oft_h1_basis Module Reference

Detailed Description

Base scalar H^1 FE class and basis evaluation.

• FE Construction
• Basis evaluation
  • Interpolation
  • Gradient

Authors

Chris Hansen

Date

August 2011

Data Types
type	oft_h1_bfem
	Needs docs. More...
type	oft_h1_fem
	Needs docs. More...

Functions/Subroutines
logical function	oft_2d_h1_cast (self, source)
	Cast abstract FE type to 2D H^1 finite element type.
logical function	oft_3d_h1_cast (self, source)
	Cast abstract FE type to 3D H^1 finite element type.
subroutine	oft_bh1_eval (self, face, dof, f, val)
	Evaluate H^1 interpolation function on the boundary.
subroutine	oft_bh1_geval (self, face, dof, f, val, gop)
	Evaluate H^1 gradient function on the boundary.
subroutine	oft_h1_d2eval (self, cell, dof, f, val, g2op)
	Evaluate H^1 gradient function.
subroutine	oft_h1_d2evalc (order, dof, f, val)
	Evaluate cell based gradient functions.
subroutine	oft_h1_d2evale (order, ed, el, dof, f, val)
	Evaluate edge based gradient functions.
subroutine	oft_h1_d2evalf (order, fc, el, dof, f, val)
	Evaluate cell based gradient functions.
subroutine	oft_h1_eval (self, cell, dof, f, val)
	Evaluate H^1 interpolation function.
subroutine	oft_h1_eval_all (self, cell, f, rop)
	Evaluate all H^1 interpolation functions.
subroutine	oft_h1_evalc (order, dof, f, val)
	Evaluate cell based interpolation functions.
subroutine	oft_h1_evale (order, ed, dof, f, val)
	Evaluate edge based interpolation functions.
subroutine	oft_h1_evalf (order, fc, dof, f, val)
	Evaluate face based interpolation functions.
subroutine	oft_h1_evalp (order, pt, f, val)
	Evaluate point based interpolation functions.
subroutine	oft_h1_geval (self, cell, dof, f, val, gop)
	Evaluate H^1 gradient function.
subroutine	oft_h1_geval_all (self, cell, f, rop, gop)
	Evaluate all H^1 interpolation functions.
subroutine	oft_h1_gevalc (order, dof, f, val)
	Evaluate cell based curl functions.
subroutine	oft_h1_gevale (order, ed, dof, f, val)
	Evaluate edge based curl functions.
subroutine	oft_h1_gevalf (order, fc, dof, f, val)
	Evaluate face based curl functions.
subroutine	oft_h1_gevalp (order, pt, f, val)
	Evaluate point based gradient functions.
subroutine	oft_h1_setup (mg_mesh, order, ml_h1_obj, ml_bh1_obj, minlev)
	Construct H^1 scalar FE on each mesh level.
subroutine	oft_h1_setup_surf (self, tmesh, order)
	Needs docs.
subroutine	oft_h1_setup_vol (self, tmesh, order)
	Needs docs.

Variables
integer(i4), parameter	oft_h1_id = 2
	FE type ID.

Function/Subroutine Documentation

oft_2d_h1_cast()

logical function oft_2d_h1_cast	(	class(oft_h1_bfem), intent(out), pointer	self,
		class(oft_afem_type), intent(in), target	source
	)

Cast abstract FE type to 2D H^1 finite element type.

The source matrix must be oft_h1_bfem or a child class, otherwise pointer will be returned as null and success == .FALSE.

Parameters

[out]	self	Reference to source object with desired class
[in]	source	Source object to reference

Returns

Cast success flag

oft_3d_h1_cast()

logical function oft_3d_h1_cast	(	class(oft_h1_fem), intent(out), pointer	self,
		class(oft_afem_type), intent(in), target	source
	)

Cast abstract FE type to 3D H^1 finite element type.

The source matrix must be oft_h1_fem or a child class, otherwise pointer will be returned as null and success == .FALSE.

Parameters

[out]	self	Reference to source object with desired class
[in]	source	Source object to reference

Returns

Cast success flag

oft_bh1_eval()

subroutine oft_bh1_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 H^1 interpolation function on the boundary.

Note

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

Parameters

[in]	self	H^1 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)

oft_bh1_geval()

subroutine oft_bh1_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 H^1 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	H^1 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	Gradient of H^1 element (dof) at point (f) [3]
[in]	gop	Face Jacobian matrix at point (f) [3,3]

oft_h1_d2eval()

subroutine oft_h1_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 H^1 gradient function.

Note

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

Parameters

[in]	self	H^1 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 H^1 element (dof) at point (f) [3]
[in]	g2op	Cell Jacobian matrix at point (f) [3,4]

oft_h1_d2evalc()

subroutine oft_h1_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.

Parameters

[in]	order	Needs docs
[in]	dof	Needs docs
[in]	f	Needs docs
[out]	val	Needs docs

oft_h1_d2evale()

subroutine oft_h1_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.

Parameters

[in]	order	Needs docs
[in]	ed	Needs docs
[in]	el	Needs docs
[in]	dof	Needs docs

oft_h1_d2evalf()

subroutine oft_h1_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.

Parameters

[in]	order	Needs docs
[in]	fc	Needs docs
[in]	el	Needs docs
[in]	dof	Needs docs

oft_h1_eval()

subroutine oft_h1_eval	(	class(oft_h1_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 H^1 interpolation function.

Note

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

Parameters

[in]	self	H^1 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_h1_eval_all()

subroutine oft_h1_eval_all	(	class(oft_h1_fem), intent(in)	self,
		integer(i4), intent(in)	cell,
		real(r8), dimension(:), intent(in)	f,
		real(r8), dimension(:), intent(out), contiguous	rop
	)

Evaluate all H^1 interpolation functions.

Note

Evaluation is performed in logical coordinates

Parameters

[in]	self	H^1 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_h1_evalc()

subroutine oft_h1_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.

Parameters

[in]	order	Needs docs
[in]	dof	Needs docs
[in]	f	Needs docs
[out]	val	Needs docs

oft_h1_evale()

subroutine oft_h1_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.

Parameters

[in]	order	Needs docs
[in]	ed	Needs docs
[in]	dof	Needs docs
[in]	f	Needs docs
[out]	val	Needs docs

oft_h1_evalf()

subroutine oft_h1_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.

Parameters

[in]	order	Needs docs
[in]	fc	Needs docs
[in]	dof	Needs docs
[in]	f	Needs docs
[out]	val	Needs docs

oft_h1_evalp()

subroutine oft_h1_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.

Parameters

[in]	order	Needs docs
[in]	pt	Needs docs
[in]	f	Needs docs
[out]	val	Needs docs

oft_h1_geval()

subroutine oft_h1_geval	(	class(oft_h1_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 H^1 gradient function.

Note

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

Parameters

[in]	self	H^1 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 H^1 element (dof) at point (f) [3]
[in]	gop	Cell Jacobian matrix at point (f) [3,4]

oft_h1_geval_all()

subroutine oft_h1_geval_all	(	class(oft_h1_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 H^1 interpolation functions.

Note

Evaluation is performed in logical coordinates

Parameters

[in]	self	H^1 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_h1_gevalc()

subroutine oft_h1_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.

Parameters

[in]	order	Needs docs
[in]	dof	Needs docs
[in]	f	Needs docs
[out]	val	Needs docs

oft_h1_gevale()

subroutine oft_h1_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.

Parameters

[in]	order	Needs docs
[in]	ed	Needs docs
[in]	dof	Needs docs
[in]	f	Needs docs
[out]	val	Needs docs

oft_h1_gevalf()

subroutine oft_h1_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.

Parameters

[in]	order	Needs docs
[in]	fc	Needs docs
[in]	dof	Needs docs
[in]	f	Needs docs
[out]	val	Needs docs

oft_h1_gevalp()

subroutine oft_h1_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.

Parameters

[in]	order	Needs docs
[in]	pt	Needs docs
[in]	f	Needs docs
[out]	val	Needs docs

oft_h1_setup()

subroutine oft_h1_setup	(	type(multigrid_mesh), intent(inout), target	mg_mesh,
		integer(i4), intent(in)	order,
		type(oft_ml_fem_type), intent(inout), optional	ml_h1_obj,
		type(oft_ml_fem_type), intent(inout), optional	ml_bh1_obj,
		integer(i4), intent(in), optional	minlev
	)

Construct H^1 scalar FE on each mesh level.

Note

Highest supported representation is Quartic

Parameters

[in]	order	Order of representation desired
[in]	minlev	Lowest level to construct

oft_h1_setup_surf()

subroutine oft_h1_setup_surf	(	class(oft_afem_type), intent(out), pointer	self,
		class(oft_bmesh), intent(in), target	tmesh,
		integer(i4), intent(in)	order
	)

Needs docs.

Parameters

[out]	self	Needs docs
[in]	tmesh	Needs docs
[in]	order	Order of representation desired

oft_h1_setup_vol()

subroutine oft_h1_setup_vol	(	class(oft_afem_type), intent(out), pointer	self,
		class(oft_mesh), intent(in), target	tmesh,
		integer(i4), intent(in)	order
	)

Needs docs.

Parameters

[out]	self	Needs docs
[in]	tmesh	Needs docs
[in]	order	Order of representation desired

Variable Documentation

oft_h1_id

integer(i4), parameter oft_h1_id = 2

FE type ID.