Welcome to the tutorial on the fundamentals of the Nektar++ framework where we will look at how to perform Differentiation using the Nektar++ LibUtilities library. If you have not already downloaded and installed Nektar++, please do so by visiting http://www.nektar.info, where you can also find the User-Guide with the instructions on how to install the library.
This tutorial requires:
Nektar++ compiled libraries and include files compiled from source so additional code can be compiled with the framework libraries
After completing this tutorial, you should be familiar with:
The concept of differentiation using classical Gauss and Gauss-Lobatto rules in a standard interval ξ ∈ [-1,1];
Using the Nektar++ programming concepts of a NekMatrix, an Array, a
PointsKey and the PointsManager to generate Gaussian quadrature zeros and
differentiation matrices;
Differentiating in the standard segment (ξ ∈ [-1,1]) and quadrilateral region (ξ ∈ [-1,1] × [-1,1]);
The mathematical concept of mapping a general quadrilateral region to the standard region, evaluating the jacobian of this mapping and using this to evaluate a derivative in a general straight sided quadrilateral region.
Installed and tested Nektar++ v5.7.0 compiled from source. We will refer to the
directory where you installed Nektar++ as $NEKDIST for the remainder of the
tutorial.
The tutorial folder also contains:
CMakeList.txt
LocDifferentiation2D.cpp
StdDifferentiation1D.cpp
StdDifferentiation2D.cpp
Make a directory of your chosing, for example tutorial, and download the tutorial files
from fundamentals-differentiation.tar.gz into this directory.
Unpack the tutorial files by using
tar -xzvf fundamentals-differentiation.tar.gz
to produce a directory fundamentals-differentiation with subdirectories called
tutorial and complete.
Change to the
fundamentals-differentiation/tutorial
directory and configure the tutorial examples for compilation by typing the command
cmake -DCMAKE_PREFIX_PATH=$NEKDIST/build .
You should now see a file called Makefile in this directory.
Change to the
$NEKDIST/tutorial/fundamentals-differentiation/complete
directory and configure the completed version of the tutorial examples for compilation by again typing the command
cmake -DCMAKE_PREFIX_PATH=$NEKDIST/build
You should now see a file called Makefile in this directory.