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_scalar_bfem
	Lagrange operator container. More...
type	oft_scalar_fem
	Lagrange operator container. More...

Functions/Subroutines
logical function	oft_2d_lagrange_cast (self, source)
	Cast abstract FE type to 2D lagrange finite element type.
logical function	oft_3d_lagrange_cast (self, source)
	Cast abstract FE type to 3D lagrange finite element type.
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 (lag_rep)
	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_setup (mg_mesh, order, ml_lag_obj, ml_blag_obj, ml_vlag_obj, 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 FE object.

Variables
integer(i4), parameter	oft_lagrange_id = 1
	FE type ID.

Function/Subroutine Documentation

oft_2d_lagrange_cast()

logical function oft_2d_lagrange_cast	(	class(oft_scalar_bfem), intent(out), pointer	self,
		class(oft_afem_type), intent(in), target	source
	)

Cast abstract FE type to 2D lagrange finite element type.

The source matrix must be oft_scalar_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_lagrange_cast()

logical function oft_3d_lagrange_cast	(	class(oft_scalar_fem), intent(out), pointer	self,
		class(oft_afem_type), intent(in), target	source
	)

Cast abstract FE type to 3D lagrange finite element type.

The source matrix must be oft_scalar_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_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	Second derivatives of function [6]
[in]	g2op	Grid Hessian [6,6]

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]	face	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]	face	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

(

class(oft_scalar_fem), intent(inout)

lag_rep

)

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	Second derivatives of function [6]
[in]	g2op	Grid Hessian [6,6]

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
[in]	gop	Gradient of lagrange element (dof) at point (f) [3]
[out]	val	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]	order	Needs docs
[out]	ed_nodes	Needs docs
[out]	fc_nodes	Needs docs
[out]	c_nodes	Needs docs

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_setup()

subroutine oft_lag_setup	(	type(multigrid_mesh), intent(inout), target	mg_mesh,
		integer(i4), intent(in)	order,
		type(oft_ml_fem_type), intent(inout), optional, target	ml_lag_obj,
		type(oft_ml_fem_type), intent(inout), optional	ml_blag_obj,
		type(oft_ml_fem_comp_type), intent(inout), optional	ml_vlag_obj,
		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
[in]	minlev	Lowest level to construct

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

[out]	self	Needs docs
[in]	tmesh	Needs docs
[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

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

scalar_bfem_delete()

subroutine scalar_bfem_delete

(

class(oft_scalar_bfem), intent(inout)

self

)

Destroy boundary FE object.

scalar_fem_delete()

subroutine scalar_fem_delete

(

class(oft_scalar_fem), intent(inout)

self

)

Destroy FE object.

Variable Documentation

oft_lagrange_id

integer(i4), parameter oft_lagrange_id = 1

FE type ID.