Nektar++

A major challenge which arises when one aims to develop a software package that implements the spectral/hp element method is to implement the mathematical structure of the method in a digestible and coherent matter. Obviously, there are many ways to encapsulate the fundamental concepts related to the spectral/hp element method, depending on e.g. the intended goal of the developer or the chosen programming language. We will (without going in too much detail) give a an overview of how we have chosen to abstract and implement spectral/hp elements in the Nektar++ library. However, we want to emphasise that this is not the only possible choice.
Five different sublibraries, employing this characteristic pattern, are provided in the full Nektar++ library:
This structure can also be related to the formulation of a global spectral/hp element expansion, i.e.
A more detailed overview of the Nektar++ structure, including an overview of the most important classes per sublibrary, is depicted in the figure below.