GeomFactors.h

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////////////////////////////////////////////////////////////////////////////////
//
//  File: GeomFactors.h
//
//  For more information, please see: http://www.nektar.info/
//
//  The MIT License
//
//  Copyright (c) 2006 Division of Applied Mathematics, Brown University (USA),
//  Department of Aeronautics, Imperial College London (UK), and Scientific
//  Computing and Imaging Institute, University of Utah (USA).
//
//  Permission is hereby granted, free of charge, to any person obtaining a
//  copy of this software and associated documentation files (the "Software"),
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//  OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
//  FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
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//
//  Description: Geometric Factors base class
//
////////////////////////////////////////////////////////////////////////////////
 
#ifndef NEKTAR_SPATIALDOMAINS_GEOMFACTORS_H
#define NEKTAR_SPATIALDOMAINS_GEOMFACTORS_H
 
#include <unordered_set>
 
#include <LibUtilities/BasicUtils/HashUtils.hpp>
#include <LibUtilities/Foundations/Basis.h>
#include <SpatialDomains/SpatialDomains.hpp>
#include <SpatialDomains/SpatialDomainsDeclspec.h>
#include <StdRegions/StdExpansion.h>
#include <StdRegions/StdRegions.hpp>
 
namespace Nektar
{
namespace SpatialDomains
{
// Forward declarations
class GeomFactors;
class Geometry;
 
typedef std::shared_ptr<Geometry> GeometrySharedPtr;
 
/// Equivalence test for GeomFactors objects
SPATIAL_DOMAINS_EXPORT bool operator==(const GeomFactors &lhs,
                                       const GeomFactors &rhs);
 
/// Pointer to a GeomFactors object.
typedef std::shared_ptr<GeomFactors> GeomFactorsSharedPtr;
/// A vector of GeomFactor pointers.
typedef std::vector<GeomFactorsSharedPtr> GeomFactorsVector;
/// An unordered set of GeomFactor pointers.
typedef std::unordered_set<GeomFactorsSharedPtr> GeomFactorsSet;
/// Storage type for derivative of mapping.
typedef Array<OneD, Array<OneD, Array<OneD, NekDouble>>> DerivStorage;
 
/// Calculation and storage of geometric factors associated with the
/// mapping from StdRegions reference elements to a given LocalRegions
/// physical element in the mesh.
class GeomFactors
{
public:
    /// Constructor for GeomFactors class.
    GeomFactors(const GeomType gtype, const int coordim,
                const StdRegions::StdExpansionSharedPtr &xmap,
                const Array<OneD, Array<OneD, NekDouble>> &coords);
 
    /// Copy constructor.
    GeomFactors(const GeomFactors &S);
 
    /// Tests if two GeomFactors classes are equal.
    SPATIAL_DOMAINS_EXPORT friend bool operator==(const GeomFactors &lhs,
                                                  const GeomFactors &rhs);
 
    /// Destructor.
    SPATIAL_DOMAINS_EXPORT ~GeomFactors();
 
    /// Return the derivative of the mapping with respect to the
    /// reference coordinates,
    /// \f$\frac{\partial \chi_i}{\partial \xi_j}\f$.
    inline DerivStorage GetDeriv(const LibUtilities::PointsKeyVector &keyTgt);
 
    /// Return the Jacobian of the mapping and cache the result.
    inline const Array<OneD, const NekDouble> GetJac(
        const LibUtilities::PointsKeyVector &keyTgt);
 
    /// Return the Laplacian coefficients \f$g_{ij}\f$.
    inline const Array<TwoD, const NekDouble> GetGmat(
        const LibUtilities::PointsKeyVector &keyTgt);
 
    /// Return the derivative of the reference coordinates with respect
    /// to the mapping, \f$\frac{\partial \xi_i}{\partial \chi_j}\f$.
    inline const Array<TwoD, const NekDouble> GetDerivFactors(
        const LibUtilities::PointsKeyVector &keyTgt);
 
    /// Returns moving frames
    inline void GetMovingFrames(const LibUtilities::PointsKeyVector &keyTgt,
                                const SpatialDomains::GeomMMF MMFdir,
                                const Array<OneD, const NekDouble> &CircCentre,
                                Array<OneD, Array<OneD, NekDouble>> &outarray);
 
    /// Returns whether the geometry is regular or deformed.
    inline GeomType GetGtype();
 
    /// Determine if element is valid and not self-intersecting.
    inline bool IsValid() const;
 
    /// Return the number of dimensions of the coordinate system.
    inline int GetCoordim() const;
 
    /// Computes a hash of this GeomFactors element.
    inline size_t GetHash();
 
protected:
    /// Type of geometry (e.g. eRegular, eDeformed, eMovingRegular).
    GeomType m_type;
    /// Dimension of expansion.
    int m_expDim;
    /// Dimension of coordinate system.
    int m_coordDim;
    /// Validity of element (Jacobian positive)
    bool m_valid;
 
    /// Principle tangent direction for MMF.
    enum GeomMMF m_MMFDir;
 
    /// Stores information about the expansion.
    StdRegions::StdExpansionSharedPtr m_xmap;
    /// Stores coordinates of the geometry.
    Array<OneD, Array<OneD, NekDouble>> m_coords;
    /// Jacobian vector cache
    std::map<LibUtilities::PointsKeyVector, Array<OneD, NekDouble>> m_jacCache;
    /// DerivFactors vector cache
    std::map<LibUtilities::PointsKeyVector, Array<TwoD, NekDouble>>
        m_derivFactorCache;
    /// Return the Xmap;
    inline StdRegions::StdExpansionSharedPtr &GetXmap();
 
private:
    /// Tests if the element is valid and not self-intersecting.
    void CheckIfValid();
 
    SPATIAL_DOMAINS_EXPORT DerivStorage
    ComputeDeriv(const LibUtilities::PointsKeyVector &keyTgt) const;
 
    /// Return the Jacobian of the mapping and cache the result.
    SPATIAL_DOMAINS_EXPORT Array<OneD, NekDouble> ComputeJac(
        const LibUtilities::PointsKeyVector &keyTgt) const;
 
    /// Computes the Laplacian coefficients \f$g_{ij}\f$.
    SPATIAL_DOMAINS_EXPORT Array<TwoD, NekDouble> ComputeGmat(
        const LibUtilities::PointsKeyVector &keyTgt) const;
 
    /// Return the derivative of the reference coordinates with respect
    /// to the mapping, \f$\frac{\partial \xi_i}{\partial \chi_j}\f$.
    SPATIAL_DOMAINS_EXPORT Array<TwoD, NekDouble> ComputeDerivFactors(
        const LibUtilities::PointsKeyVector &keyTgt) const;
 
    SPATIAL_DOMAINS_EXPORT void ComputeMovingFrames(
        const LibUtilities::PointsKeyVector &keyTgt,
        const SpatialDomains::GeomMMF MMFdir,
        const Array<OneD, const NekDouble> &CircCentre,
        Array<OneD, Array<OneD, NekDouble>> &movingframes);
 
    /// Perform interpolation of data between two point
    /// distributions.
    void Interp(const LibUtilities::PointsKeyVector &src_points,
                const Array<OneD, const NekDouble> &src,
                const LibUtilities::PointsKeyVector &tgt_points,
                Array<OneD, NekDouble> &tgt) const;
 
    /// Compute the transpose of the cofactors matrix
    void Adjoint(const Array<TwoD, const NekDouble> &src,
                 Array<TwoD, NekDouble> &tgt) const;
 
    void ComputePrincipleDirection(
        const LibUtilities::PointsKeyVector &keyTgt,
        const SpatialDomains::GeomMMF MMFdir,
        const Array<OneD, const NekDouble> &CircCentre,
        Array<OneD, Array<OneD, NekDouble>> &output);
 
    void VectorNormalise(Array<OneD, Array<OneD, NekDouble>> &array);
 
    void VectorCrossProd(const Array<OneD, const Array<OneD, NekDouble>> &v1,
                         const Array<OneD, const Array<OneD, NekDouble>> &v2,
                         Array<OneD, Array<OneD, NekDouble>> &v3);
};
 
/// A hash functor for geometric factors. Utilises
/// GeomFactors::GetHash.
struct GeomFactorsHash
{
    std::size_t operator()(GeomFactorsSharedPtr const &p) const
    {
        return p->GetHash();
    }
};
 
/**
 * @param   tpoints     Target point distributions.
 * @returns             Derivative evaluated at target point
 *                      distributions.
 * @see                 GeomFactors::ComputeDeriv
 */
inline DerivStorage GeomFactors::GetDeriv(
    const LibUtilities::PointsKeyVector &tpoints)
{
    return ComputeDeriv(tpoints);
}
 
/**
 * Returns cached value if available, otherwise computes Jacobian and
 * stores result in cache.
 *
 * @param   keyTgt      Target point distributions.
 * @returns             Jacobian evaluated at target point
 *                      distributions.
 * @see                 GeomFactors::ComputeJac
 */
inline const Array<OneD, const NekDouble> GeomFactors::GetJac(
    const LibUtilities::PointsKeyVector &keyTgt)
{
    auto x = m_jacCache.find(keyTgt);
 
    if (x != m_jacCache.end())
    {
        return x->second;
    }
 
    m_jacCache[keyTgt] = ComputeJac(keyTgt);
 
    return m_jacCache[keyTgt];
}
 
/**
 * @param   keyTgt      Target point distributions.
 * @returns             Inverse metric tensor evaluated at target point
 *                      distributions.
 * @see                 GeomFactors::ComputeGmat
 */
inline const Array<TwoD, const NekDouble> GeomFactors::GetGmat(
    const LibUtilities::PointsKeyVector &keyTgt)
{
    return ComputeGmat(keyTgt);
}
 
/**
 * Returns cached value if available, otherwise computes derivative
 * factors and stores result in cache.
 *
 * @param   keyTgt      Target point distributions.
 * @returns             Derivative factors evaluated at target point
 *                      distributions.
 * @see                 GeomFactors::ComputeDerivFactors
 */
inline const Array<TwoD, const NekDouble> GeomFactors::GetDerivFactors(
    const LibUtilities::PointsKeyVector &keyTgt)
{
    auto x = m_derivFactorCache.find(keyTgt);
 
    if (x != m_derivFactorCache.end())
    {
        return x->second;
    }
 
    m_derivFactorCache[keyTgt] = ComputeDerivFactors(keyTgt);
 
    return m_derivFactorCache[keyTgt];
}
 
inline void GeomFactors::GetMovingFrames(
    const LibUtilities::PointsKeyVector &keyTgt,
    const SpatialDomains::GeomMMF MMFdir,
    const Array<OneD, const NekDouble> &CircCentre,
    Array<OneD, Array<OneD, NekDouble>> &outarray)
{
    ComputeMovingFrames(keyTgt, MMFdir, CircCentre, outarray);
}
 
/**
 * A geometric shape is considered regular if it has constant geometric
 * information, and deformed if this information changes throughout the
 * shape.
 * @returns             The type of geometry.
 * @see GeomType
 */
inline GeomType GeomFactors::GetGtype()
{
    return m_type;
}
 
/**
 * This is greater than or equal to the expansion dimension.
 * @returns             The dimension of the coordinate system.
 */
inline int GeomFactors::GetCoordim() const
{
    return m_coordDim;
}
 
/**
 * The validity test is performed by testing if the Jacobian is
 * negative at any point in the shape.
 * @returns             True if the element is not self-intersecting.
 */
inline bool GeomFactors::IsValid() const
{
    return m_valid;
}
 
/**
 * The hash is computed from the geometry type, expansion dimension,
 * coordinate dimension and Jacobian.
 * @returns             Hash of this GeomFactors object.
 */
inline size_t GeomFactors::GetHash()
{
    LibUtilities::PointsKeyVector ptsKeys  = m_xmap->GetPointsKeys();
    const Array<OneD, const NekDouble> jac = GetJac(ptsKeys);
 
    size_t hash = 0;
    hash_combine(hash, (int)m_type, m_expDim, m_coordDim);
    if (m_type == eDeformed)
    {
        hash_range(hash, jac.begin(), jac.end());
    }
    else
    {
        hash_combine(hash, jac[0]);
    }
    return hash;
}
 
StdRegions::StdExpansionSharedPtr &GeomFactors::GetXmap(void)
{
    return m_xmap;
}
 
} // namespace SpatialDomains
} // namespace Nektar
 
#endif