oft_h0_basis Module Reference

Detailed Description

Base Nedelec H0 FE class and basis evaluation.

• FE Construction
• Basis evaluation
  • Interpolation
  • Gradient

Authors

Chris Hansen

Date

August 2011

Data Types
type	h0_ops
	Needs docs. More...
type	oft_h0_bfem
	Needs docs. More...
type	oft_h0_fem
	Needs docs. More...

Functions/Subroutines
subroutine	oft_bh0_eval (self, face, dof, f, val)
	Evaluate Nedelec H0 interpolation function on the boundary.
subroutine	oft_bh0_geval (self, face, dof, f, val, gop)
	Evaluate Nedelec H0 gradient function on the boundary.
subroutine	oft_h0_d2eval (self, cell, dof, f, val, g2op)
	Evaluate lagrange gradient function.
subroutine	oft_h0_d2evalc (order, dof, f, val)
	Evaluate cell based gradient functions.
subroutine	oft_h0_d2evale (order, ed, el, dof, f, val)
	Evaluate edge based gradient functions.
subroutine	oft_h0_d2evalf (order, fc, el, dof, f, val)
	Evaluate cell based gradient functions.
subroutine	oft_h0_eval (self, cell, dof, f, val)
	Evaluate Nedelec H0 interpolation function.
subroutine	oft_h0_eval_all (self, cell, f, rop)
	Evaluate all lagrange interpolation functions.
subroutine	oft_h0_eval_all2 (self, cell, f, rop)
	Evaluate all lagrange interpolation functions (quadratic)
subroutine	oft_h0_eval_all3 (self, cell, f, rop)
	Evaluate all lagrange interpolation functions (cubic)
subroutine	oft_h0_eval_all4 (self, cell, f, rop)
	Evaluate all lagrange interpolation functions (quartic)
subroutine	oft_h0_eval_all5 (self, cell, f, rop)
	Evaluate all lagrange interpolation functions (quartic)
subroutine	oft_h0_evalc (order, dof, f, val)
	Evaluate cell based interpolation functions.
subroutine	oft_h0_evale (order, ed, dof, f, val)
	Evaluate edge based interpolation functions.
subroutine	oft_h0_evalf (order, fc, dof, f, val)
	Evaluate face based interpolation functions.
subroutine	oft_h0_evalp (order, pt, f, val)
	Evaluate point based interpolation functions.
subroutine	oft_h0_geval (self, cell, dof, f, val, gop)
	Evaluate Nedelec H0 gradient function.
subroutine	oft_h0_geval_all (self, cell, f, rop, gop)
	Evaluate all lagrange interpolation functions.
subroutine	oft_h0_geval_all2 (self, cell, f, rop, gop)
	Evaluate all lagrange interpolation functions (quadratic)
subroutine	oft_h0_geval_all3 (self, cell, f, rop, gop)
	Evaluate all lagrange interpolation functions (cubic)
subroutine	oft_h0_geval_all4 (self, cell, f, rop, gop)
	Evaluate all lagrange interpolation functions (quartic)
subroutine	oft_h0_geval_all5 (self, cell, f, rop, gop)
	Evaluate all lagrange interpolation functions (quartic)
subroutine	oft_h0_gevalc (order, dof, f, val)
	Evaluate cell based curl functions.
subroutine	oft_h0_gevale (order, ed, dof, f, val)
	Evaluate edge based curl functions.
subroutine	oft_h0_gevalf (order, fc, dof, f, val)
	Evaluate face based curl functions.
subroutine	oft_h0_gevalp (order, pt, f, val)
	Evaluate point based gradient functions.
subroutine	oft_h0_set_level (level)
	Set the current level for Nedelec H0 finite elements.
subroutine	oft_h0_setup (order, minlev)
	Construct Nedelec H0 scalar FE on each mesh level.

Variables
logical, private	hex_mesh = .FALSE.
type(oft_ml_fem_type), target	ml_oft_bh0
	ML container for all FE representations.
type(oft_ml_fem_type), target	ml_oft_h0
	ML container for all FE representations.
type(h0_ops), dimension(:), pointer	ml_oft_h0_ops
	ML container for all operators.
type(oft_h0_bfem), pointer	oft_bh0
	Active FE representation.
type(oft_h0_bfem), pointer	oft_bh0_lin
	Highest linear element representation.
class(oft_h0_fem), pointer	oft_h0
	Active FE representation.
integer(i4)	oft_h0_blevel =0
	Highest level on base meshes.
integer(i4), parameter	oft_h0_id = 2
	FE type ID.
integer(i4)	oft_h0_lev = 0
	Active FE level.
integer(i4)	oft_h0_level = 0
	Active FE level.
class(oft_h0_fem), pointer	oft_h0_lin
	Highest linear element representation.
integer(i4)	oft_h0_lin_level = 0
	Highest linear element level.
integer(i4)	oft_h0_minlev = 0
	Lowest level for multilevel runs.
integer(i4)	oft_h0_nlevels = 0
	Number of total levels.
type(h0_ops), pointer	oft_h0_ops
	Active operators.
type(h0_ops), pointer	oft_h0_ops_lin
	Highest linear element operators.

Function/Subroutine Documentation

oft_bh0_eval()

subroutine oft_bh0_eval	(	class(oft_bfem_type), 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 Nedelec H0 interpolation function on the boundary.

Note

Evaluation is performed in logical coordinates with the resulting vector in physical coordinates.

Parameters

[in]	self	Nedelec type for evaluation (bfem)
[in]	face	Face for evaluation
[in]	dof	Element to evaluate
[in]	f	Position on face in logical space [4]
[out]	val	Value of interpolation function (dof) at point (f)
[in]	gop	Face Jacobian matrix at point (f) [3,3]

oft_bh0_geval()

subroutine oft_bh0_geval	(	class(oft_bfem_type), 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(:,:), intent(in), optional	gop
	)

Evaluate Nedelec H0 gradient function on the boundary.

Note

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

Parameters

[in]	self	Nedelec type for evaluation (bfem)
[in]	face	Face for evaluation
[in]	dof	Element to evaluate
[in]	f	Position on face in logical space [4]
[out]	val	Curl of nedelec element (dof) at point (f) [3]
[in]	gop	Face Jacobian matrix at point (f) [3,3]

oft_h0_d2eval()

subroutine oft_h0_d2eval	(	class(oft_fem_type), 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)	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_h0_d2evalc()

subroutine oft_h0_d2evalc	(	integer(i4), intent(in)	order,
		integer(i4), intent(in)	dof,
		real(r8), dimension(:), intent(in)	f,
		real(r8), dimension(10), intent(out)	val
	)

Evaluate cell based gradient functions.

oft_h0_d2evale()

subroutine oft_h0_d2evale	(	integer(i4), intent(in)	order,
		integer(i4), dimension(2), intent(in)	ed,
		integer(i4), intent(in)	el,
		integer(i4), intent(in)	dof,
		real(r8), dimension(:), intent(in)	f,
		real(r8), dimension(10), intent(out)	val
	)

Evaluate edge based gradient functions.

oft_h0_d2evalf()

subroutine oft_h0_d2evalf	(	integer(i4), intent(in)	order,
		integer(i4), dimension(3), intent(in)	fc,
		integer(i4), intent(in)	el,
		integer(i4), intent(in)	dof,
		real(r8), dimension(:), intent(in)	f,
		real(r8), dimension(10), intent(out)	val
	)

Evaluate cell based gradient functions.

oft_h0_eval()

subroutine oft_h0_eval	(	class(oft_h0_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 Nedelec H0 interpolation function.

Note

Evaluation is performed in logical coordinates with the resulting vector in physical coordinates.

Parameters

[in]	self	Nedelec 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)
[in]	gop	Cell Jacobian matrix at point (f) [3,4]

oft_h0_eval_all()

subroutine oft_h0_eval_all	(	class(oft_h0_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_h0_eval_all2()

subroutine oft_h0_eval_all2	(	class(oft_fem_type), intent(in)	self,
		integer(i4), intent(in)	cell,
		real(r8), dimension(4), intent(in)	f,
		real(r8), dimension(10), intent(out)	rop
	)

Evaluate all lagrange interpolation functions (quadratic)

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_h0_eval_all3()

subroutine oft_h0_eval_all3	(	class(oft_fem_type), intent(in)	self,
		integer(i4), intent(in)	cell,
		real(r8), dimension(4), intent(in)	f,
		real(r8), dimension(20), intent(out)	rop
	)

Evaluate all lagrange interpolation functions (cubic)

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_h0_eval_all4()

subroutine oft_h0_eval_all4	(	class(oft_fem_type), intent(in)	self,
		integer(i4), intent(in)	cell,
		real(r8), dimension(4), intent(in)	f,
		real(r8), dimension(35), intent(out)	rop
	)

Evaluate all lagrange interpolation functions (quartic)

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_h0_eval_all5()

subroutine oft_h0_eval_all5	(	class(oft_fem_type), intent(in)	self,
		integer(i4), intent(in)	cell,
		real(r8), dimension(4), intent(in)	f,
		real(r8), dimension(56), intent(out)	rop
	)

Evaluate all lagrange interpolation functions (quartic)

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_h0_evalc()

subroutine oft_h0_evalc	(	integer(i4), intent(in)	order,
		integer(i4), intent(in)	dof,
		real(r8), dimension(:), intent(in)	f,
		real(r8), intent(out)	val
	)

Evaluate cell based interpolation functions.

oft_h0_evale()

subroutine oft_h0_evale	(	integer(i4), intent(in)	order,
		integer(i4), dimension(2), intent(in)	ed,
		integer(i4), intent(in)	dof,
		real(r8), dimension(:), intent(in)	f,
		real(r8), intent(out)	val
	)

Evaluate edge based interpolation functions.

oft_h0_evalf()

subroutine oft_h0_evalf	(	integer(i4), intent(in)	order,
		integer(i4), dimension(3), intent(in)	fc,
		integer(i4), intent(in)	dof,
		real(r8), dimension(:), intent(in)	f,
		real(r8), intent(out)	val
	)

Evaluate face based interpolation functions.

oft_h0_evalp()

subroutine oft_h0_evalp	(	integer(i4), intent(in)	order,
		integer(i4), intent(in)	pt,
		real(r8), dimension(:), intent(in)	f,
		real(r8), intent(out)	val
	)

Evaluate point based interpolation functions.

oft_h0_geval()

subroutine oft_h0_geval	(	class(oft_h0_fem), intent(in)	self,
		integer(i4), intent(in)	cell,
		integer(i4), intent(in)	dof,
		real(r8), dimension(:), intent(in)	f,
		real(r8), dimension(:), intent(out)	val,
		real(r8), dimension(:,:), intent(in)	gop
	)

Evaluate Nedelec H0 gradient function.

Note

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

Parameters

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

oft_h0_geval_all()

subroutine oft_h0_geval_all	(	class(oft_h0_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_h0_geval_all2()

subroutine oft_h0_geval_all2	(	class(oft_fem_type), intent(in)	self,
		integer(i4), intent(in)	cell,
		real(r8), dimension(4), intent(in)	f,
		real(r8), dimension(3,10), intent(out)	rop,
		real(r8), dimension(3,4), intent(in)	gop
	)

Evaluate all lagrange interpolation functions (quadratic)

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_h0_geval_all3()

subroutine oft_h0_geval_all3	(	class(oft_fem_type), intent(in)	self,
		integer(i4), intent(in)	cell,
		real(r8), dimension(4), intent(in)	f,
		real(r8), dimension(3,20), intent(out)	rop,
		real(r8), dimension(3,4), intent(in)	gop
	)

Evaluate all lagrange interpolation functions (cubic)

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_h0_geval_all4()

subroutine oft_h0_geval_all4	(	class(oft_fem_type), intent(in)	self,
		integer(i4), intent(in)	cell,
		real(r8), dimension(4), intent(in)	f,
		real(r8), dimension(3,35), intent(out)	rop,
		real(r8), dimension(3,4), intent(in)	gop
	)

Evaluate all lagrange interpolation functions (quartic)

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_h0_geval_all5()

subroutine oft_h0_geval_all5	(	class(oft_fem_type), intent(in)	self,
		integer(i4), intent(in)	cell,
		real(r8), dimension(4), intent(in)	f,
		real(r8), dimension(3,56), intent(out)	rop,
		real(r8), dimension(3,4), intent(in)	gop
	)

Evaluate all lagrange interpolation functions (quartic)

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_h0_gevalc()

subroutine oft_h0_gevalc	(	integer(i4), intent(in)	order,
		integer(i4), intent(in)	dof,
		real(r8), dimension(:), intent(in)	f,
		real(r8), dimension(4), intent(out)	val
	)

Evaluate cell based curl functions.

oft_h0_gevale()

subroutine oft_h0_gevale	(	integer(i4), intent(in)	order,
		integer(i4), dimension(2), intent(in)	ed,
		integer(i4), intent(in)	dof,
		real(r8), dimension(4), intent(in)	f,
		real(r8), dimension(4), intent(out)	val
	)

Evaluate edge based curl functions.

oft_h0_gevalf()

subroutine oft_h0_gevalf	(	integer(i4), intent(in)	order,
		integer(i4), dimension(3), intent(in)	fc,
		integer(i4), intent(in)	dof,
		real(r8), dimension(:), intent(in)	f,
		real(r8), dimension(4), intent(out)	val
	)

Evaluate face based curl functions.

oft_h0_gevalp()

subroutine oft_h0_gevalp	(	integer(i4), intent(in)	order,
		integer(i4), intent(in)	pt,
		real(r8), dimension(:), intent(in)	f,
		real(r8), dimension(4), intent(out)	val
	)

Evaluate point based gradient functions.

oft_h0_set_level()

subroutine oft_h0_set_level

(

integer(i4), intent(in)

level

)

Set the current level for Nedelec H0 finite elements.

Parameters

[in]

level

Desired level

oft_h0_setup()

subroutine oft_h0_setup	(	integer(i4), intent(in)	order,
		integer(i4), intent(in), optional	minlev
	)

Construct Nedelec H0 scalar FE on each mesh level.

Note

Highest supported representation is Quartic.

Parameters

[in]

order

Order of representation desired

Variable Documentation

hex_mesh

logical, private hex_mesh = .FALSE.

private

ml_oft_bh0

type(oft_ml_fem_type), target ml_oft_bh0

ML container for all FE representations.

ml_oft_h0

type(oft_ml_fem_type), target ml_oft_h0

ML container for all FE representations.

ml_oft_h0_ops

type(h0_ops), dimension(:), pointer ml_oft_h0_ops

ML container for all operators.

oft_bh0

type(oft_h0_bfem), pointer oft_bh0

Active FE representation.

oft_bh0_lin

type(oft_h0_bfem), pointer oft_bh0_lin

Highest linear element representation.

oft_h0

class(oft_h0_fem), pointer oft_h0

Active FE representation.

oft_h0_blevel

integer(i4) oft_h0_blevel =0

Highest level on base meshes.

oft_h0_id

integer(i4), parameter oft_h0_id = 2

FE type ID.

oft_h0_lev

integer(i4) oft_h0_lev = 0

Active FE level.

oft_h0_level

integer(i4) oft_h0_level = 0

Active FE level.

oft_h0_lin

class(oft_h0_fem), pointer oft_h0_lin

Highest linear element representation.

oft_h0_lin_level

integer(i4) oft_h0_lin_level = 0

Highest linear element level.

oft_h0_minlev

integer(i4) oft_h0_minlev = 0

Lowest level for multilevel runs.

oft_h0_nlevels

integer(i4) oft_h0_nlevels = 0

Number of total levels.

oft_h0_ops

type(h0_ops), pointer oft_h0_ops

Active operators.

oft_h0_ops_lin

type(h0_ops), pointer oft_h0_ops_lin

Highest linear element operators.