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mainpage.h
Go to the documentation of this file.
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/**
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* @mainpage The Nektar++ library
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*
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* Nektar++ is an open source software
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* library currently being developed and designed to provide a toolbox
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* of data structures and algorithms which implement the spectral/hp
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* element method. Nektar++ is the continuation and adaptation of the
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* <A
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* HREF="http://www2.imperial.ac.uk/ssherw/spectralhp/nektar">Nektar</A>
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* flow solver. As opposed to its predecessor which focused on solving
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* fluid dynamics problems, Nektar++ is implemented as a C++
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* object-oriented toolkit which allows developers to implement
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* spectral element solvers for a variety of different engineering
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* problems.
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*
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* The structure of the Nektar++ library, a collection of different
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* sublibraries, is based upon the typical structure of a global
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* spectral/hp approximation, which is characterized by:
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* - <b>The elemental decomposition of the problem</b><BR> As for all finite
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* element methods, the computational domain is partitioned into a
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* mesh of many small subdomains or elements. Analogously, the
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* spectral/hp solution is expanded into a series of local expansions,
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* each with support on a single element. This elemental
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* representation enables the treatment of operations on a local
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* elemental basis rather than on global level. This not only
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* simplifies the formulation but also allows many operations to be
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* performed more efficiently.
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* - <b>The introduction of a standard region</b><BR>
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* The introduction of a standard region allows the
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* expansion basis to be defined just once, that is only on the
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* standard region. All other elements then can be considered as the
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* image of the standard element under a parametric
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* mapping. Consequently, the elemental operations of integration and
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* differentiation can all be executed on the standard element,
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* subject to a proper treatment of the transformation from local
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* (world space) to standard (reference space) coordinates. For
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* curved-sided elements, the mapping from standard element to local
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* element is generally done using an <em>iso-parametric</em>
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* representation. In this case, the local geometry is represented
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* with an expansion of the same form and polynomial order as the
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* unknown variables.
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*
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* This structure, supplemented with building blocks such as block
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* matrix linear algebra routines and automatic data coordinating
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* objects, can be encapsulated in an efficient object-oriented C++
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* implementation.
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*
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* This conceptual
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* approach of the software leads to a high user-flexibility,
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* including the selection of the preferred expansion basis, its
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* polynomial order and the preferred numerical quadrature.
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*
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* The website of the Nektar++ project can be found on: http://www.nektar.info
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*/
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