilation is done by invokingmake again. The following executables are generated:

• ./TestQuadratureRules_mastersolution: Runs the mastersolution.
• ./TestQuadratureRules_test_mastersolution: Runs unit tests on all important functions of the mastersolution.
• ./TestQuadratureRules_mysolution: Runs the students code, i.e. the one inmysolution/.
• ./TestQuadratureRules_test_mysolution: Runs unit tests the students code, i.e. the one inmysolution/.

There is two folders calledhomeworks/. One contains the source files and one contains the executables:

.├── build (was created by you)│   ├── homeworks│   :   ├── TestQuadratureRules│       :   ├── TestQuadratureRules_mastersolution      (executable)│           ├── TestQuadratureRules_mysolution          (executable)│           ├── TestQuadratureRules_test_mastersolution (executable)│           ├── TestQuadratureRules_test_mysolution     (executable)│           :│├── homeworks:   ├── TestQuadratureRules    :   ├── mastersolution (folder containing source files)        ├── mysolution     (folder containing source files, to be modified by you)        ├── templates      (folder containing source files)        :

LehrFEM++ is already installed on the linux student computers in the ETH main building. You can even use them remotely by typing in your terminal

ssh -X <nethz_username>@slab1.ethz.ch

where<nethz_username> has the be replaced by your ETH username. To set up your local repository on the student computers, type:

cd /tmpgit clone git@github.com:erickschulz/NPDECODES.gitmv NPDECODES ~cd ~/NPDECODESmkdir buildcd buildexport HUNTER_ROOT=/opt/libs/NumPDEcmake ..

The first four lines are due to limited resources on the student computers. Setting the environment variableHUNTER_ROOT tells CMake where to look for the preinstalled libraries. This environment variable is local to your terminal, i.e. has to be redefined if you start a new terminal. Apart from this, you can use the folder~/NPDECODES in the same way you would for the approach in the previous section. However, you have only very little memory available on the student computers. We therefore recommend to only build one problem at a time.

Mac users, after updating to macOS Catalina 10.15.4, are receiving this error. The workaround is as follows: Navigate your terminal into the folderNPDECODES/ and type:

brew install gcc@8    #install gcc version 8, needs brew to be installed first...gcc-8 --version       #check if gcc-8 was installed properlyg++-8 --version       #check if g++-8 was installed properlyrm -rf build          #delete the old build foldermkdir build           #recreate it

If this has succeeded, you need to build the codes using the gcc compiler by defining the environment variablesCC andCXX. This is done by navigating a terminal intoNPDECODES/build/ and running:

export CC=gcc-8export CXX=g++-8cmake ..

If the installation is successful, you can than build your codes usingmake as before. Note that the gcc version under OSX usulally just links to clang. However, the procedure above installs the actual gcc compiler.