oomph::OneDimHermite Namespace Reference

One Dimensional Hermite shape functions. More...

Functions
void	shape (const double &s, double Psi[2][2])
	Constructor sets the values of the shape functions at the position s. More...
void	dshape (const double &s, double DPsi[2][2])
	Derivatives of 1D Hermite shape functions. More...
void	d2shape (const double &s, double DPsi[2][2])
	Second derivatives of the Hermite shape functions. More...

Detailed Description

One Dimensional Hermite shape functions.

Function Documentation

d2shape()

void oomph::OneDimHermite::d2shape ( const double &  s, double  DPsi[2][2]  )

inline

Second derivatives of the Hermite shape functions.

    {
      // Node 0
      DPsi[0][0] = 1.5 * s;
      DPsi[0][1] = 0.5 * (3.0 * s - 1.0);
      // Node 1
      DPsi[1][0] = -1.5 * s;
      DPsi[1][1] = 0.5 * (3.0 * s + 1.0);
    }

References s.

Referenced by oomph::QHermiteElement< DIM >::d2shape_local().

dshape()

void oomph::OneDimHermite::dshape ( const double &  s, double  DPsi[2][2]  )

inline

Derivatives of 1D Hermite shape functions.

    {
      // Node 0
      DPsi[0][0] = 0.75 * (s * s - 1.0);
      DPsi[0][1] = 0.25 * (3.0 * s * s - 2.0 * s - 1.0);
      // Node 1
      DPsi[1][0] = 0.75 * (1.0 - s * s);
      DPsi[1][1] = 0.25 * (3.0 * s * s + 2.0 * s - 1.0);
    }

References s.

Referenced by oomph::QHermiteElement< DIM >::d2shape_local(), oomph::QHermiteElement< DIM >::dshape_local(), and oomph::DShape::operator=().

shape()

void oomph::OneDimHermite::shape ( const double &  s, double  Psi[2][2]  )

inline

Constructor sets the values of the shape functions at the position s.

    {
      // Node 0
      Psi[0][0] = 0.25 * (s * s * s - 3.0 * s + 2.0);
      Psi[0][1] = 0.25 * (s * s * s - s * s - s + 1.0);
      // Node 1
      Psi[1][0] = 0.25 * (2.0 + 3.0 * s - s * s * s);
      Psi[1][1] = 0.25 * (s * s * s + s * s - s - 1.0);
    }

References s.

Referenced by oomph::QHermiteElement< DIM >::d2shape_local(), oomph::QHermiteElement< DIM >::dshape_local(), oomph::Shape::operator=(), and oomph::QHermiteElement< DIM >::shape().