#include <ElemUtil.hpp>

Inheritance diagram for moab::Element::SpectralQuad:

Collaboration diagram for moab::Element::SpectralQuad:

Public Member Functions
	SpectralQuad (const std::vector< CartVect > &vertices)

	SpectralQuad (int order, double x, double y, double *z)

	SpectralQuad (int order)

	SpectralQuad ()

virtual	~SpectralQuad ()

void	set_gl_points (double x, double y, double *z)

virtual CartVect	evaluate (const CartVect &xi) const
	Evaluate the map on $x_i$ (calculate $\vec x = F($\vec \xi)$ ) More...

virtual CartVect	ievaluate (const CartVect &x, double tol=1e-6, const CartVect &x0=CartVect(0.0)) const
	Evaluate the inverse map (calculate $\vec \xi = F^-1($\vec x)$ to given tolerance) More...

virtual Matrix3	jacobian (const CartVect &xi) const
	Evaluate the map's Jacobi matrix. More...

double	evaluate_scalar_field (const CartVect &xi, const double *field_vertex_values) const
	Evaluate a scalar field at a point given field values at the vertices. More...

double	integrate_scalar_field (const double *field_vertex_values) const
	Integrate a scalar field over the element given field values at the vertices. More...

bool	inside_nat_space (const CartVect &xi, double &tol) const
	decide if within the natural param space, with a tolerance More...

void	Init (int order)

void	freedata ()

void	compute_gl_positions ()

void	get_gl_points (double &x, double &y, double *&z, int &size)

Public Member Functions inherited from moab::Element::Map
	Map (const std::vector< CartVect > &v)
	Construct a Map defined by the given std::vector of vertices. More...

	Map (const unsigned int n)
	Construct a Map defined by n vertices. More...

virtual	~Map ()

virtual Matrix3	ijacobian (const CartVect &xi) const
	Evaluate the inverse of the Jacobi matrix. More...

virtual double	det_jacobian (const CartVect &xi) const
	Evaluate the determinate of the Jacobi matrix. More...

virtual double	det_ijacobian (const CartVect &xi) const
	Evaluate the determinate of the inverse Jacobi matrix. More...

unsigned int	size ()
	Size of the vertices vector. More...

const std::vector< CartVect > &	get_vertices ()
	Retrieve vertices. More...

virtual void	set_vertices (const std::vector< CartVect > &v)
	Set vertices. More...

virtual bool	inside_box (const CartVect &xi, double &tol) const

Protected Attributes
realType *	_xyz [3]

Protected Attributes inherited from moab::Element::Map
std::vector< CartVect >	vertex

Static Protected Attributes
static int	_n

static realType *	_z [2]

static lagrange_data	_ld [2]

static opt_data_2	_data

static realType *	_odwork

static bool	_init = false

static realType *	_glpoints

Detailed Description

Definition at line 421 of file ElemUtil.hpp.

Constructor & Destructor Documentation

◆ SpectralQuad() [1/4]

moab::Element::SpectralQuad::SpectralQuad ( const std::vector< CartVect > & vertices )

inline

Definition at line 424 of file ElemUtil.hpp.

                                                               : Map( vertices )
         {
             _xyz[0] = _xyz[1] = _xyz[2] = NULL;
         };

References _xyz.

◆ SpectralQuad() [2/4]

moab::Element::SpectralQuad::SpectralQuad	(	int	order,
		double *	x,
		double *	y,
		double *	z
	)

Definition at line 18 of file SpectralQuad.cpp.

                                                                        : Map( 0 )
 {
     Init( order );
     _xyz[0] = x;
     _xyz[1] = y;
     _xyz[2] = z;
 }

References _xyz, and Init().

◆ SpectralQuad() [3/4]

moab::Element::SpectralQuad::SpectralQuad ( int order )

Definition at line 25 of file SpectralQuad.cpp.

                                       : Map( 4 )
 {
     Init( order );
     _xyz[0] = _xyz[1] = _xyz[2] = NULL;
 }

References _xyz, and Init().

◆ SpectralQuad() [4/4]

moab::Element::SpectralQuad::SpectralQuad ( )

Definition at line 16 of file SpectralQuad.cpp.

16 : Map( 0 ) {}

◆ ~SpectralQuad()

moab::Element::SpectralQuad::~SpectralQuad ( )

virtual

Definition at line 30 of file SpectralQuad.cpp.

 {
     if( _init ) freedata();
     _init = false;
 }

References _init, and freedata().

Member Function Documentation

◆ compute_gl_positions()

void moab::Element::SpectralQuad::compute_gl_positions ( )

Definition at line 1367 of file ElemUtil.cpp.

     {
         // will need to use shape functions on a simple linear quad to compute gl points
         // so we know the position of gl points in parametric space, we will just compute those
         // from the 3d vertex position (corner nodes of the quad), using simple mapping
         assert( this->vertex.size() == 4 );
         static double corner_xi[4][2] = { { -1., -1. }, { 1., -1. }, { 1., 1. }, { -1., 1. } };
         // we will use the cached lobatto nodes in parametric space _z[d] (the same in both
         // directions)
         int indexGL = 0;
         int n2      = _n * _n;
         for( int i = 0; i < _n; i++ )
         {
             double eta = _z[0][i];
             for( int j = 0; j < _n; j++ )
             {
                 double csi = _z[1][j];  // we could really use the same _z[0] array of lobatto nodes
                 CartVect pos( 0.0 );
                 for( int k = 0; k < 4; k++ )
                 {
                     const double N_k = ( 1 + csi * corner_xi[k][0] ) * ( 1 + eta * corner_xi[k][1] );
                     pos += N_k * vertex[k];
                 }
                 pos *= 0.25;                           // these are x, y, z of gl points; reorder them
                 _glpoints[indexGL]          = pos[0];  // x
                 _glpoints[indexGL + n2]     = pos[1];  // y
                 _glpoints[indexGL + 2 * n2] = pos[2];  // z
                 indexGL++;
             }
         }
         // now, we can set the _xyz pointers to internal memory allocated to these!
         _xyz[0] = &( _glpoints[0] );
         _xyz[1] = &( _glpoints[n2] );
         _xyz[2] = &( _glpoints[2 * n2] );
     }

References _glpoints, _n, _xyz, and _z.

Referenced by test_spectral_quad().

◆ evaluate()

CartVect moab::Element::SpectralQuad::evaluate ( const CartVect & xi ) const

virtual

Evaluate the map on $x_i$ (calculate $\vec x = F($\vec \xi)$ )

Implements moab::Element::Map.

Definition at line 1298 of file ElemUtil.cpp.

     {
         // piece that we shouldn't want to cache
         int d = 0;
         for( d = 0; d < 2; d++ )
         {
             lagrange_0( &_ld[d], xi[d] );
         }
         CartVect result;
         for( d = 0; d < 3; d++ )
         {
             result[d] = tensor_i2( _ld[0].J, _ld[0].n, _ld[1].J, _ld[1].n, _xyz[d], _odwork );
         }
         return result;
     }

References _ld, _odwork, _xyz, lagrange_0(), and tensor_i2().

◆ evaluate_scalar_field()

double moab::Element::SpectralQuad::evaluate_scalar_field	(	const CartVect &	xi,
		const double *	field_vertex_values
	)		const

virtual

Evaluate a scalar field at a point given field values at the vertices.

Implements moab::Element::Map.

Definition at line 1343 of file ElemUtil.cpp.

     {
         // piece that we shouldn't want to cache
         int d;
         for( d = 0; d < 2; d++ )
         {
             lagrange_0( &_ld[d], xi[d] );
         }
  
         double value = tensor_i2( _ld[0].J, _ld[0].n, _ld[1].J, _ld[1].n, field, _odwork );
         return value;
     }

References _ld, _odwork, lagrange_0(), and tensor_i2().

◆ freedata()

void moab::Element::SpectralQuad::freedata ( )

Definition at line 60 of file SpectralQuad.cpp.

 {
     for( int d = 0; d < 2; d++ )
     {
         free( _z[d] );
         lagrange_free( &_ld[d] );
     }
     opt_free_2( &_data );
     free( _odwork );
     free( _glpoints );
 }

References _data, _glpoints, _ld, _odwork, _z, lagrange_free(), and opt_free_2().

Referenced by Init(), and ~SpectralQuad().

◆ get_gl_points()

void moab::Element::SpectralQuad::get_gl_points	(	double *&	x,
		double *&	y,
		double *&	z,
		int &	size
	)

Definition at line 1402 of file ElemUtil.cpp.

     {
         x     = (double*)_xyz[0];
         y     = (double*)_xyz[1];
         z     = (double*)_xyz[2];
         psize = _n * _n;
     }

References _n, and _xyz.

Referenced by test_spectral_quad().

◆ ievaluate()

CartVect moab::Element::SpectralQuad::ievaluate	(	const CartVect &	x,
		double	tol = `1e-6`,
		const CartVect &	x0 = `CartVect( 0.0 )`
	)		const

virtual

Evaluate the inverse map (calculate $\vec \xi = F^-1($\vec x)$ to given tolerance)

Reimplemented from moab::Element::Map.

Definition at line 1314 of file ElemUtil.cpp.

     {
         // find nearest point
         realType x_star[3];
         xyz.get( x_star );
  
         realType r[2] = { 0, 0 };  // initial guess for parametric coords
         unsigned c    = opt_no_constraints_3;
         realType dist = opt_findpt_2( &_data, (const realType**)_xyz, x_star, r, &c );
         // if it did not converge, get out with throw...
         if( dist > 0.9e+30 )
         {
             std::vector< CartVect > dummy;
             throw Map::EvaluationError( xyz, dummy );
         }
  
         // c tells us if we landed inside the element or exactly on a face, edge, or node
         // also, dist shows the distance to the computed point.
         // copy parametric coords back
         return CartVect( r[0], r[1], 0. );
     }

References _data, _xyz, moab::CartVect::get(), opt_findpt_2(), and opt_no_constraints_3.

◆ Init()

void moab::Element::SpectralQuad::Init ( int order )

Definition at line 35 of file SpectralQuad.cpp.

 {
     if( _init && _n == order ) return;
     if( _init && _n != order )
     {
         // TODO: free data cached
         freedata();
     }
     // compute stuff that depends only on order
     _init = true;
     _n    = order;
     // duplicates! n is the same in all directions !!!
     for( int d = 0; d < 2; d++ )
     {
         _z[d] = tmalloc( double, _n );
         lobatto_nodes( _z[d], _n );
         lagrange_setup( &_ld[d], _z[d], _n );
     }
     opt_alloc_2( &_data, _ld );
  
     unsigned int nf = _n * _n, ne = _n, nw = 2 * _n * _n + 3 * _n;
     _odwork   = tmalloc( double, 6 * nf + 9 * ne + nw );
     _glpoints = tmalloc( double, 3 * nf );
 }

References _data, _glpoints, _init, _ld, _n, _odwork, _z, freedata(), lagrange_setup(), lobatto_nodes(), opt_alloc_2(), and tmalloc.

Referenced by SpectralQuad().

◆ inside_nat_space()

bool moab::Element::SpectralQuad::inside_nat_space	(	const CartVect &	xi,
		double &	tol
	)		const

virtual

decide if within the natural param space, with a tolerance

Implements moab::Element::Map.

Definition at line 1360 of file ElemUtil.cpp.

     {
         // just look at the box+tol here
         return ( xi[0] >= -1. - tol ) && ( xi[0] <= 1. + tol ) && ( xi[1] >= -1. - tol ) && ( xi[1] <= 1. + tol );
     }

◆ integrate_scalar_field()

double moab::Element::SpectralQuad::integrate_scalar_field ( const double * field_vertex_values ) const

virtual

Integrate a scalar field over the element given field values at the vertices.

Implements moab::Element::Map.

Definition at line 1355 of file ElemUtil.cpp.

     {
         return 0.;  // not implemented
     }

◆ jacobian()

Matrix3 moab::Element::SpectralQuad::jacobian ( const CartVect & xi ) const

virtual

Evaluate the map's Jacobi matrix.

Implements moab::Element::Map.

Definition at line 132 of file SpectralQuad.cpp.

 {
     // not implemented
     Matrix3 J( 0. );
     return J;
 }

◆ set_gl_points()

void moab::Element::SpectralQuad::set_gl_points	(	double *	x,
		double *	y,
		double *	z
	)

Definition at line 72 of file SpectralQuad.cpp.

 {
     _xyz[0] = x;
     _xyz[1] = y;
     _xyz[2] = z;
 }

References _xyz.

Member Data Documentation

◆ _data

opt_data_2 moab::Element::SpectralQuad::_data

staticprotected

Definition at line 456 of file ElemUtil.hpp.

Referenced by freedata(), ievaluate(), Init(), and moab::SpectralQuad::reverseEvalFcn().

◆ _glpoints

realType * moab::Element::SpectralQuad::_glpoints

staticprotected

Definition at line 461 of file ElemUtil.hpp.

Referenced by compute_gl_positions(), freedata(), and Init().

◆ _init

bool moab::Element::SpectralQuad::_init = false

staticprotected

Definition at line 460 of file ElemUtil.hpp.

Referenced by Init(), and ~SpectralQuad().

◆ _ld

lagrange_data moab::Element::SpectralQuad::_ld

staticprotected

Definition at line 455 of file ElemUtil.hpp.

Referenced by moab::SpectralQuad::evalFcn(), evaluate(), evaluate_scalar_field(), freedata(), and Init().

◆ _n

int moab::Element::SpectralQuad::_n

staticprotected

Definition at line 453 of file ElemUtil.hpp.

Referenced by compute_gl_positions(), get_gl_points(), and Init().

◆ _odwork

realType * moab::Element::SpectralQuad::_odwork

staticprotected

Definition at line 457 of file ElemUtil.hpp.

Referenced by moab::SpectralQuad::evalFcn(), evaluate(), evaluate_scalar_field(), freedata(), and Init().

◆ _xyz

realType* moab::Element::SpectralQuad::_xyz[3]

protected

Definition at line 466 of file ElemUtil.hpp.

Referenced by compute_gl_positions(), moab::SpectralQuad::evalFcn(), evaluate(), get_gl_points(), ievaluate(), moab::SpectralQuad::reverseEvalFcn(), set_gl_points(), and SpectralQuad().

◆ _z

realType * moab::Element::SpectralQuad::_z

staticprotected

Definition at line 454 of file ElemUtil.hpp.

Referenced by compute_gl_positions(), freedata(), and Init().

The documentation for this class was generated from the following files:

Public Member Functions

Protected Attributes

Static Protected Attributes

Detailed Description

Constructor & Destructor Documentation

◆ SpectralQuad() [1/4]

◆ SpectralQuad() [2/4]

◆ SpectralQuad() [3/4]

◆ SpectralQuad() [4/4]

◆ ~SpectralQuad()

Member Function Documentation

◆ compute_gl_positions()

◆ evaluate()

◆ evaluate_scalar_field()

◆ freedata()

◆ get_gl_points()

◆ ievaluate()

◆ Init()

◆ inside_nat_space()

◆ integrate_scalar_field()

◆ jacobian()

◆ set_gl_points()

Member Data Documentation

◆ _data

◆ _glpoints

◆ _init

◆ _ld

◆ _n

◆ _odwork

◆ _xyz

◆ _z