SIMPLE SOLUTIONS

# BASIS(7RHEOLEF) - Linux man page online | Overview, conventions, and miscellany

Polynomial basis.

Chapter
rheolef-6.7
basis(7rheolef) rheolef-6.7 basis(7rheolef)

## NAME

basis - polynomial basis

## SYNOPSYS

The basis class defines functions that evaluates a polynomial basis and its derivatives on a point. The polynomial basis is designated by a string, e.g. "P0", "P1", "P2", "bub‐ ble",... indicating the basis. The basis depends also of the reference element: triangle, square, tetrahedron (see reference_element(2)). For instance, on a square, the "P1" string designates the common Q1 four-nodes basis on the reference square. The nodes associated to the Lagrange polynomial basis are also available by its associated accessor.

## IMPLEMENTATION NOTE

The basis class is a see smart_pointer(2)) class on a basis_rep class that is a pure vir‐ tual base class for effective bases, e.g. basis_P1, basis_P1, etc.

## IMPLEMENTATION

template<class T> class basis_basic : public smart_pointer<basis_rep<T> > { public: // typedefs: typedef basis_rep<T> rep; typedef smart_pointer<rep> base; typedef typename basis_rep<T>::size_type size_type; // allocators: basis_basic (std::string name = ""); // accessors: std::string name() const; size_type degree() const; size_type size (reference_element hat_K) const; void hat_node( reference_element hat_K, std::vector<point_basic<T> >& hat_node) const; void hat_node( reference_element hat_K, typename std::vector<point_basic<T> >::iterator hat_node) const; void eval( reference_element hat_K, const point_basic<T>& hat_x, std::vector<T>& values) const; void eval( reference_element hat_K, const point_basic<T>& hat_x, typename std::vector<T>::iterator values) const; void grad_eval( reference_element hat_K, const point_basic<T>& hat_x, std::vector<point_basic<T> >& values) const; void grad_eval( reference_element hat_K, const point_basic<T>& hat_x, typename std::vector<point_basic<T> >::iterator values) const; }; typedef basis_basic<Float> basis;