oft_quadmesh_type Module Reference

Detailed Description

Quadralateral boundary mesh definitions.

Author

Chris Hansen

Date

October 2018

Data Types
type	oft_quadmesh
	Quadralateral boundary mesh type. More...

Functions/Subroutines
subroutine	quad_2d_grid (order, xnodes, inodesp, inodese, inodesf)
pure real(r8) function, dimension(4)	quad_get_bary (flog)
subroutine	quad_grid_orient (oflag, order, finds)
subroutine	quad_grid_orient_inv (oflag, order, finds)
integer(i4) function, dimension(2)	quadmesh_get_io_sizes (self)
	Get variable sizes following tessellation.
real(r8) function, dimension(3)	quadmesh_glogphys (self, face, j, f)
	Compute the partial derivative of the physical coordinates with a specific logical coordinate.
subroutine	quadmesh_hessian (self, cell, f, g2op, k)
	Compute the second order jacobians for a grid cell.
integer(i4) function	quadmesh_in_cell (self, f, tol)
	Logical locations of vertices.
subroutine	quadmesh_invert_face (self, i)
	Invert cell to produce positive volume.
subroutine	quadmesh_jacinv (a, c, j)
	Invert a 2x2 matrix.
subroutine	quadmesh_jacobian (self, cell, f, gop, j)
	Compute the jacobian matrix and its determinant for a grid cell.
subroutine	quadmesh_load (self, filename)
	Load quadmesh from transfer file.
real(r8) function, dimension(3)	quadmesh_log2phys (self, cell, f)
	Map from logical to physical coordinates.
subroutine	quadmesh_norm (self, i, f, n)
	Compute the unit normal vector to a face.
subroutine	quadmesh_phys2log (self, cell, pt, f)
	Map from physical to logical coordinates.
subroutine	quadmesh_quad_rule (self, order, quad_rule)
	Create quadrature rule for tetrahedra.
subroutine	quadmesh_save (self, filename)
	Load trimesh from transfer file.
subroutine	quadmesh_set_order (self, order)
	Load trimesh from transfer file.
subroutine	quadmesh_setup (self, cad_type, has_parent)
	Load quadmesh from transfer file.
subroutine	quadmesh_tang (self, i, f, t)
	Compute a orthonormal set of axis tangential to a face.
subroutine	quadmesh_tessellate (self, rtmp, lctmp, order)
	Driver for order specific tessellation subroutines.
subroutine	quadmesh_vlog (self, i, f)
	Logical locations of vertices.

Variables
integer(i4), dimension(2, 4), parameter	inodes1p = RESHAPE((/ 1,1, 2,1, 2,2, 1,2/), (/2,4/))
integer(i4), dimension(2, 4), parameter	inodes2e = RESHAPE((/ 2,1, 3,2, 2,3, 1,2/), (/2,4/))
integer(i4), dimension(2), parameter	inodes2f = (/2,2/)
integer(i4), dimension(2, 4), parameter	inodes2p = RESHAPE((/ 1,1, 3,1, 3,3, 1,3/), (/2,4/))
integer(i4), dimension(2, 4), parameter	inodesp_base = RESHAPE((/ 0,0, 1,0, 1,1, 0,1/), (/2,4/))
integer(i4), dimension(4), parameter	quad_bary_map = [-2,1,2,-1]
integer(i4), dimension(2, 4), parameter	quad_ed =RESHAPE((/1,2, 2,3, 3,4, 4,1/), (/2,4/))
	Quad edge list.

Function/Subroutine Documentation

quad_2d_grid()

subroutine quad_2d_grid	(	integer(i4), intent(in)	order,
		real(r8), dimension(:), intent(out), pointer	xnodes,
		integer(i4), dimension(2,4), intent(out)	inodesp,
		integer(i4), dimension(:,:,:), intent(out), pointer	inodese,
		integer(i4), dimension(:,:), intent(out), pointer	inodesf
	)

quad_get_bary()

pure real(r8) function, dimension(4) quad_get_bary

(

real(r8), dimension(:), intent(in)

flog

)

quad_grid_orient()

subroutine quad_grid_orient	(	integer(i4), intent(in)	oflag,
		integer(i4), intent(in)	order,
		integer(i4), dimension(:), intent(inout)	finds
	)

quad_grid_orient_inv()

subroutine quad_grid_orient_inv	(	integer(i4), intent(in)	oflag,
		integer(i4), intent(in)	order,
		integer(i4), dimension(:), intent(inout)	finds
	)

quadmesh_get_io_sizes()

integer(i4) function, dimension(2) quadmesh_get_io_sizes

(

class(oft_quadmesh), intent(in)

self

)

Get variable sizes following tessellation.

quadmesh_glogphys()

real(r8) function, dimension(3) quadmesh_glogphys	(	class(oft_quadmesh), intent(in)	self,
		integer, intent(in)	face,
		integer, intent(in)	j,
		real(r8), dimension(2), intent(in)	f
	)

Compute the partial derivative of the physical coordinates with a specific logical coordinate.

Driver function calls mapping specific function depending on mesh order.

Parameters

[in]	self	Mesh containing cell
[in]	i	Index of cell for evaulation
[in]	k	Logical coordinate for differentiation
[in]	f	Logical coordinate in cell [4]

Returns

pt \( \frac{\partial r}{\partial f_k} \) [3]

quadmesh_hessian()

subroutine quadmesh_hessian	(	class(oft_quadmesh), intent(in)	self,
		integer(i4), intent(in)	cell,
		real(r8), dimension(:), intent(in)	f,
		real(r8), dimension(:,:), intent(out)	g2op,
		real(r8), dimension(:,:), intent(out)	k
	)

Compute the second order jacobians for a grid cell.

Parameters

[in]	self	Mesh containing cell
[in]	cell	Index of cell for evaulation
[in]	f	Logical coordinate in cell [4]
[out]	g2op	Second order Jacobian matrix \( (\frac{\partial x_i}{\partial \lambda_l} \frac{\partial x_j}{\partial \lambda_k})^{-1} \) [6,6]
[out]	K	Gradient correction matrix \( \frac{\partial^2 x_i}{\partial \lambda_k \partial \lambda_l}\) [6,3]

quadmesh_in_cell()

integer(i4) function quadmesh_in_cell	(	class(oft_quadmesh), intent(in)	self,
		real(r8), dimension(:), intent(in)	f,
		real(r8), intent(in)	tol
	)

Logical locations of vertices.

Parameters

[in]	self	Mesh containing cell
[in]	i	Index of cell for evaulation
[in]	f	Logical coordinate in cell [4]

Returns

Physical position [3]

quadmesh_invert_face()

subroutine quadmesh_invert_face	(	class(oft_quadmesh), intent(inout)	self,
		integer(i4), intent(in)	i
	)

Invert cell to produce positive volume.

quadmesh_jacinv()

subroutine quadmesh_jacinv	(	real(r8), dimension(2,2), intent(in)	a,
		real(r8), dimension(2,2), intent(out)	c,
		real(r8), intent(out)	j
	)

Invert a 2x2 matrix.

Parameters

[in]	A	Matrix to invert
[out]	C	\( A^{-1} \)
[out]	j	|A|

quadmesh_jacobian()

subroutine quadmesh_jacobian	(	class(oft_quadmesh), intent(in)	self,
		integer(i4), intent(in)	cell,
		real(r8), dimension(:), intent(in)	f,
		real(r8), dimension(:,:), intent(out)	gop,
		real(r8), intent(out)	j
	)

Compute the jacobian matrix and its determinant for a grid cell.

Driver function calls mapping specific function depending on mesh order.

Parameters

[in]	self	Mesh containing cell
[in]	cell	Index of cell for evaulation
[in]	f	Logical coordinate in cell [4]
[out]	gop	Jacobian matrix ( \( \frac{\partial x_i}{\partial \lambda_j} \) ) [3,4] (optional)
[out]	j	Jacobian of transformation from logical to physical coordinates (optional)

quadmesh_load()

subroutine quadmesh_load	(	class(oft_quadmesh), intent(inout)	self,
		character(len=*), intent(in)	filename
	)

Load quadmesh from transfer file.

quadmesh_log2phys()

real(r8) function, dimension(3) quadmesh_log2phys	(	class(oft_quadmesh), intent(in)	self,
		integer, intent(in)	cell,
		real(r8), dimension(:), intent(in)	f
	)

Map from logical to physical coordinates.

Driver function calls mapping specific function depending on mesh order.

Parameters

[in]	self	Mesh containing cell
[in]	cell	Index of cell for evaulation
[in]	f	Logical coordinate in cell [4]

Returns

pt Physical position [3]

quadmesh_norm()

subroutine quadmesh_norm	(	class(oft_quadmesh), intent(in), target	self,
		integer(i4), intent(in)	i,
		real(r8), dimension(:), intent(in)	f,
		real(r8), dimension(3), intent(out)	n
	)

Compute the unit normal vector to a face.

Parameters

[in]	self	Mesh containing face
[in]	i	Index of face for evaulation
[in]	f	Logical coordinate on face [3]
[out]	n	Normal vector [3]

quadmesh_phys2log()

subroutine quadmesh_phys2log	(	class(oft_quadmesh), intent(in)	self,
		integer(i4), intent(in)	cell,
		real(r8), dimension(3), intent(in)	pt,
		real(r8), dimension(:), intent(out)	f
	)

Map from physical to logical coordinates.

Parameters

[in]	self	Mesh containing cell
[in]	cell	Index of cell for evaulation
[in]	pt	Physical position [3]

Returns

f Logical coordinates within the cell [4]

quadmesh_quad_rule()

subroutine quadmesh_quad_rule	(	class(oft_quadmesh), intent(in)	self,
		integer(i4), intent(in)	order,
		type(oft_quad_type), intent(out)	quad_rule
	)

Create quadrature rule for tetrahedra.

Parameters

[in]	self	Mesh containing cell
[in]	i	Index of cell for evaulation
[in]	f	Logical coordinate in cell [4]

Returns

Physical position [3]

quadmesh_save()

subroutine quadmesh_save	(	class(oft_quadmesh), intent(in)	self,
		character(len=*), intent(in)	filename
	)

Load trimesh from transfer file.

quadmesh_set_order()

subroutine quadmesh_set_order	(	class(oft_quadmesh), intent(inout)	self,
		integer(i4), intent(in)	order
	)

Load trimesh from transfer file.

quadmesh_setup()

subroutine quadmesh_setup	(	class(oft_quadmesh), intent(inout)	self,
		integer(i4), intent(in)	cad_type,
		logical, intent(in)	has_parent
	)

Load quadmesh from transfer file.

quadmesh_tang()

subroutine quadmesh_tang	(	class(oft_quadmesh), intent(in), target	self,
		integer(i4), intent(in)	i,
		real(r8), dimension(:), intent(in)	f,
		real(r8), dimension(3,2), intent(out)	t
	)

Compute a orthonormal set of axis tangential to a face.

Parameters

[in]	self	Mesh containing face
[in]	i	Index of face for evaulation
[in]	f	Logical coordinate on face [3]
[out]	t	Orthonormal vectors [3,2]

quadmesh_tessellate()

subroutine quadmesh_tessellate	(	class(oft_quadmesh), intent(in)	self,
		real(r8), dimension(:,:), intent(out), pointer	rtmp,
		integer(i4), dimension(:,:), intent(out), pointer	lctmp,
		integer(i4), intent(in)	order
	)

Driver for order specific tessellation subroutines.

Note

The maximum tessellation order currently supported is 4.

Warning

Cell lists are returned with zero based indexing.

Parameters

[in]	self	Mesh to tessellate
[out]	rtmp	Tessellated mesh points [3,np_tess]
[out]	lctmp	Tessellated cell list [4,nc_tess]
[in]	order	Desired tessellation order

quadmesh_vlog()

subroutine quadmesh_vlog	(	class(oft_quadmesh), intent(in)	self,
		integer(i4), intent(in)	i,
		real(r8), dimension(:), intent(out)	f
	)

Logical locations of vertices.

Parameters

[in]	self	Mesh containing cell
[in]	i	Index of cell for evaulation
[in]	f	Logical coordinate in cell [4]

Returns

Physical position [3]

Variable Documentation

inodes1p

integer(i4), dimension(2,4), parameter inodes1p = RESHAPE((/ 1,1, 2,1, 2,2, 1,2/), (/2,4/))

inodes2e

integer(i4), dimension(2,4), parameter inodes2e = RESHAPE((/ 2,1, 3,2, 2,3, 1,2/), (/2,4/))

inodes2f

integer(i4), dimension(2), parameter inodes2f = (/2,2/)

inodes2p

integer(i4), dimension(2,4), parameter inodes2p = RESHAPE((/ 1,1, 3,1, 3,3, 1,3/), (/2,4/))

inodesp_base

integer(i4), dimension(2,4), parameter inodesp_base = RESHAPE((/ 0,0, 1,0, 1,1, 0,1/), (/2,4/))

quad_bary_map

integer(i4), dimension(4), parameter quad_bary_map = [-2,1,2,-1]

quad_ed

integer(i4), dimension(2,4), parameter quad_ed =RESHAPE((/1,2, 2,3, 3,4, 4,1/), (/2,4/))

Quad edge list.