line2d2.h

// -*-C++-*-
// ==========================================================================
// Module libfe
// File line2d2.h
// Declaration of unstructured 2-D element class Line2D2
// (2-noded line, 1st order shape functions)
//
//
// Node arrangement:  
// -----------------          The local element has node coordinates
//                                N0 = (0,0)
//                                N1 = (1,0)
// N0+-------+N1
//                            Sides:  side 0 contains N0 
//                                    side 1 contains N1
//                         
//                    
//
// Inheritance:
// ------------
// Element
// ---> Element_Unstructured
//      ---> Element_Unstructured_2D
//           ---> Line2D2
// ==========================================================================

#ifndef __LINE2D2_H
#define __LINE2D2_H

#include "toastdef.h"

//class Surface;
static RVector tmp2(2);

class Line2D2: public Element_Unstructured_2D {
public:

    Line2D2();
    Line2D2 (const Line2D2& el);
    ~Line2D2();
    // constructors, destructor

    Element *Copy();

    void Initialise (const NodeList& nlist);

    BYTE Type () const { return ELID_LINE2D2; }
    // returns element type id

    unsigned long GetCaps () const { return ELCAPS_SUBSAMPLING; }
    // Return element capability flags

    int nNode() const { return 2; }
    // returns number of nodes per element

    int nSide () const { return 2; };
    // number of sides per element

    int nSideNode (int /*side*/) const { return 1; };
    // returns number of nodes attached to side 'side'

    int SideNode (int side, int node) const;
    // returns number of 'node'-th node of side 'side'

    double SideSize (int sd, const NodeList &nlist) const {return 0;};
    // returns length of side 'sd'

    Point Local (const NodeList& nlist, const Point& glob) const;
    // returns the local coordinate corresponding to global coordinate 'glob'

    Point NodeLocal (int node) const;
    // returns local coordinates of node 'node'
#ifdef DO_THE_REST
    int QuadRule (int order, const double **wght, const Point **absc) const;

    Point SurfToLocal (int side, const Point &p) const;
    // Map 1-D surface point p (0-1) along side 'side' into 2-D local coords

    RVector DirectionCosine (int side, RDenseMatrix &jacin);
    // returns a vector of direction cosines in global coordinates of the
    // normal to side 'side'.

    const RVector &LNormal (int side) const;

    bool GContains (const Point& glob, const NodeList& nlist) const;
    // returns TRUE if point 'glob' (in global coordinates) is within the
    // element. nlist is the mesh node coordinate list
#else
    Point SurfToLocal (int side, const Point &p) const
    { return tmp2; }
    RVector DirectionCosine (int side, RDenseMatrix &jacin)
    { return tmp2; }
    const RVector &LNormal (int side) const
    {static RVector tmp(2); return tmp;};
    bool GContains (const Point& glob, const NodeList& nlist) const
    { return false; }
  
#endif
    bool LContains (const Point& loc, bool pad = true) const;
    // returns TRUE if point 'loc' (in local coordinates of the element) is
    // within the standard triangle

    RVector LocalShapeF (const Point &loc) const;
    // vector of shape functions u_i(loc) at point 'loc' given in local
    // element coordinates

    RDenseMatrix LocalShapeD (const Point &loc) const;
    // 2x3 matrix of shape function derivatives (d u_j)/(d x_i) at point 'loc'
    // given in local element coordinates

    RVector GlobalShapeF (const NodeList& nlist, const Point& glob) const;
    // returns the shape functions for each node at a point, given in global
    // coordinates

    RDenseMatrix GlobalShapeD (const NodeList& nlist, const Point& glob) const;
    // returns derivatives of shape functions in global coordinates at point
    // `glob', given in global coordinates

    double IntF (int i) const;

    RSymMatrix IntFF () const;
    // Return integral over element of product of shape functions:
    // FF = Int_el { F_i(r) F_j(r) } dr

    double IntFF (int i, int j) const;
    // Return a single element of IntFF

    double IntFFF (int i, int j, int k) const;
    // returns a single element of integral over element of product of three
    // shape functions:
    // IntFFF = Int_el { F_i(r) * F_j(r) * F_k(r) } dr



    RSymMatrix IntPFF (const RVector& P) const;
    // Returns integral over element of product of two shape functions and a
    // function P defined on nodes:
    // PFF = Int_el { P(r) F_i(r) F_J(r) } dr
    // Vector P contains the complete nodal solution for the mesh

    double IntPFF (int i, int j, const RVector& P) const;
    // Returns a single element of IntPFF

    RVector IntFD (int i, int j) const;
    // Returns single (vector) element of FD integral over element:
    // IntFD = Int_el { F_i(r) D_j(r) } dr

    double IntFDD (int i, int j, int k) const
    { return intdd.Get(j,k) * 0.5; }
    // returns a single element of integral over element:
    // IntFDD = Int_el { F_i(r) * D_j(r) * D_k(r) } dr

    RSymMatrix IntPDD (const RVector& P) const
    { return intdd * ((P[Node[0]]+P[Node[1]])/2.0); }
    // Returns integral over element of product of two shape derivatives and a
    // function P defined in nodal basis:
    // PDD = Int_el { P(r) D_i(r) D_j(r) } dr
    // Vector P contains the complete nodal solution for the mesh

    double IntPDD (int i, int j, const RVector &P) const
    { return intdd.Get(i,j) * ((P[Node[0]]+P[Node[1]])/2.0); }
    // Returns a single element of IntPDD

    double BndIntFFSide (int i, int j, int sd)
    { ERROR_UNDEF; return 0; }

    RSymMatrix BndIntPFF (const RVector &P) const
    { return intbff * ((P[Node[0]]+P[Node[1]])/2.0); }
    // This is a hack! Really P would have to be taken into the integral,
    // rather than just averaged.

    double BndIntPFF (int i, int j, const RVector &P) const
    { return intbff.Get(i,j) * ((P[Node[0]]+P[Node[1]])/2.0); }
    // Returns a single element of BndIntPFF

    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.

    double IntFdd (int i, int j, int k, int l, int m) const;
    // Int u_i du_j/dx_l du_k/dx_m dr

    double IntPdd (const RVector &p, int j, int k, int l, int m) const;
    // Int f(r) du_j/dx_l du_k/dx_m dr
    // where f(r) is given as a nodal vector

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

    double BndIntFFSide (int i, int j, int sd);
    // Int [u_i u_j] dr along side sd

    RVector BndIntFX (int side, double (*func)(const Point&),
        const NodeList &nlist) const;
    // See element.h for description

    RVector BndIntFCos (int side, const Surface *surf, const RVector &cntcos,
        double sigma, double sup, const NodeList &nlist) const;
    // See element.h for description

    RVector BndIntFCos (int side, const RVector &cntcos, double a,
        const NodeList &nlist) const;
    // See element.h for description

    RVector BndIntFDelta (int side, const Surface *surf, const RVector &pos,
        const NodeList &nlist) const;
    // See element.h for description

    int GetLocalSubsampleAbsc (const Point *&absc) const;
    // returns abscissae in local coords for numerical integration by uniform
    // subsampling. Return value is the number of samples returned in 'absc'

    int GetBndSubsampleAbsc (int side, const Point *&absc) const;
    // abscissae for numerical integration over boundary side in local
    // coordinates of boundary element (dim-1). Use SurfToLocal to convert
    // into local element coordinates

    int GlobalIntersection (const NodeList &nlist, const Point &p1,
        const Point &p2, Point **list);
    // Same as 'Intersection' but p1 and p2 given in global coords
    // The return list however is still in local coords

    int Intersection (const Point &p1, const Point &p2, Point** pi);
    // creates a list of points where the line defined by p1 and p2 intersects
    // the element (in local coordinates) or starts/ends within the element.
    // Returns the length of the list
#else
    int GlobalIntersection (const NodeList &nlist, const Point &p1,
        const Point &p2, Point **list)
    {return 0;}
    int Intersection (const Point &p1, const Point &p2, Point** pi)
    {return 0;}
#endif
protected:

    double ComputeSize (const NodeList &nlist) const;
    // area of triangle in global coordinates

    RSymMatrix ComputeIntDD (const NodeList &nlist) const;
    // Returns integral over element of product of shape derivatives:
    // DD = Int_el { D_i(r) D_j(r) } dr

    void ComputeIntFD (const NodeList &nlist);
    // Calculates the FD integrals over the element:
    // IntFD = Int_el { F_i(r) D_j(r) } dr
#ifdef DO_THE_REST

    RSymMatrix ComputeBndIntFF (const NodeList& nlist) const;
    // Returns line integral of product of two shape functions along sides of
    // the element which belong to the mesh boundary
    // If the element does not contain any boundary sides then the returned
    // matrix is empty.
#else
    RSymMatrix ComputeBndIntFF (const NodeList& nlist) const
    { RSymMatrix tmp(2); return tmp; }
  
#endif
  //private:

    double *intfd_0, *intfd_1;
    // IntFD matrix storage

    double a0, b0, a1, b1;
    // triangle line geometry parameters

#ifdef LINE2D2_STORE_INTFF
    RSymMatrix intff;
    // stores integral over element of product of shape functions
    // Int_el { F_i(r) F_j(r) } dr
    // set by Initialise
#endif

};

#endif