curved::Geometry Class Reference

Curved geometry of one rank's mesh. Faces are curved where they lie on a curved surface, and in 3D where they share an edge with one (blended from their edges). Reference coordinates of a face, in its node order: 2D s in [-1, 1] from node 0 to node 1; triangles (u, v) with x = v0 + u (v1 - v0) + v (v2 - v0) when flat; quadrilaterals (s, t) in [-1, 1]^2, nodes 0..3 at (-1, -1), (1, -1), (1, 1), (-1, 1). More...

#include <curved.h>

Public Member Functions
	Geometry (const Mesh &mesh, const Surfaces &surfaces)
bool	face_is_curved (uint32_t f) const
bool	cell_is_curved (uint32_t c) const
uint32_t	n_curved_faces () const
double	max_shape_offset () const
	Largest distance of a node of a projected edge from its analytic shape, relative to the edge's length (0 if none).
void	eval (uint32_t f, const double *xi, Vec3 &x, Vec3 *dx) const
	Point x of face f at reference coordinates xi, and its derivatives dx[k] = dx / dxi_k (k < N_DIM - 1), in the frame of the face's cell 0.
Vec3	area_vector (uint32_t f) const
	The area vector int n dS of face f (out of its cell 0), exact for its edges.
void	face_rule (uint32_t f, const std::vector< std::array< double, 2 > > &ref, const std::vector< double > &ref_w, std::vector< Vec3 > &x, std::vector< Vec3 > &n, std::vector< double > &w) const
	Quadrature of face f from a rule on its flat reference element (weights summing to the reference measure: 2 on edges and quadrilaterals, 1 on triangles, as the flat rules): points, unit normals out of cell 0, and area elements, whose area vectors sum exactly to area_vector(f).
void	cell_rule (uint32_t c, int degree, std::vector< Vec3 > &x, std::vector< double > &w) const
	Points and signed weights integrating polynomials of the given degree over cell c (curved or not), in the cell's frame: cones from its vertex average over its faces.

Detailed Description

Curved geometry of one rank's mesh. Faces are curved where they lie on a curved surface, and in 3D where they share an edge with one (blended from their edges). Reference coordinates of a face, in its node order: 2D s in [-1, 1] from node 0 to node 1; triangles (u, v) with x = v0 + u (v1 - v0) + v (v2 - v0) when flat; quadrilaterals (s, t) in [-1, 1]^2, nodes 0..3 at (-1, -1), (1, -1), (1, 1), (-1, 1).

Constructor & Destructor Documentation

Geometry()

curved::Geometry::Geometry	(	const Mesh &	mesh,
		const Surfaces &	surfaces
	)

Member Function Documentation

area_vector()

Vec3 curved::Geometry::area_vector

(

uint32_t

f

)

const

The area vector int n dS of face f (out of its cell 0), exact for its edges.

cell_is_curved()

bool curved::Geometry::cell_is_curved ( uint32_t  c ) const

inline

cell_rule()

void curved::Geometry::cell_rule	(	uint32_t	c,
		int	degree,
		std::vector< Vec3 > &	x,
		std::vector< double > &	w
	)		const

Points and signed weights integrating polynomials of the given degree over cell c (curved or not), in the cell's frame: cones from its vertex average over its faces.

eval()

void curved::Geometry::eval	(	uint32_t	f,
		const double *	xi,
		Vec3 &	x,
		Vec3 *	dx
	)		const

Point x of face f at reference coordinates xi, and its derivatives dx[k] = dx / dxi_k (k < N_DIM - 1), in the frame of the face's cell 0.

face_is_curved()

bool curved::Geometry::face_is_curved ( uint32_t  f ) const

inline

face_rule()

void curved::Geometry::face_rule	(	uint32_t	f,
		const std::vector< std::array< double, 2 > > &	ref,
		const std::vector< double > &	ref_w,
		std::vector< Vec3 > &	x,
		std::vector< Vec3 > &	n,
		std::vector< double > &	w
	)		const

Quadrature of face f from a rule on its flat reference element (weights summing to the reference measure: 2 on edges and quadrilaterals, 1 on triangles, as the flat rules): points, unit normals out of cell 0, and area elements, whose area vectors sum exactly to area_vector(f).

max_shape_offset()

double curved::Geometry::max_shape_offset

(

)

const

Largest distance of a node of a projected edge from its analytic shape, relative to the edge's length (0 if none).

n_curved_faces()

uint32_t curved::Geometry::n_curved_faces ( ) const

inline

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

• /home/runner/work/mallard/mallard/mallard/src/mesh/curved.h
• /home/runner/work/mallard/mallard/mallard/src/mesh/curved.cpp