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Structure.h
Go to the documentation of this file.
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/**
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* \page pageStructure Structure
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A major challenge which arises when one aims to develop a software
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package that implements the spectral/hp element method is to implement
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the mathematical structure of the method in a digestible and coherent
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matter. Obviously, there are many ways to encapsulate the fundamental
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concepts related to the spectral/hp element method, depending on e.g.
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the intended goal of the developer or the chosen programming
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language. We will (without going in too much
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detail) give a an overview of how we have chosen to abstract and
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implement spectral/hp elements in the \a Nektar++ library.
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However, we want to emphasise that this is not the only possible choice.
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Five different sublibraries, employing this characteristic pattern,
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are provided in the full \a Nektar++ library:
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- the standard elemental region sublibrary (@link Nektar#StdRegions StdRegions @endlink library)
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- the parametric mapping sublibrary (@link Nektar#SpatialDomains SpatialDomains @endlink library)
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- the local elemental region sublibrary (@link Nektar#LocalRegions LocalRegions @endlink library)
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- the global region sublibrary (@link Nektar#MultiRegions MultiRegions @endlink library)
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- the supporting utilities sublibrary (@link Nektar#LibUtilities LibUtilities @endlink library)
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This structure can also be related to the formulation of a global
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spectral/hp element expansion, i.e.
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\f[
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u(\boldsymbol{x})=\overbrace{\sum_{e\in\mathcal{E}}\underbrace{\sum_{n\in\mathcal{N}}\phi^e_n(\boldsymbol{x})\hat{u}^e_n}_{\mbox{\scriptsize{LocalRegions library}}}}^{\mbox{\scriptsize{MultiRegions library}}}=\sum_{e\in\mathcal{E}}\underbrace{\sum_{n\in\mathcal{N}}\phi^{std}_n\overbrace{(\left[\chi^e\right]^{-1}(\boldsymbol{x}))}^{\mbox{\scriptsize{SpatialDomains library}}}\hat{u}^e_n}_{\mbox{\scriptsize{StdRegions library}}}.
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\f]
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A more detailed overview of the \a Nektar++ structure, including an
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overview of the most important classes per sublibrary, is depicted in
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the figure below.
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* \image html overview.png "Main structure of \a Nektar++"
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*/
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