oft_lag_basis Module Reference

Detailed Description

Base Lagrange FE class and basis evaluation.

• FE Construction
• Basis evaluation
  • Interpolation
  • Gradient

Authors

Chris Hansen

Date

August 2011

Data Types
type	oft_lag_ops
	Lagrange operator container. More...
type	oft_scalar_bfem
	Lagrange operator container. More...
type	oft_scalar_fem
	Lagrange operator container. More...

Functions/Subroutines
subroutine	oft_blag_d2eval (self, cell, dof, f, val, g2op)
	Evaluate lagrange gradient function.
subroutine	oft_blag_eval (self, face, dof, f, val)
	Evaluate lagrange interpolation function.
subroutine	oft_blag_geval (self, face, dof, f, val, gop)
	Evaluate lagrange gradient function.
subroutine	oft_blag_npos (self, cell, dof, f)
	Retrieve lagrange node locations in logical coordinates.
subroutine	oft_lag_boundary
	Compute surface normals for use in boundary conditions.
subroutine	oft_lag_d2eval (self, cell, dof, f, val, g2op)
	Evaluate lagrange gradient function.
subroutine	oft_lag_eval (self, cell, dof, f, val)
	Evaluate lagrange interpolation function.
subroutine	oft_lag_eval_all (self, cell, f, rop)
	Evaluate all lagrange interpolation functions.
subroutine	oft_lag_geval (self, cell, dof, f, val, gop)
	Evaluate lagrange gradient function.
subroutine	oft_lag_geval_all (self, cell, f, rop, gop)
	Evaluate all lagrange interpolation functions.
subroutine	oft_lag_nodes (order, ed_nodes, fc_nodes, c_nodes)
	Retrieve all lagrange node locations in logical coordinates.
subroutine	oft_lag_npos (self, cell, dof, f)
	Retrieve lagrange node locations in logical coordinates.
subroutine	oft_lag_set_level (level)
	Set the current level for lagrange finite elements.
subroutine	oft_lag_setup (order, minlev)
	Construct lagrange scalar FE on each mesh level.
subroutine	oft_lag_setup_bmesh (self, tmesh, order)
	Construct lagrange scalar FE for a given order.
subroutine	oft_lag_setup_vol (self, tmesh, order)
	Construct lagrange scalar FE for a given order.
subroutine	scalar_bfem_delete (self)
	Destroy boundary FE object.
subroutine	scalar_fem_delete (self)
	Destroy boundary FE object.
subroutine	tet_eval_all2 (self, cell, f, rop)
	Needs docs.
subroutine	tet_eval_all3 (self, cell, f, rop)
	Needs docs.
subroutine	tet_eval_all4 (self, cell, f, rop)
	Needs docs.
subroutine	tet_geval_all2 (self, cell, f, gop, rop)
	Needs docs.
subroutine	tet_geval_all3 (self, cell, f, gop, rop)
	Needs docs.
subroutine	tet_geval_all4 (self, cell, f, gop, rop)
	Needs docs.

Variables
logical, private	hex_mesh = .FALSE.
type(oft_ml_fem_type), target	ml_oft_blagrange
	ML container for all FE representations.
type(oft_ml_fem_type), target	ml_oft_lagrange
	ML container for all FE representations.
type(oft_lag_ops), dimension(:), pointer	ml_oft_lagrange_ops
	ML container for all operators.
type(oft_ml_fem_comp_type)	ml_oft_vlagrange
	ML container for vector representation.
type(oft_scalar_bfem), pointer	oft_blagrange
	Active FE representation.
type(oft_scalar_bfem), pointer	oft_blagrange_lin
	Highest linear element representation.
type(oft_scalar_fem), pointer	oft_lagrange
	Active FE representation.
integer(i4)	oft_lagrange_blevel = 0
	Highest level on base meshes.
integer(i4), parameter	oft_lagrange_id = 1
	FE type ID.
integer(i4)	oft_lagrange_lev = 0
	Active FE level.
integer(i4)	oft_lagrange_level = 0
	Active FE level.
type(oft_scalar_fem), pointer	oft_lagrange_lin
	Highest linear element representation.
integer(i4)	oft_lagrange_lin_level = 0
	Highest linear element level.
integer(i4)	oft_lagrange_minlev = 0
	Lowest constructed level.
integer(i4)	oft_lagrange_nlevels = 0
	Number of total levels.
type(oft_lag_ops), pointer	oft_lagrange_ops
	Active operators.
type(oft_lag_ops), pointer	oft_lagrange_ops_lin
	Highest linear element operators.
type(oft_fem_comp_type), pointer	oft_vlagrange
	Active vector representation.

Function/Subroutine Documentation

oft_blag_d2eval()

subroutine oft_blag_d2eval	(	class(oft_scalar_bfem), intent(in)	self,
		integer(i4), intent(in)	cell,
		integer(i4), intent(in)	dof,
		real(r8), dimension(:), intent(in)	f,
		real(r8), dimension(6), intent(out)	val,
		real(r8), dimension(6,6), intent(in), optional	g2op
	)

Evaluate lagrange gradient function.

Note

Evaluation is performed in logical coordinates with the resulting gradient with respect to physical coordinates.

Parameters

[in]	self	Lagrange type for evaluation
[in]	cell	Cell for evaluation
[in]	dof	Element to evaluate
[in]	f	Position in cell in logical space
[out]	val	Gradient of lagrange element (dof) at point (f) [3]
[in]	gop	Cell Jacobian matrix at point (f) [3,4]

oft_blag_eval()

subroutine oft_blag_eval	(	class(oft_scalar_bfem), intent(in)	self,
		integer(i4), intent(in)	face,
		integer(i4), intent(in)	dof,
		real(r8), dimension(:), intent(in)	f,
		real(r8), intent(out)	val
	)

Evaluate lagrange interpolation function.

Note

Evaluation is performed in logical coordinates.

Parameters

[in]	self	Lagrange type for evaluation
[in]	cell	Cell for evaluation
[in]	dof	Element to evaluate
[in]	f	Position in cell in logical space
[out]	val	Value of interpolation function (dof) at point (f)

oft_blag_geval()

subroutine oft_blag_geval	(	class(oft_scalar_bfem), intent(in)	self,
		integer(i4), intent(in)	face,
		integer(i4), intent(in)	dof,
		real(r8), dimension(:), intent(in)	f,
		real(r8), dimension(3), intent(out)	val,
		real(r8), dimension(3,3), intent(in), optional	gop
	)

Evaluate lagrange gradient function.

Note

Evaluation is performed in logical coordinates with the resulting gradient with respect to physical coordinates.

Parameters

[in]	self	Lagrange type for evaluation
[in]	cell	Cell for evaluation
[in]	dof	Element to evaluate
[in]	f	Position in cell in logical space
[out]	val	Gradient of lagrange element (dof) at point (f) [3]
[in]	gop	Cell Jacobian matrix at point (f) [3,4]

oft_blag_npos()

subroutine oft_blag_npos	(	class(oft_scalar_bfem), intent(in)	self,
		integer(i4), intent(in)	cell,
		integer(i4), intent(in)	dof,
		real(r8), dimension(:), intent(out)	f
	)

Retrieve lagrange node locations in logical coordinates.

Parameters

[in]	self	Lagrange type for evaluation
[in]	cell	Cell for evaluation
[in]	dof	Element to locate
[out]	f	Position of node in logical space

oft_lag_boundary()

subroutine oft_lag_boundary

Compute surface normals for use in boundary conditions.

oft_lag_d2eval()

subroutine oft_lag_d2eval	(	class(oft_scalar_fem), intent(in)	self,
		integer(i4), intent(in)	cell,
		integer(i4), intent(in)	dof,
		real(r8), dimension(:), intent(in)	f,
		real(r8), dimension(6), intent(out)	val,
		real(r8), dimension(6,10), intent(in), optional	g2op
	)

Evaluate lagrange gradient function.

Note

Evaluation is performed in logical coordinates with the resulting gradient with respect to physical coordinates.

Parameters

[in]	self	Lagrange type for evaluation
[in]	cell	Cell for evaluation
[in]	dof	Element to evaluate
[in]	f	Position in cell in logical space
[out]	val	Gradient of lagrange element (dof) at point (f) [3]
[in]	gop	Cell Jacobian matrix at point (f) [3,4]

oft_lag_eval()

subroutine oft_lag_eval	(	class(oft_scalar_fem), intent(in)	self,
		integer(i4), intent(in)	cell,
		integer(i4), intent(in)	dof,
		real(r8), dimension(:), intent(in)	f,
		real(r8), intent(out)	val
	)

Evaluate lagrange interpolation function.

Note

Evaluation is performed in logical coordinates.

Parameters

[in]	self	Lagrange type for evaluation
[in]	cell	Cell for evaluation
[in]	dof	Element to evaluate
[in]	f	Position in cell in logical space
[out]	val	Value of interpolation function (dof) at point (f)

oft_lag_eval_all()

subroutine oft_lag_eval_all	(	class(oft_scalar_fem), intent(in)	self,
		integer(i4), intent(in)	cell,
		real(r8), dimension(:), intent(in)	f,
		real(r8), dimension(:), intent(out), contiguous	rop
	)

Evaluate all lagrange interpolation functions.

Note

Evaluation is performed in logical coordinates.

Parameters

[in]	self	Lagrange type for evaluation
[in]	cell	Cell for evaluation
[in]	f	Position in cell in logical space
[out]	rop	Value of interpolation functions at point (f) [ncdofs]

oft_lag_geval()

subroutine oft_lag_geval	(	class(oft_scalar_fem), intent(in)	self,
		integer(i4), intent(in)	cell,
		integer(i4), intent(in)	dof,
		real(r8), dimension(:), intent(in)	f,
		real(r8), dimension(3), intent(out)	val,
		real(r8), dimension(:,:), intent(in)	gop
	)

Evaluate lagrange gradient function.

Note

Evaluation is performed in logical coordinates with the resulting gradient with respect to physical coordinates.

Parameters

[in]	self	Lagrange type for evaluation
[in]	cell	Cell for evaluation
[in]	dof	Element to evaluate
[in]	f	Position in cell in logical space
[out]	val	Gradient of lagrange element (dof) at point (f) [3]
[in]	gop	Cell Jacobian matrix at point (f) [3,4]

oft_lag_geval_all()

subroutine oft_lag_geval_all	(	class(oft_scalar_fem), intent(in)	self,
		integer(i4), intent(in)	cell,
		real(r8), dimension(:), intent(in)	f,
		real(r8), dimension(:,:), intent(out), contiguous	rop,
		real(r8), dimension(:,:), intent(in)	gop
	)

Evaluate all lagrange interpolation functions.

Note

Evaluation is performed in logical coordinates.

Parameters

[in]	self	Lagrange type for evaluation
[in]	cell	Cell for evaluation
[in]	f	Position in cell in logical space
[out]	rop	Value of interpolation functions at point (f) [3,ncdofs]
[in]	gop	Cell Jacobian matrix at point (f) [3,4]

oft_lag_nodes()

subroutine oft_lag_nodes	(	integer(i4), intent(in)	order,
		real(r8), dimension(:,:), intent(out), pointer	ed_nodes,
		real(r8), dimension(:,:), intent(out), pointer	fc_nodes,
		real(r8), dimension(:,:), intent(out), pointer	c_nodes
	)

Retrieve all lagrange node locations in logical coordinates.

Parameters

[in]	self	Lagrange type for evaluation
[in]	cell	Cell for evaluation
[in]	dof	Element to locate
[out]	f	Position of node in logical space

oft_lag_npos()

subroutine oft_lag_npos	(	class(oft_scalar_fem), intent(in)	self,
		integer(i4), intent(in)	cell,
		integer(i4), intent(in)	dof,
		real(r8), dimension(:), intent(out)	f
	)

Retrieve lagrange node locations in logical coordinates.

Parameters

[in]	self	Lagrange type for evaluation
[in]	cell	Cell for evaluation
[in]	dof	Element to locate
[out]	f	Position of node in logical space

oft_lag_set_level()

subroutine oft_lag_set_level

(

integer(i4), intent(in)

level

)

Set the current level for lagrange finite elements.

Parameters

[in]

level

Desired level

oft_lag_setup()

subroutine oft_lag_setup	(	integer(i4), intent(in)	order,
		integer(i4), intent(in), optional	minlev
	)

Construct lagrange scalar FE on each mesh level.

Note

Highest supported representation is quartic

Parameters

[in]

order

Order of representation desired

oft_lag_setup_bmesh()

subroutine oft_lag_setup_bmesh	(	class(oft_afem_type), intent(out), pointer	self,
		class(oft_bmesh), intent(in), target	tmesh,
		integer(i4), intent(in)	order
	)

Construct lagrange scalar FE for a given order.

Note

Highest supported representation is quartic

Parameters

[in]

order

Order of representation desired

oft_lag_setup_vol()

subroutine oft_lag_setup_vol	(	class(oft_afem_type), intent(out), pointer	self,
		class(oft_mesh), intent(in), target	tmesh,
		integer(i4), intent(in)	order
	)

Construct lagrange scalar FE for a given order.

Note

Highest supported representation is quartic

Parameters

[in]

order

Order of representation desired

scalar_bfem_delete()

subroutine scalar_bfem_delete

(

class(oft_scalar_bfem), intent(inout)

self

)

Destroy boundary FE object.

Note

Should only be used via class oft_bfem_type or children

scalar_fem_delete()

subroutine scalar_fem_delete

(

class(oft_scalar_fem), intent(inout)

self

)

Destroy boundary FE object.

Note

Should only be used via class oft_bfem_type or children

tet_eval_all2()

subroutine tet_eval_all2	(	class(oft_scalar_fem), intent(in)	self,
		integer(i4), intent(in)	cell,
		real(r8), dimension(:), intent(in)	f,
		real(r8), dimension(10), intent(out)	rop
	)

Needs docs.

tet_eval_all3()

subroutine tet_eval_all3	(	class(oft_scalar_fem), intent(in)	self,
		integer(i4), intent(in)	cell,
		real(r8), dimension(:), intent(in)	f,
		real(r8), dimension(20), intent(out)	rop
	)

Needs docs.

tet_eval_all4()

subroutine tet_eval_all4	(	class(oft_scalar_fem), intent(in)	self,
		integer(i4), intent(in)	cell,
		real(r8), dimension(:), intent(in)	f,
		real(r8), dimension(35), intent(out)	rop
	)

Needs docs.

tet_geval_all2()

subroutine tet_geval_all2	(	class(oft_scalar_fem), intent(in)	self,
		integer(i4), intent(in)	cell,
		real(r8), dimension(:), intent(in)	f,
		real(r8), dimension(3,4), intent(in)	gop,
		real(r8), dimension(3,10), intent(out)	rop
	)

Needs docs.

tet_geval_all3()

subroutine tet_geval_all3	(	class(oft_scalar_fem), intent(in)	self,
		integer(i4), intent(in)	cell,
		real(r8), dimension(:), intent(in)	f,
		real(r8), dimension(3,4), intent(in)	gop,
		real(r8), dimension(3,20), intent(out)	rop
	)

Needs docs.

tet_geval_all4()

subroutine tet_geval_all4	(	class(oft_scalar_fem), intent(in)	self,
		integer(i4), intent(in)	cell,
		real(r8), dimension(:), intent(in)	f,
		real(r8), dimension(3,4), intent(in)	gop,
		real(r8), dimension(3,35), intent(out)	rop
	)

Needs docs.

Variable Documentation

hex_mesh

logical, private hex_mesh = .FALSE.

private

ml_oft_blagrange

type(oft_ml_fem_type), target ml_oft_blagrange

ML container for all FE representations.

ml_oft_lagrange

type(oft_ml_fem_type), target ml_oft_lagrange

ML container for all FE representations.

ml_oft_lagrange_ops

type(oft_lag_ops), dimension(:), pointer ml_oft_lagrange_ops

ML container for all operators.

ml_oft_vlagrange

type(oft_ml_fem_comp_type) ml_oft_vlagrange

ML container for vector representation.

oft_blagrange

type(oft_scalar_bfem), pointer oft_blagrange

Active FE representation.

oft_blagrange_lin

type(oft_scalar_bfem), pointer oft_blagrange_lin

Highest linear element representation.

oft_lagrange

type(oft_scalar_fem), pointer oft_lagrange

Active FE representation.

oft_lagrange_blevel

integer(i4) oft_lagrange_blevel = 0

Highest level on base meshes.

oft_lagrange_id

integer(i4), parameter oft_lagrange_id = 1

FE type ID.

oft_lagrange_lev

integer(i4) oft_lagrange_lev = 0

Active FE level.

oft_lagrange_level

integer(i4) oft_lagrange_level = 0

Active FE level.

oft_lagrange_lin

type(oft_scalar_fem), pointer oft_lagrange_lin

Highest linear element representation.

oft_lagrange_lin_level

integer(i4) oft_lagrange_lin_level = 0

Highest linear element level.

oft_lagrange_minlev

integer(i4) oft_lagrange_minlev = 0

Lowest constructed level.

oft_lagrange_nlevels

integer(i4) oft_lagrange_nlevels = 0

Number of total levels.

oft_lagrange_ops

type(oft_lag_ops), pointer oft_lagrange_ops

Active operators.

oft_lagrange_ops_lin

type(oft_lag_ops), pointer oft_lagrange_ops_lin

Highest linear element operators.

oft_vlagrange

type(oft_fem_comp_type), pointer oft_vlagrange

Active vector representation.