Nektar++: Enhancing the capability and application of high-fidelity spectral/hp element methods

David Moxey*, Chris D. Cantwell, Yan Bao, Andrea Cassinelli, Giacomo Castiglioni, Sehun Chun, Emilia Juda, Ehsan Kazemi, Kilian Lackhove, Julian Marcon, Gianmarco Mengaldo, Douglas Serson, Michael Turner, Hui Xu, Joaquim Peiró, Robert M. Kirby, Spencer J. Sherwin

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

24 Citations (Scopus)


Nektar++ is an open-source framework that provides a flexible, high-performance and scalable platform for the development of solvers for partial differential equations using the high-order spectral/hp element method. In particular, Nektar++ aims to overcome the complex implementation challenges that are often associated with high-order methods, thereby allowing them to be more readily used in a wide range of application areas. In this paper, we present the algorithmic, implementation and application developments associated with our Nektar++ version 5.0 release. We describe some of the key software and performance developments, including our strategies on parallel I/O, on in situ processing, the use of collective operations for exploiting current and emerging hardware, and interfaces to enable multi-solver coupling. Furthermore, we provide details on a newly developed Python interface that enables a more rapid introduction for new users unfamiliar with spectral/hp element methods, C++ and/or Nektar++. This release also incorporates a number of numerical method developments – in particular: the method of moving frames (MMF), which provides an additional approach for the simulation of equations on embedded curvilinear manifolds and domains; a means of handling spatially variable polynomial order; and a novel technique for quasi-3D simulations (which combine a 2D spectral element and 1D Fourier spectral method) to permit spatially-varying perturbations to the geometry in the homogeneous direction. Finally, we demonstrate the new application-level features provided in this release, namely: a facility for generating high-order curvilinear meshes called NekMesh; a novel new AcousticSolver for aeroacoustic problems; our development of a ‘thick’ strip model for the modelling of fluid–structure interaction (FSI) problems in the context of vortex-induced vibrations (VIV). We conclude by commenting on some lessons learned and by discussing some directions for future code development and expansion. Program summary: Program Title: Nektar++ Program Files doi: Code Ocean Capsule: Licensing provisions: MIT Programming language: C++ External routines/libraries: Boost, METIS, FFTW, MPI, Scotch, PETSc, TinyXML, HDF5, OpenCASCADE, CWIPI Nature of problem: The Nektar++ framework is designed to enable the discretisation and solution of time-independent or time-dependent partial differential equations. Solution method: spectral/hp element method

Original languageEnglish
Article number107110
Publication statusPublished - Apr 2020


  • High-order finite element methods
  • Nektar++
  • Spectral/hp element methods


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