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Basis.h 8.50 KiB
#ifndef _BASIS_H_
#define _BASIS_H_
#include "MElement.h"
/**
@interface Basis
@brief Common Interface of all Basis
This class is the @em common @em interface for all Basis.@n
A Basis is @em set of @em linearly @em independent Polynomial%s
(or Vector%s of Polynomial%s).@n
@note
The returned matrices are the result of the evaluation
of the basis functions (at @c N points).@n
The @c i-th row of these matrices is always refering to the
@c i-th function of the basis.@n
Depending on the nature of the returned value
(@em scalar or @em vector), the columns are organized
diferently.
For @em scalar values, we have:
@li The @c j-th column of the @c i-th row is
the evaluation of the @c i-th function at the @c j-th point
For @em vectorial values, we have:
@li The @c j-th column of the @c i-th row is
the @em first @em coordinate of
the evaluation of the @c i-th function at the @c 3 @c x @c j-th point
@li The @c (@c j-th @c + @c 1 @c ) column of the @c i-th row is
the @em second @em coordinate of
the evaluation of the @c i-th function at the @c 3 @c x @c j-th point
@li The @c (@c j-th @c + @c 2 @c ) column of the @c i-th row is
the @em third @em coordinate of
the evaluation of the @c i-th function at the @c 3 @c x @c j-th point
*/
class Basis{
protected:
bool scalar;
bool local;
unsigned int order;
unsigned int type;
unsigned int dim;
unsigned int nVertex;
unsigned int nEdge;
unsigned int nFace;
unsigned int nCell;
unsigned int nFunction;
public:
// Destructor //
virtual ~Basis(void);
// Scalar & Local //
bool isScalar(void) const;
bool isLocal(void) const;
// Type of Basis //
unsigned int getOrder(void) const;
unsigned int getType(void) const; unsigned int getDim(void) const;
// Number of Functions //
unsigned int getNVertexBased(void) const;
unsigned int getNEdgeBased(void) const;
unsigned int getNFaceBased(void) const;
unsigned int getNCellBased(void) const;
unsigned int getNFunction(void) const;
// Orientations //
virtual unsigned int getNOrientation(void) const = 0;
virtual unsigned int getOrientation(const MElement& element) const = 0;
// Direct Access to Evaluated Functions //
virtual fullMatrix<double>* getFunctions(const MElement& element,
double u, double v, double w) const = 0;
virtual fullMatrix<double>* getFunctions(unsigned int orientation,
double u, double v, double w) const = 0;
// Precompute Functions //
virtual void preEvaluateFunctions(const fullMatrix<double>& point) const = 0;
virtual void preEvaluateDerivatives(const fullMatrix<double>& point) const = 0;
// Access to Precomputed Functions //
virtual const fullMatrix<double>&
getPreEvaluatedFunctions(const MElement& element) const = 0;
virtual const fullMatrix<double>&
getPreEvaluatedDerivatives(const MElement& element) const = 0;
virtual const fullMatrix<double>&
getPreEvaluatedFunctions(unsigned int orientation) const = 0;
virtual const fullMatrix<double>&
getPreEvaluatedDerivatives(unsigned int orientation) const = 0;
protected:
// 'Constructor' //
Basis(void);
};
/**
@internal
@fn Basis::Basis
Instantiate a new Basis
@endinternal
**
@fn Basis::~Basis
Deletes this Basis
**
@fn Basis::isScalar
@return Returns:
@li @c true, if this is a
@em scalar Basis
@li @c false, if this is a
@em vectorial Basis
@note
Scalar basis are sets of
Polynomial%s@n
Vectorial basis are sets of
Vector%s of Polynomial%s
**
@fn Basis::isLocal
@return Returns:
@li @c true, if this is a
@em Local Basis
@li @c false, if this is a
@em Global Basis
**
@fn Basis::getOrder
@return Returns the @em polynomial @em order of the Basis
**
@fn Basis::getType
@return Returns the @em type of the Basis:
@li 0 for 0-form
@li 1 for 1-form
@li 2 for 2-form
@li 3 for 3-form
**
@fn Basis::getDim
@return Returns the @em dimension
(@c 1D, @c 2D or @c 3D) of the Basis
**
@fn Basis::getNVertexBased
@return Returns the number of @em Vertex
@em Based functions of this Basis
**
@fn Basis::getNEdgeBased
@return Returns the number of @em Edge
@em Based functions of this Basis
**
@fn Basis::getNFaceBased
@return Returns the number of @em Face
@em Based functions of this Basis
**
@fn Basis::getNCellBased
@return Returns the number of @em Cell
@em Based functions of this Basis
**
@fn Basis::getNFunction
@return Returns the number of Polynomial%s
(or Vector%s of Polynomial%s) Functions
in this Basis
**
@fn Basis::getNOrientation
@return Returns the number of
@em orientation of this Basis
Reference Space
**
@fn Basis::getOrientation
@param element A MElement
@return Returns a number charaterizing
the @em orientation of the given element
**
@fn Basis::getFunctions(unsigned int, double, double, double) const
@param orientation A natural number defining the reference space @em orientation
@param u A @c u coordinate in the reference space of this Basis
@param v A @c v coordinate in the reference space of this Basis
@param w A @c w coordinate in the reference space of this Basis
@return Instanciates a new fullMatrix<double> with the @em evaluation
of every basis function at the given coordinates, and for the given orientation
@warning
The Instanciated Matrix must be deleted by the @em calling function
**
@fn Basis::getFunctions(const MElement&, double, double, double) const
@param element A MElement
@param u A @c u coordinate in the reference space of this Basis
@param v A @c v coordinate in the reference space of this Basis
@param w A @c w coordinate in the reference space of this Basis
@return Same as Basis::getFunction(Basis::getOrientation(@c element),
@c u, @c u, @c w)
**
@fn Basis::preEvaluateFunctions
@param point A Matrix with points coordinate
(each line is a point and got 3 coordinates, @em i.e. 3 rows)
@return Pre Evaluates every basis function at the given points
**
@fn Basis::preEvaluateDerivatives
@param point A Matrix with points coordinate
(each line is a point and got 3 coordinates, @em i.e. 3 rows)
@return Pre Evaluates every basis function @em derivative at the given points
@note
@li For 0-Form it computes the @em gradient
@li For 1-Form it computes the @em curl
@li For 2-Form it computes the @em divergence
@li For 3-Form it computes the @em ???
@todo What is the derivative of a 3-Form
(does it exists -- discontinous field nope ?) ?
**
@fn Basis::getPreEvaluatedFunctions(unsigned int) const
@param orientation A natural number defining the reference space @em orientation
@return Returns a Matrix with the PreEvaluated basis functions
(see Basis::preEvaluateFunctions()), with the given @em orientation
@note
If no PreEvaluation has been done before calling this function,
an Exception is thrown
**
@fn Basis::getPreEvaluatedDerivatives(unsigned int) const
@param orientation A natural number defining the reference space @em orientation
@return Returns a Matrix with the PreEvaluated basis functions @em derivatives
(see Basis::preEvaluateDerivatives()), with the given @em orientation
@note
If no PreEvaluation of the gradient has been done before calling this function,
an Exception is thrown
**
@fn Basis::getPreEvaluatedFunctions(const MElement&) const
@return Same as Basis::getPreEvaluatedFunctions(Basis::getOrientation(@c element))
**
@fn Basis::getPreEvaluatedDerivatives(const MElement&) const
@return Same as Basis::getPreEvaluatedDerivatives(Basis::getOrientation(@c element))
*/
//////////////////////
// Inline Functions //
//////////////////////
inline bool Basis::isScalar(void) const{
return scalar;
}
inline bool Basis::isLocal(void) const{
return local;
}
inline unsigned int Basis::getOrder(void) const{
return order;
}
inline unsigned int Basis::getType(void) const{
return type;
}
inline unsigned int Basis::getDim(void) const{
return dim;
}
inline unsigned int Basis::getNVertexBased(void) const{
return nVertex;
}
inline unsigned int Basis::getNEdgeBased(void) const{
return nEdge;
}
inline unsigned int Basis::getNFaceBased(void) const{
return nFace;
}
inline unsigned int Basis::getNCellBased(void) const{
return nCell;
}
inline unsigned int Basis::getNFunction(void) const{
return nFunction;
}
#endif