oft_hcurl_basis Module Reference

Detailed Description

Base H(Curl) FE class and basis evaluation.

• FE Construction
• Basis evaluation
  • Interpolation
  • Curl

Authors

Chris Hansen

Date

August 2011

Data Types
type	oft_hcurl_bfem
	Needs docs. More...
type	oft_hcurl_fem
	Needs docs. More...

Functions/Subroutines
subroutine	hcurl_2d_grid (order, inds)
	Need docs.
subroutine	hcurl_3d_grid (order, inds)
	Need docs.
logical function	oft_2d_hcurl_cast (self, source)
	Cast abstract FE type to 2D H(Curl) finite element type.
logical function	oft_3d_hcurl_cast (self, source)
	Cast abstract FE type to 3D H(Curl) finite element type.
subroutine	oft_bhcurl_ceval (self, face, dof, f, val, gop)
	Evaluate H(Curl) curl function on the boundary.
subroutine	oft_bhcurl_eval (self, face, dof, f, val, gop)
	Evaluate H(Curl) interpolation function on the boundary.
subroutine	oft_hcurl_ceval (self, cell, dof, f, val, gop)
	Evaluate H(Curl) curl function in the interior.
subroutine	oft_hcurl_ceval_all (self, cell, f, rop, cgop)
	Evaluate all lagrange interpolation functions.
subroutine	oft_hcurl_cevalc (order, dof, f, grads, val)
	Evaluate cell based curl functions.
subroutine	oft_hcurl_cevale (order, ed, dof, f, grads, val)
	Evaluate edge based curl functions.
subroutine	oft_hcurl_cevalf (order, fc, dof, f, grads, val)
	Evaluate face based curl functions.
subroutine	oft_hcurl_eval (self, cell, dof, f, val, gop)
	Evaluate H(Curl) interpolation function in the interior.
subroutine	oft_hcurl_eval_all (self, cell, f, rop, gop)
	Evaluate all lagrange interpolation functions.
subroutine	oft_hcurl_evalc (order, dof, f, val)
	Evaluate cell based interpolation functions.
subroutine	oft_hcurl_evale (order, ed, dof, f, val)
	Evaluate edge based interpolation functions.
subroutine	oft_hcurl_evalf (order, fc, dof, f, val)
	Evaluate face based interpolation functions.
subroutine	oft_hcurl_get_cgops (gop, cgop)
	Get cross-products of spatial jacobian vectors.
subroutine	oft_hcurl_grad_setup (ml_hcurl_obj, ml_h1_obj, ml_hcurl_grad_obj, ml_h1grad_obj, minlev)
	Construct a vector FE space for H(Curl) and it's compliment ( \( \nabla H^1 \))
subroutine	oft_hcurl_setup (mg_mesh, order, ml_hcurl_obj, ml_bhcurl_obj, minlev)
	Construct H(Curl) FE basis on each mesh level.
subroutine	oft_hcurl_setup_surf (self, tmesh, order)
	Needs docs.
subroutine	oft_hcurl_setup_vol (self, tmesh, order)
	Needs docs.

Variables
integer(i4), dimension(4, 4), parameter	cgop_map = RESHAPE((/0,-1,-2,-3,1,0,-4,-5,2,4,0,-6,3,5,6,0/), (/4,4/))
integer(i4), parameter	oft_hcurl_id = 3
	FE type ID.

Function/Subroutine Documentation

hcurl_2d_grid()

subroutine hcurl_2d_grid	(	integer(i4), intent(in)	order,
		integer(i4), dimension(:,:), intent(out), pointer	inds
	)

Need docs.

hcurl_3d_grid()

subroutine hcurl_3d_grid	(	integer(i4), intent(in)	order,
		integer(i4), dimension(:,:), intent(out), pointer	inds
	)

Need docs.

oft_2d_hcurl_cast()

logical function oft_2d_hcurl_cast	(	class(oft_hcurl_bfem), intent(out), pointer	self,
		class(oft_afem_type), intent(in), target	source
	)

Cast abstract FE type to 2D H(Curl) finite element type.

The source matrix must be oft_hcurl_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_hcurl_cast()

logical function oft_3d_hcurl_cast	(	class(oft_hcurl_fem), intent(out), pointer	self,
		class(oft_afem_type), intent(in), target	source
	)

Cast abstract FE type to 3D H(Curl) finite element type.

The source matrix must be oft_hcurl_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_bhcurl_ceval()

subroutine oft_bhcurl_ceval	(	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(Curl) curl function on the boundary.

Note

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

Parameters

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

oft_bhcurl_eval()

subroutine oft_bhcurl_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), dimension(3), intent(out)	val,
		real(r8), dimension(:,:), intent(in), optional	gop
	)

Evaluate H(Curl) interpolation function on the boundary.

Note

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

Parameters

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

oft_hcurl_ceval()

subroutine oft_hcurl_ceval	(	class(oft_hcurl_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(3,4), intent(in)	gop
	)

Evaluate H(Curl) curl function in the interior.

Note

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

Parameters

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

oft_hcurl_ceval_all()

subroutine oft_hcurl_ceval_all	(	class(oft_hcurl_fem), intent(in)	self,
		integer(i4), intent(in)	cell,
		real(r8), dimension(4), intent(in)	f,
		real(r8), dimension(:,:), intent(out), contiguous	rop,
		real(r8), dimension(3,6), intent(in)	cgop
	)

Evaluate all lagrange interpolation functions.

Note

Evaluation is performed in logical coordinates

Parameters

[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]	cgop	Cross-products of spatial jacobian vectors

oft_hcurl_cevalc()

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

Evaluate cell based curl functions.

oft_hcurl_cevale()

subroutine oft_hcurl_cevale	(	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), dimension(3,4), intent(in)	grads,
		real(r8), dimension(3), intent(out)	val
	)

Evaluate edge based curl functions.

oft_hcurl_cevalf()

subroutine oft_hcurl_cevalf	(	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(3,4), intent(in)	grads,
		real(r8), dimension(3), intent(out)	val
	)

Evaluate face based curl functions.

oft_hcurl_eval()

subroutine oft_hcurl_eval	(	class(oft_hcurl_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(Curl) interpolation function in the interior.

Note

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

Parameters

[in]	cell	Cell for evaluation
[in]	dof	Element to evaluate
[in]	f	Position in cell in logical space [4]
[in]	gop	Value of interpolation function (dof) at point (f) [3]
[out]	val	Cell Jacobian matrix at point (f) [3,4]

oft_hcurl_eval_all()

subroutine oft_hcurl_eval_all	(	class(oft_hcurl_fem), intent(in)	self,
		integer(i4), intent(in)	cell,
		real(r8), dimension(4), intent(in)	f,
		real(r8), dimension(:,:), intent(out), contiguous	rop,
		real(r8), dimension(3,4), intent(in)	gop
	)

Evaluate all lagrange interpolation functions.

Note

Evaluation is performed in logical coordinates

Parameters

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

oft_hcurl_evalc()

subroutine oft_hcurl_evalc	(	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 interpolation functions.

oft_hcurl_evale()

subroutine oft_hcurl_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), dimension(4), intent(out)	val
	)

Evaluate edge based interpolation functions.

oft_hcurl_evalf()

subroutine oft_hcurl_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), dimension(4), intent(out)	val
	)

Evaluate face based interpolation functions.

oft_hcurl_get_cgops()

subroutine oft_hcurl_get_cgops	(	real(r8), dimension(3,4), intent(in)	gop,
		real(r8), dimension(3,6), intent(out)	cgop
	)

Get cross-products of spatial jacobian vectors.

oft_hcurl_grad_setup()

subroutine oft_hcurl_grad_setup	(	type(oft_ml_fem_type), intent(inout), target	ml_hcurl_obj,
		type(oft_ml_fem_type), intent(inout)	ml_h1_obj,
		type(oft_ml_fem_comp_type), intent(inout)	ml_hcurl_grad_obj,
		type(oft_ml_fem_type), intent(inout), target	ml_h1grad_obj,
		integer(i4), intent(in), optional	minlev
	)

Construct a vector FE space for H(Curl) and it's compliment ( \( \nabla H^1 \))

oft_hcurl_setup()

subroutine oft_hcurl_setup	(	type(multigrid_mesh), intent(inout), target	mg_mesh,
		integer(i4), intent(in)	order,
		type(oft_ml_fem_type), intent(inout), optional	ml_hcurl_obj,
		type(oft_ml_fem_type), intent(inout), optional	ml_bhcurl_obj,
		integer(i4), intent(in), optional	minlev
	)

Construct H(Curl) FE basis on each mesh level.

Note

Highest supported representation is quadratic.

Parameters

[in]

order

Order of representation desired

oft_hcurl_setup_surf()

subroutine oft_hcurl_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_hcurl_setup_vol()

subroutine oft_hcurl_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

cgop_map

integer(i4), dimension(4,4), parameter cgop_map = RESHAPE((/0,-1,-2,-3,1,0,-4,-5,2,4,0,-6,3,5,6,0/), (/4,4/))

oft_hcurl_id

integer(i4), parameter oft_hcurl_id = 3

FE type ID.