The Nektar++ library

Nektar++ is an open source software library currently being developed and designed to provide a toolbox of data structures and algorithms which implement the spectral/hp element method. Nektar++ is the continuation and adaptation of the Nektar flow solver. As opposed to its predecessor which focused on solving fluid dynamics problems, Nektar++ is implemented as a C++ object-oriented toolkit which allows developers to implement spectral element solvers for a variety of different engineering problems.

The structure of the Nektar++ library, a collection of different sublibraries, is based upon the typical structure of a global spectral/hp approximation, which is characterized by:

  • The elemental decomposition of the problem
    As for all finite element methods, the computational domain is partitioned into a mesh of many small subdomains or elements. Analogously, the spectral/hp solution is expanded into a series of local expansions, each with support on a single element. This elemental representation enables the treatment of operations on a local elemental basis rather than on global level. This not only simplifies the formulation but also allows many operations to be performed more efficiently.
  • The introduction of a standard region
    The introduction of a standard region allows the expansion basis to be defined just once, that is only on the standard region. All other elements then can be considered as the image of the standard element under a parametric mapping. Consequently, the elemental operations of integration and differentiation can all be executed on the standard element, subject to a proper treatment of the transformation from local (world space) to standard (reference space) coordinates. For curved-sided elements, the mapping from standard element to local element is generally done using an iso-parametric representation. In this case, the local geometry is represented with an expansion of the same form and polynomial order as the unknown variables.

This structure, supplemented with building blocks such as block matrix linear algebra routines and automatic data coordinating objects, can be encapsulated in an efficient object-oriented C++ implementation.

This conceptual approach of the software leads to a high user-flexibility, including the selection of the preferred expansion basis, its polynomial order and the preferred numerical quadrature.

The website of the Nektar++ project can be found on: