Detailed Description

Lagrange FE operator definitions.

Operator construction
- MOP: mass matrix \( \int \left( u^T v \right) dV \)
- LOP: laplacian matrix \( \int \left( \nabla u^T \cdot \nabla v \right) dV \)
- PDOP: parallel diffusion matrix \( \int \left( \nabla u^T \cdot \hat{b} \hat{b} \cdot \nabla v \right) dV \)
- VMOP: vector mass matrix \( \int \left( u^T \cdot v \right) dV \)
Interpolation classes
Field projection (to plotting mesh)
Boundary conditions
Multi-Grid setup and operators
Default preconditioner setup
- Optimal smoother calculation

Authors: Chris Hansen

Date: August 2011

Data Types
type	oft_lag_ginterp
	Interpolate \( \nabla \) of a Lagrange field. More...

type	oft_lag_rinterp
	Interpolate a Lagrange field. More...

type	oft_lag_vcinterp
	Interpolate \( \nabla \times \) of a Lagrange vector field. More...

type	oft_lag_vdinterp
	Interpolate \( \nabla \) of a Lagrange vector field. More...

type	oft_lag_vrinterp
	Interpolate a Lagrange vector field. More...

type	oft_lag_zerob
	Zero Lagrange FE vector at all global boundary nodes. More...

type	oft_lag_zerogrnd
	Zero Lagrange FE vector at all global grounding node(s) More...

type	oft_vlag_zerob
	Zero all components of vector Lagrange FE vector at all global boundary nodes. More...

type	oft_vlag_zeron
	Zero normal component of vector Lagrange FE vector at all global boundary nodes. More...

type	oft_vlag_zerot
	Zero tangential component of vector Lagrange FE vector at all global boundary nodes. More...

Functions/Subroutines
subroutine	lag_base_pop (self, acors, afine)
	Transfer a base level Lagrange scalar field to the next MPI level.

subroutine	lag_base_push (self, afine, acors)
	Transfer a MPI level Lagrange scalar field to the base level.

subroutine	lag_div (fe_rep, a, reg)
	Compute the divergence of a Lagrange vector field.

subroutine	lag_getlop_pre (ml_lag_rep, pre, mats, level, nlevels)
	Construct default MG preconditioner for LAG::LOP.

subroutine	lag_ginterp_apply (self, cell, f, gop, val)
	Reconstruct the gradient of a Lagrange scalar field.

subroutine	lag_lop_eigs (ml_lag_rep, minlev)
	Compute eigenvalues and smoothing coefficients for the operator LAG::LOP.

subroutine	lag_mloptions ()
	Read-in options for the basic Lagrange ML preconditioners.

subroutine	lag_rinterp (self, cell, f, gop, val)
	Reconstruct a Lagrange scalar field.

subroutine	lag_rinterp_delete (self)
	Destroy temporary internal storage and nullify references.

subroutine	lag_rinterp_setup (self, lag_rep)
	Setup interpolator for Lagrange scalar fields.

subroutine	lag_setup_interp (ml_lag_rep, ml_vlag_rep)
	Construct interpolation matrices on each MG level.

subroutine	lag_vbc_diag (lag_rep, j_lag, bc_type, nn)
	Get diagonal entries for a given boundary condition and desired node in a Lagrange vector field.

subroutine	lag_vbc_tensor (lag_rep, j_lag, bc_type, nn)
	Get boundary condition tensor for desired node in a Lagrange vector field.

subroutine	lag_vcinterp (self, cell, f, gop, val)
	Reconstruct the curl of a Lagrange vector field.

subroutine	lag_vdinterp (self, cell, f, gop, val)
	Reconstruct \( \nabla v \) for a Lagrange vector field.

subroutine	lag_vrinterp (self, cell, f, gop, val)
	Reconstruct a Lagrange vector field.

subroutine	lag_vrinterp_delete (self)
	Destroy temporary internal storage and nullify references.

subroutine	lag_vrinterp_setup (self, lag_rep)
	Setup interpolator for Lagrange vector fields.

subroutine	oft_lag_getlop (fe_rep, mat, bc)
	Construct laplacian matrix for Lagrange scalar representation.

subroutine	oft_lag_getmop (fe_rep, mat, bc)
	Construct mass matrix for Lagrange scalar representation.

subroutine	oft_lag_getpdop (fe_rep, mat, field, bc, perp, be_flag)
	Construct parallel diffusion matrix for Lagrange scalar representation.

subroutine	oft_lag_project (fe_rep, field, x)
	Project a scalar field onto a lagrange basis.

subroutine	oft_lag_project_div (fe_rep, field, x)
	Project the divergence of a scalar field onto a lagrange basis.

subroutine	oft_lag_vgetmop (vlag_rep, mat, bc)
	Construct mass matrix for Lagrange vector representation.

subroutine	oft_lag_vproject (fe_rep, field, x)
	Project a vector field onto a lagrange basis.

subroutine	vzerob_apply (self, a)
	Zero a surface Lagrange vector field at all edge nodes.

subroutine	vzerob_delete (self)
	Destroy temporary internal storage and nullify references.

subroutine	vzeron_apply (self, a)
	Zero normal component of a Lagrange vector field at boundary nodes.

subroutine	vzerot_apply (self, a)
	Zero tangential component of a Lagrange vector field at boundary nodes.

subroutine	zerob_apply (self, a)
	Zero a Lagrange scalar field at all boundary nodes.

subroutine	zerob_delete (self)
	Destroy temporary internal storage and nullify references.

subroutine	zerogrnd_apply (self, a)
	Zero a Lagrange scalar field at the global grounding node.

Variables
real(r8), dimension(fem_max_levels)	df_lop =-1.d99

real(r8), dimension(fem_max_levels), private	df_pdop =-1.d99

integer(i4), dimension(fem_max_levels)	nu_lop =0

integer(i4), dimension(fem_max_levels), private	nu_pdop =0

real(r8), dimension(:,:), pointer	oft_lag_gop => NULL()

real(r8), dimension(:), pointer	oft_lag_rop => NULL()

Function/Subroutine Documentation

◆ lag_base_pop()

subroutine lag_base_pop	(	class(oft_ml_fe_vecspace), intent(inout)	self,
		class(oft_vector), intent(inout)	acors,
		class(oft_vector), intent(inout)	afine
	)

Transfer a base level Lagrange scalar field to the next MPI level.

Parameters

[in,out]	acors	Vector to transfer
[in,out]	afine	Fine vector from transfer

◆ lag_base_push()

subroutine lag_base_push	(	class(oft_ml_fe_vecspace), intent(inout)	self,
		class(oft_vector), intent(inout)	afine,
		class(oft_vector), intent(inout)	acors
	)

Transfer a MPI level Lagrange scalar field to the base level.

Parameters

[in,out]	afine	Needs docs
[in,out]	acors	Needs docs

◆ lag_div()

subroutine lag_div	(	class(oft_afem_type), intent(inout), target	fe_rep,
		class(oft_vector), intent(inout)	a,
		real(r8), intent(out)	reg
	)

Compute the divergence of a Lagrange vector field.

Parameters

[in,out]	a	Input field
[out]	reg	\( \int_v \nabla \cdot a \; dV \)

◆ lag_getlop_pre()

subroutine lag_getlop_pre	(	type(oft_ml_fem_type), intent(inout), target	ml_lag_rep,
		class(oft_solver), intent(out), pointer	pre,
		type(oft_matrix_ptr), dimension(:), intent(inout), pointer	mats,
		integer(i4), intent(in), optional	level,
		integer(i4), intent(in), optional	nlevels
	)

Construct default MG preconditioner for LAG::LOP.

Parameters

[out]	pre	Needs docs
[in,out]	mats	Needs docs
[in]	level	Needs docs
[in]	nlevels	Needs docs

◆ lag_ginterp_apply()

subroutine lag_ginterp_apply	(	class(oft_lag_ginterp), intent(inout)	self,
		integer(i4), intent(in)	cell,
		real(r8), dimension(:), intent(in)	f,
		real(r8), dimension(3,4), intent(in)	gop,
		real(r8), dimension(:), intent(out)	val
	)

Reconstruct the gradient of a Lagrange scalar field.

Parameters

[in]	cell	Cell for interpolation
[in]	f	Position in cell in logical coord [4]
[in]	gop	Logical gradient vectors at f [3,4]
[out]	val	Reconstructed gradient at f [3]

◆ lag_lop_eigs()

subroutine lag_lop_eigs	(	type(oft_ml_fem_type), intent(inout), target	ml_lag_rep,
		integer(i4), intent(in)	minlev
	)

Compute eigenvalues and smoothing coefficients for the operator LAG::LOP.

Parameters

[in] minlev Needs docs

◆ lag_mloptions()

subroutine lag_mloptions

Read-in options for the basic Lagrange ML preconditioners.

◆ lag_rinterp()

subroutine lag_rinterp	(	class(oft_lag_rinterp), intent(inout)	self,
		integer(i4), intent(in)	cell,
		real(r8), dimension(:), intent(in)	f,
		real(r8), dimension(3,4), intent(in)	gop,
		real(r8), dimension(:), intent(out)	val
	)

Reconstruct a Lagrange scalar field.

Parameters

[in]	cell	Cell for interpolation
[in]	f	Position in cell in logical coord [4]
[in]	gop	Logical gradient vectors at f [3,4]
[out]	val	Reconstructed field at f [1]

◆ lag_rinterp_delete()

subroutine lag_rinterp_delete ( class(oft_lag_rinterp), intent(inout) self )

Destroy temporary internal storage and nullify references.

◆ lag_rinterp_setup()

subroutine lag_rinterp_setup	(	class(oft_lag_rinterp), intent(inout)	self,
		class(oft_afem_type), intent(inout), target	lag_rep
	)

Setup interpolator for Lagrange scalar fields.

Fetches local representation used for interpolation from vector object

◆ lag_setup_interp()

subroutine lag_setup_interp	(	class(oft_ml_fem_type), intent(inout)	ml_lag_rep,
		class(oft_ml_fem_comp_type), intent(inout), optional	ml_vlag_rep
	)

Construct interpolation matrices on each MG level.

◆ lag_vbc_diag()

subroutine lag_vbc_diag	(	class(oft_scalar_fem), intent(inout), target	lag_rep,
		integer(i4), intent(in)	j_lag,
		integer(i4), intent(in)	bc_type,
		real(r8), dimension(3,3), intent(out)	nn
	)

Get diagonal entries for a given boundary condition and desired node in a Lagrange vector field.

Parameters

[in]	j_lag	Local index of Lagrange node
[in]	bc_type	Desired BC (1 -> norm, 2-> tang)
[out]	nn	Diagonal entries (3,3)

◆ lag_vbc_tensor()

subroutine lag_vbc_tensor	(	class(oft_scalar_fem), intent(inout), target	lag_rep,
		integer(i4), intent(in)	j_lag,
		integer(i4), intent(in)	bc_type,
		real(r8), dimension(3,3), intent(out)	nn
	)

Get boundary condition tensor for desired node in a Lagrange vector field.

Parameters

[in]	j_lag	Local index of Lagrange node
[in]	bc_type	Desired BC (1 -> norm, 2-> tang)
[out]	nn	BC tensor (3,3)

◆ lag_vcinterp()

subroutine lag_vcinterp	(	class(oft_lag_vcinterp), intent(inout)	self,
		integer(i4), intent(in)	cell,
		real(r8), dimension(:), intent(in)	f,
		real(r8), dimension(3,4), intent(in)	gop,
		real(r8), dimension(:), intent(out)	val
	)

Reconstruct the curl of a Lagrange vector field.

Parameters

[in]	cell	Cell for interpolation
[in]	f	Position in cell in logical coord [4]
[in]	gop	Logical gradient vectors at f [3,4]
[out]	val	Reconstructed field at f [3]

◆ lag_vdinterp()

subroutine lag_vdinterp	(	class(oft_lag_vdinterp), intent(inout)	self,
		integer(i4), intent(in)	cell,
		real(r8), dimension(:), intent(in)	f,
		real(r8), dimension(3,4), intent(in)	gop,
		real(r8), dimension(:), intent(out)	val
	)

Reconstruct \( \nabla v \) for a Lagrange vector field.

The tensor is packed using reshape, to retrieve use

dv = reshape(val,(/3,3/))

Parameters

[in]	cell	Cell for interpolation
[in]	f	Position in cell in logical coord [4]
[in]	gop	Logical gradient vectors at f [3,4]
[out]	val	Reconstructed field at f [3]

◆ lag_vrinterp()

subroutine lag_vrinterp	(	class(oft_lag_vrinterp), intent(inout)	self,
		integer(i4), intent(in)	cell,
		real(r8), dimension(:), intent(in)	f,
		real(r8), dimension(3,4), intent(in)	gop,
		real(r8), dimension(:), intent(out)	val
	)

Reconstruct a Lagrange vector field.

Parameters

[in]	cell	Cell for interpolation
[in]	f	Position in cell in logical coord [4]
[in]	gop	Logical gradient vectors at f [3,4]
[out]	val	Reconstructed field at f [3]

◆ lag_vrinterp_delete()

subroutine lag_vrinterp_delete ( class(oft_lag_vrinterp), intent(inout) self )

Destroy temporary internal storage and nullify references.

◆ lag_vrinterp_setup()

subroutine lag_vrinterp_setup	(	class(oft_lag_vrinterp), intent(inout)	self,
		class(oft_afem_type), intent(inout), target	lag_rep
	)

Setup interpolator for Lagrange vector fields.

Fetches local representation used for interpolation from vector object

◆ oft_lag_getlop()

subroutine oft_lag_getlop	(	class(oft_afem_type), intent(inout), target	fe_rep,
		class(oft_matrix), intent(inout), pointer	mat,
		character(len=*), intent(in)	bc
	)

Construct laplacian matrix for Lagrange scalar representation.

Supported boundary conditions

‘'none’Full matrix -'zerob'Dirichlet for all boundary DOF -'grnd'` Dirichlet for only groundin point
Parameters

[in,out] mat Matrix object

[in] bc Boundary condition

◆ oft_lag_getmop()

subroutine oft_lag_getmop	(	class(oft_afem_type), intent(inout), target	fe_rep,
		class(oft_matrix), intent(inout), pointer	mat,
		character(len=*), intent(in)	bc
	)

Construct mass matrix for Lagrange scalar representation.

Supported boundary conditions

‘'none’Full matrix -'zerob'` Dirichlet for all boundary DOF
Parameters

[in,out] mat Matrix object

[in] bc Boundary condition

◆ oft_lag_getpdop()

subroutine oft_lag_getpdop	(	class(oft_afem_type), intent(inout), target	fe_rep,
		class(oft_matrix), intent(inout), pointer	mat,
		class(fem_interp), intent(inout)	field,
		character(len=*), intent(in)	bc,
		real(r8), intent(in), optional	perp,
		logical, dimension(:), intent(in), optional	be_flag
	)

Construct parallel diffusion matrix for Lagrange scalar representation.

Supported boundary conditions

‘'none’Full matrix -'zerob'Dirichlet for all boundary DOF -'grnd'` Dirichlet for only groundin point

Parameters

[in,out]	mat	Matrix object
[in,out]	field	Vector field defining \( \hat{b} \)
[in]	bc	Boundary condition
[in]	perp	Value of perpendicular conductivity (optional)
[in]	be_flag	Flag for dirichlet nodes if different from boundary [ne] (optional)

◆ oft_lag_project()

subroutine oft_lag_project	(	class(oft_afem_type), intent(inout), target	fe_rep,
		class(fem_interp), intent(inout)	field,
		class(oft_vector), intent(inout)	x
	)

Project a scalar field onto a lagrange basis.

Note: This subroutine only performs the integration of the field with test functions for a Lagrange basis. To retrieve the correct projection the result must be multiplied by the inverse of LAG::MOP

Parameters

[in,out]	field	Scalar field for projection
[in,out]	x	Field projected onto Lagrange basis

◆ oft_lag_project_div()

subroutine oft_lag_project_div	(	class(oft_afem_type), intent(inout), target	fe_rep,
		class(fem_interp), intent(inout)	field,
		class(oft_vector), intent(inout)	x
	)

Project the divergence of a scalar field onto a lagrange basis.

Note: This subroutine only performs the integration of the field with test functions for a Lagrange basis. To retrieve the correct projection the result must be multiplied by the inverse of LAG::MOP

Parameters

[in,out]	field	Scalar field for projection
[in,out]	x	Field projected onto Lagrange basis

◆ oft_lag_vgetmop()

subroutine oft_lag_vgetmop	(	class(oft_fem_comp_type), intent(inout), target	vlag_rep,
		class(oft_matrix), intent(inout), pointer	mat,
		character(len=*), intent(in)	bc
	)

Construct mass matrix for Lagrange vector representation.

Supported boundary conditions

‘'none’Full matrix -'all'Dirichlet for all components at boundary -'norm'Dirichlet for normal component at boundary -'tang'` Dirichlet for tangential component at boundary
Parameters

[in,out] mat Matrix object

[in] bc Boundary condition

◆ oft_lag_vproject()

subroutine oft_lag_vproject	(	class(oft_afem_type), intent(inout), target	fe_rep,
		class(fem_interp), intent(inout)	field,
		class(oft_vector), intent(inout)	x
	)

Project a vector field onto a lagrange basis.

Note: This subroutine only performs the integration of the field with test functions for a Lagrange basis. To retrieve the correct projection the result must be multiplied by the inverse of LAG::VMOP

Parameters

[in,out]	field	Vector field for projection
[in,out]	x	Field projected onto Lagrange basis

◆ vzerob_apply()

subroutine vzerob_apply	(	class(oft_vlag_zerob), intent(inout)	self,
		class(oft_vector), intent(inout)	a
	)

Zero a surface Lagrange vector field at all edge nodes.

Parameters

[in,out] a Field to be zeroed

◆ vzerob_delete()

subroutine vzerob_delete ( class(oft_vlag_zerob), intent(inout) self )

Destroy temporary internal storage and nullify references.

◆ vzeron_apply()

subroutine vzeron_apply	(	class(oft_vlag_zeron), intent(inout)	self,
		class(oft_vector), intent(inout)	a
	)

Zero normal component of a Lagrange vector field at boundary nodes.

Parameters

[in,out] a Field to be zeroed

◆ vzerot_apply()

subroutine vzerot_apply	(	class(oft_vlag_zerot), intent(inout)	self,
		class(oft_vector), intent(inout)	a
	)

Zero tangential component of a Lagrange vector field at boundary nodes.

Parameters

[in,out] a Field to be zeroed

◆ zerob_apply()

subroutine zerob_apply	(	class(oft_lag_zerob), intent(inout)	self,
		class(oft_vector), intent(inout)	a
	)

Zero a Lagrange scalar field at all boundary nodes.

Parameters

[in,out] a Field to be zeroed

◆ zerob_delete()

subroutine zerob_delete ( class(oft_lag_zerob), intent(inout) self )

Destroy temporary internal storage and nullify references.

◆ zerogrnd_apply()

subroutine zerogrnd_apply	(	class(oft_lag_zerogrnd), intent(inout)	self,
		class(oft_vector), intent(inout)	a
	)

Zero a Lagrange scalar field at the global grounding node.

Note: The possition of this node is defined by the mesh pointer igrnd in mesh

Parameters

[in,out] a Field to be zeroed

Variable Documentation

◆ df_lop

real(r8), dimension(fem_max_levels) df_lop =-1.d99

◆ df_pdop

real(r8), dimension(fem_max_levels), private df_pdop =-1.d99

private

◆ nu_lop

integer(i4), dimension(fem_max_levels) nu_lop =0

◆ nu_pdop

integer(i4), dimension(fem_max_levels), private nu_pdop =0

private

◆ oft_lag_gop

real(r8), dimension(:,:), pointer oft_lag_gop => NULL()

◆ oft_lag_rop

real(r8), dimension(:), pointer oft_lag_rop => NULL()

Detailed Description

Data Types

Functions/Subroutines

Variables

Function/Subroutine Documentation

◆ lag_base_pop()

◆ lag_base_push()

◆ lag_div()

◆ lag_getlop_pre()

◆ lag_ginterp_apply()

◆ lag_lop_eigs()

◆ lag_mloptions()

◆ lag_rinterp()

◆ lag_rinterp_delete()

◆ lag_rinterp_setup()

◆ lag_setup_interp()

◆ lag_vbc_diag()

◆ lag_vbc_tensor()

◆ lag_vcinterp()

◆ lag_vdinterp()

◆ lag_vrinterp()

◆ lag_vrinterp_delete()

◆ lag_vrinterp_setup()

◆ oft_lag_getlop()

◆ oft_lag_getmop()

◆ oft_lag_getpdop()

◆ oft_lag_project()

◆ oft_lag_project_div()

◆ oft_lag_vgetmop()

◆ oft_lag_vproject()

◆ vzerob_apply()

◆ vzerob_delete()

◆ vzeron_apply()

◆ vzerot_apply()

◆ zerob_apply()

◆ zerob_delete()

◆ zerogrnd_apply()

Variable Documentation

◆ df_lop

◆ df_pdop

◆ nu_lop

◆ nu_pdop

◆ oft_lag_gop

◆ oft_lag_rop