oft_quadmesh_type Module Reference

Detailed Description

Quadralateral boundary mesh definitions.

Author

Chris Hansen

Date

October 2018

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

Functions/Subroutines
subroutine, public	quad_2d_grid (order, xnodes, inodesp, inodese, inodesf)
	Needs docs.
pure real(r8) function, dimension(4)	quad_get_bary (flog)
	Map from orthogonal logical coordinates to barycentric logical coordinates.
subroutine, public	quad_grid_orient (oflag, order, finds)
	Needs docs.
subroutine	quad_grid_orient_inv (oflag, order, finds)
	Needs docs.
real(r8) function, dimension(3)	quadmesh_glogphys (self, cell, 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 spatial hessian matrices for a given cell at a given logical position.
integer(i4) function	quadmesh_in_cell (self, f, tol)
	Test if logical position lies within the base cell.
subroutine	quadmesh_invert_face (self, cell)
	Turn cell "inside out", used to ensure consistent orientations.
subroutine	quadmesh_jacinv (a, c, j)
	Invert a 2x2 matrix.
subroutine	quadmesh_jacobian (self, cell, f, gop, j)
	Compute the spatial jacobian matrix and its determinant for a given cell at a given logical position.
subroutine	quadmesh_load (self, filename, ascii)
	Load trimesh from transfer file.
real(r8) function, dimension(3)	quadmesh_log2phys (self, cell, f)
	Map from logical to physical coordinates in a given cell.
subroutine	quadmesh_norm (self, cell, f, n)
	Get unit normal for surface at a given point in a given cell.
subroutine	quadmesh_phys2log (self, cell, pt, f)
	Map from physical to logical coordinates in a given cell.
subroutine	quadmesh_quad_rule (self, order, quad_rule)
	Retrieve suitable quadrature rule for triangular mesh with given order.
subroutine	quadmesh_save (self, filename, ascii)
	Save trimesh from transfer file.
subroutine	quadmesh_set_order (self, order)
	Set maximum order of spatial mapping.
subroutine	quadmesh_setup (self, cad_type, has_parent)
	Setup mesh with implementation specifics (cell_np, cell_ne, etc.)
subroutine	quadmesh_tang (self, cell, f, t)
	Get tangent basis set for surface at a given point in a given cell.
subroutine	quadmesh_tessellate (self, rtmp, lctmp, order)
	Tessellate mesh onto lagrange FE nodes of specified order (usually for plotting)
integer(i4) function, dimension(2)	quadmesh_tessellated_sizes (self)
	Get sizes of arrays returned by trimesh_tessellate.
subroutine	quadmesh_vlog (self, i, f)
	Get position in logical space of cell vertex i

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, public 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
	)

Needs docs.

quad_get_bary()

pure real(r8) function, dimension(4) quad_get_bary ( real(r8), dimension(:), intent(in)  flog )

private

Map from orthogonal logical coordinates to barycentric logical coordinates.

Parameters

[in]

flog

Position in orthogonal logical coordinates [2]

Returns

Position in barycentric logical coordinates [4]

quad_grid_orient()

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

Needs docs.

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  )

private

Needs docs.

quadmesh_glogphys()

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

private

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 object
[in]	cell	Index of cell for evaulation
[in]	j	Needs docs
[in]	f	Logical coordinate in cell [4]

Returns

\( \frac{\partial r}{\partial f_k} \) [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  )

private

Compute the spatial hessian matrices for a given cell at a given logical position.

Warning

Not presently supported for quadrilateral meshes

Parameters

[in]	self	Mesh object
[in]	cell	Index of cell for evaulation
[in]	f	Logical coordinate in cell [4]
[out]	g2op	Second order Jacobian matrix \( (\frac{\partial x_i}{\partial \lambda_l} \frac{\partial x_j}{\partial \lambda_k})^{-1} \)
[out]	k	Gradient correction matrix \( \frac{\partial^2 x_i}{\partial \lambda_k \partial \lambda_l}\) [10,3]

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  )

private

Test if logical position lies within the base cell.

Returns

Position f is inside the base cell?

Parameters

[in]	self	Mesh object
[in]	f	Logical coordinate to evaluate
[in]	tol	Tolerance for test

quadmesh_invert_face()

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

private

Turn cell "inside out", used to ensure consistent orientations.

Parameters

[in,out]	self	Mesh object
[in]	cell	Maximum order of spatial mapping

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  )

private

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  )

private

Compute the spatial jacobian matrix and its determinant for a given cell at a given logical position.

Parameters

[in]	self	Mesh object
[in]	cell	Index of cell for evaulation
[in]	f	Logical coordinate in cell [3]
[out]	gop	Jacobian matrix \( (\frac{\partial x_i}{\partial \lambda_j})^{-1} \) [3,4]
[out]	j	Jacobian of transformation from logical to physical coordinates

quadmesh_load()

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

private

Load trimesh from transfer file.

Parameters

[in,out]	self	Mesh object
[in]	filename	File to load mesh from
[in]	ascii	Mesh stored in ASCII format?

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  )

private

Map from logical to physical coordinates in a given cell.

Parameters

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

Returns

Physical position [3]

quadmesh_norm()

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

private

Get unit normal for surface at a given point in a given cell.

Parameters

[in]	self	Mesh object
[in]	cell	Cell containing point
[in]	f	Logical coordinates in cell
[out]	n	Unit normal [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  )

private

Map from physical to logical coordinates in a given cell.

Parameters

[in]	self	Mesh object
[in]	cell	Index of cell for evaulation
[in]	pt	Physical position [3]
[out]	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  )

private

Retrieve suitable quadrature rule for triangular mesh with given order.

Parameters

[in]	self	Mesh object
[in]	order	Desired order of quadrature rule
[out]	quad_rule	Resulting quadrature rule

quadmesh_save()

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

private

Save trimesh from transfer file.

Parameters

[in]	self	Mesh object
[in]	filename	File to save mesh to
[in]	ascii	Save file in ASCII format?

quadmesh_set_order()

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

private

Set maximum order of spatial mapping.

Parameters

[in,out]	self	Mesh object
[in]	order	Maximum order of spatial mapping

quadmesh_setup()

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

private

Setup mesh with implementation specifics (cell_np, cell_ne, etc.)

Parameters

[in,out]	self	Mesh object
[in]	cad_type	CAD/mesh interface ID number
[in]	has_parent	Is this mesh the/a surface of a volume mesh?

quadmesh_tang()

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

private

Get tangent basis set for surface at a given point in a given cell.

Parameters

[in]	self	Mesh object
[in]	cell	Cell containing point
[in]	f	Logical coordinates in cell
[out]	t	Unit tangent basis set [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  )

private

Tessellate mesh onto lagrange FE nodes of specified order (usually for plotting)

Note

The maximum tessellation order currently supported is 4 (may be lower for certain mesh types).

Warning

Cell lists are returned with zero based indexing

Parameters

[in]	self	Mesh object
[out]	rtmp	Tessellated point list [3,:]
[out]	lctmp	Tessellated cell list [selfncp,:]
[in]	order	Tessellation order

quadmesh_tessellated_sizes()

integer(i4) function, dimension(2) quadmesh_tessellated_sizes ( class(oft_quadmesh), intent(in)  self )

private

Get sizes of arrays returned by trimesh_tessellate.

Parameters

[in]

self

Mesh object

Returns

Array sizes following tessellation [np_tess,nc_tess]

quadmesh_vlog()

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

private

Get position in logical space of cell vertex i

Parameters

[in]	self	Mesh object
[in]	i	Vertex to locate
[out]	f	Logical coordinates of vertex i

Variable Documentation

inodes1p

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

private

inodes2e

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

private

inodes2f

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

private

inodes2p

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

private

inodesp_base

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

private

quad_bary_map

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

private

quad_ed

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

Quad edge list.