tri6.h

// -*-C++-*-
// ==========================================================================
// Module libfe
// File tri6.h
// Declaration of class Triangle6
//
// 6-noded triangle for implementation of quadratic shape functions
//
// Node arrangement:   N2           N3 is on side 0
// -----------------    +           N4 is on side 1
//                      |\          N5 is on side 2
//                      | \         ---------------
//                      |  \        The local element has node coordinates
//                    N5+   +N4           N0 = (0,0)
//                      |    \            N1 = (1,0)
//                      |     \           N2 = (0,1)
//                      |      \          N3 = (0.5,0)
//                    N0+---+---+N1       N4 = (0.5,0.5)
//                          N3            N5 = (0,0.5)
//
// Inheritance:
// ------------
// Element
//  ---> Element_Unstructured
//       ---> Element_Unstructured_2D
//            ---> Triangle6
// ==========================================================================

#ifndef __TRI6_H
#define __TRI6_H

class FELIB Triangle6: public Element_Unstructured_2D {
public:

    Triangle6() { Node = new int[nNode()]; }
    Triangle6 (const Triangle6 &el);
    ~Triangle6() { delete []Node; }

    Element *Copy();

    void Initialise (const NodeList& nlist);

    BYTE Type() const { return ELID_TRI6; }
    unsigned long GetCaps () const { return ELCAPS_SUBSAMPLING; }
    int nNode() const { return 6; }
    int nSide() const { return 3; }
    int nSideNode (int /*side*/) const { return 3; }
    int SideNode (int side, int node) const;

    Point Local (const NodeList& nlist, const Point& glob) const;
    Point NodeLocal (int node) const;
    RVector DirectionCosine (int side, RDenseMatrix& jacin);
    const RVector &LNormal (int side) const;
    bool LContains (const Point& loc, bool pad = true) const;
    bool GContains (const Point& glob, const NodeList& nlist) const;

    RVector LocalShapeF (const Point &loc) const;
    RDenseMatrix LocalShapeD (const Point &loc) const;
    RVector GlobalShapeF (const NodeList& nlist, const Point& glob) const;
    RDenseMatrix GlobalShapeD (const NodeList& nlist, const Point& glob) const;

    double IntF (int i) const;

    RSymMatrix IntFF() const;

    double IntFF (int i, int j) const;

    double IntFFF (int i, int j, int k) const;

    RSymMatrix IntPFF (const RVector& P) const;

    double IntPFF (int i, int j, const RVector& P) const;

    RVector IntFD (int i, int j) const;

    double IntFDD (int i, int j, int k) const;

    RSymMatrix IntPDD (const RVector& P) const
    { ERROR_UNDEF; return RSymMatrix(); }

    double IntPDD (int i, int j, const RVector &P) const;

    double BndIntFSide (int i, int sd);
    double BndIntFFSide (int i, int j, int sd);

    RSymMatrix BndIntPFF (const RVector &P) const
    { ERROR_UNDEF; return RSymMatrix(); }

    double BndIntPFF (int i, int j, const RVector &P) const;

    double IntFd (int i, int j, int k) const;
    // Returns a single element of Int [u_i du_j/dx_k] dr

    double IntPd (const RVector &P, int j, int k) const;
    // Returns Int [p(r) du_j/dx_k] dr where p(r) is defined by its nodal
    // basis coefficients P.

    RSymMatrix Intdd() const;
    // returns matrix of mixed derivatives

    RVector BndIntFCos (int side, const Surface *surf, const RVector &cntcos,
        double sigma, double sup, const NodeList &nlist) const;
    RVector BndIntFCos (int side, const RVector &cntcos, double a,
        const NodeList &nlist) const;
    RVector BndIntFDelta (int side, const Surface *surf, const RVector &pos,
        const NodeList &nlist) const;
    int GetLocalSubsampleAbsc (const Point *&absc) const;
    int GlobalIntersection (const NodeList &nlist, const Point &p1,
        const Point &p2, Point **list)
    { ERROR_UNDEF; return 0; }
    int Intersection (const Point &p1, const Point &p2, Point** pi)
    { ERROR_UNDEF; return 0; }

protected:

    double ComputeSize (const NodeList &nlist) const;
    RSymMatrix ComputeIntDD (const NodeList &nlist) const;
    void ComputeIntFD (const NodeList &nlist);
    RSymMatrix ComputeBndIntFF (const NodeList& nlist) const;

    double a0, b0, c0, a1, b1, c1, a2, b2, c2;
    // triangle geometry parameters

    RDenseMatrix intfd_0, intfd_1; // IntFD storage

private:

#ifdef TRI6_STORE_INTFF
    SymMatrix intff;
    // stores integral over element of product of shape functions
    // Int_el { F_i(r) F_j(r) } dr
    // set by Initialise
#endif

};

#endif // !__TRI6_H