oft_lag_operators Module Reference

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...

Functions/Subroutines
subroutine	lag_base_pop (acors, afine)
	Transfer a base level Lagrange scalar field to the next MPI level.
subroutine	lag_base_push (afine, acors)
	Transfer a MPI level Lagrange scalar field to the base level.
subroutine	lag_div (a, reg)
	Compute the divergence of a Lagrange vector field.
subroutine	lag_getlop_pre (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_ginterpmatrix (mat)
	Construct interpolation matrix for polynomial levels.
subroutine	lag_inject (afine, acors)
	Inject a fine level Lagrange scalar field to the next coarsest level.
subroutine	lag_interp (acors, afine)
	Interpolate a coarse level Lagrange scalar field to the next finest level.
subroutine	lag_lop_eigs (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_pinterpmatrix (mat)
	Construct interpolation matrix for polynomial levels.
subroutine	lag_rinterp (self, cell, f, gop, val)
	Reconstruct a Lagrange scalar field.
subroutine	lag_rinterp_delete (self)
	Destroy temporary internal storage.
subroutine	lag_rinterp_setup (self)
	Setup interpolator for Lagrange scalar fields.
subroutine	lag_setup_interp (create_vec)
	Construct interpolation matrices on each MG level.
subroutine	lag_vbc_diag (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 (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_vinject (afine, acors)
	Inject a fine level Lagrange scalar field to the next coarsest level.
subroutine	lag_vinterp (acors, afine)
	Interpolate a coarse level Lagrange scalar field to the next finest level.
subroutine	lag_vrinterp (self, cell, f, gop, val)
	Reconstruct a Lagrange vector field.
subroutine	lag_vrinterp_delete (self)
	Setup interpolator for Lagrange vector fields.
subroutine	lag_vrinterp_setup (self)
	Setup interpolator for Lagrange vector fields.
subroutine	lag_vzerob (a)
	Zero a surface Lagrange vector field at all edge nodes.
subroutine	lag_vzeron (a)
	Zero normal component of a Lagrange vector field at boundary nodes.
subroutine	lag_vzerot (a)
	Zero tangential component of a Lagrange vector field at boundary nodes.
subroutine	lag_zerob (a)
	Zero a Lagrange scalar field at all boundary nodes.
subroutine	lag_zerogrnd (a)
	Zero a Lagrange scalar field at the global grounding node.
subroutine	oft_lag_getlop (mat, bc)
	Construct laplacian matrix for Lagrange scalar representation.
subroutine	oft_lag_getmop (mat, bc)
	Construct mass matrix for Lagrange scalar representation.
subroutine	oft_lag_getpdop (mat, field, bc, perp, be_flag)
	Construct parallel diffusion matrix for Lagrange scalar representation.
subroutine	oft_lag_project (field, x)
	Project a scalar field onto a lagrange basis.
subroutine	oft_lag_project_div (field, x)
	Project the divergence of a scalar field onto a lagrange basis.
subroutine	oft_lag_vgetmop (mat, bc)
	Construct mass matrix for Lagrange vector representation.
subroutine	oft_lag_vproject (field, x)
	Project a vector field onto a lagrange basis.

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_vector), intent(inout)	acors,
		class(oft_vector), intent(inout)	afine
	)

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

Parameters

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

lag_base_push()

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

lag_div()

subroutine lag_div	(	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	(	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.

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.

Note

Should only be used via class oft_lag_ginterp

Parameters

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

lag_ginterpmatrix()

subroutine lag_ginterpmatrix

(

class(oft_matrix), intent(inout), pointer

mat

)

Construct interpolation matrix for polynomial levels.

lag_inject()

subroutine lag_inject	(	class(oft_vector), intent(inout)	afine,
		class(oft_vector), intent(inout)	acors
	)

Inject a fine level Lagrange scalar field to the next coarsest level.

Note

The global Lagrange level in decremented by one in this subroutine

Parameters

[in]	afine	Vector to inject
[in,out]	acors	Coarse vector from injection

lag_interp()

subroutine lag_interp	(	class(oft_vector), intent(inout)	acors,
		class(oft_vector), intent(inout)	afine
	)

Interpolate a coarse level Lagrange scalar field to the next finest level.

Note

The global Lagrange level in incremented by one in this subroutine

Parameters

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

lag_lop_eigs()

subroutine lag_lop_eigs

(

integer(i4), intent(in)

minlev

)

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

lag_mloptions()

subroutine lag_mloptions

Read-in options for the basic Lagrange ML preconditioners.

lag_pinterpmatrix()

subroutine lag_pinterpmatrix

(

class(oft_matrix), intent(inout), pointer

mat

)

Construct interpolation matrix for polynomial levels.

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.

Note

Should only be used via class oft_lag_rinterp

Parameters

[in]	cell	Cell for interpolation
[in]	f	Possition 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.

Note

Should only be used via class oft_lag_rinterp or children

lag_rinterp_setup()

subroutine lag_rinterp_setup

(

class(oft_lag_rinterp), intent(inout)

self

)

Setup interpolator for Lagrange scalar fields.

Fetches local representation used for interpolation from vector object

Note

Should only be used via class oft_lag_rinterp or children

lag_setup_interp()

subroutine lag_setup_interp

(

logical, intent(in), optional

create_vec

)

Construct interpolation matrices on each MG level.

lag_vbc_diag()

subroutine lag_vbc_diag	(	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	(	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.

Note

Should only be used via class oft_lag_vcinterp

Parameters

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

Note

Should only be used via class oft_lag_vdinterp

Parameters

[in]	cell	Cell for interpolation
[in]	f	Possition in cell in logical coord [4]
[in]	gop	Logical gradient vectors at f [3,4]
[out]	val	Reconstructed tensor at f [9]

lag_vinject()

subroutine lag_vinject	(	class(oft_vector), intent(inout)	afine,
		class(oft_vector), intent(inout)	acors
	)

Inject a fine level Lagrange scalar field to the next coarsest level.

Note

The global Lagrange level in decremented by one in this subroutine

Parameters

[in]	afine	Vector to inject
[in,out]	acors	Coarse vector from injection

lag_vinterp()

subroutine lag_vinterp	(	class(oft_vector), intent(inout)	acors,
		class(oft_vector), intent(inout)	afine
	)

Interpolate a coarse level Lagrange scalar field to the next finest level.

Note

The global Lagrange level in incremented by one in this subroutine

Parameters

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

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.

Note

Should only be used via class oft_lag_vrinterp

Parameters

[in]	cell	Cell for interpolation
[in]	f	Possition 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

)

Setup interpolator for Lagrange vector fields.

Fetches local representation used for interpolation from vector object

Note

Should only be used via class oft_lag_vrinterp or children

lag_vrinterp_setup()

subroutine lag_vrinterp_setup

(

class(oft_lag_vrinterp), intent(inout)

self

)

Setup interpolator for Lagrange vector fields.

Fetches local representation used for interpolation from vector object

Note

Should only be used via class oft_lag_vrinterp or children

lag_vzerob()

subroutine lag_vzerob

(

class(oft_vector), intent(inout)

a

)

Zero a surface Lagrange vector field at all edge nodes.

Parameters

[in,out]

a

Field to be zeroed

lag_vzeron()

subroutine lag_vzeron

(

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

lag_vzerot()

subroutine lag_vzerot

(

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

lag_zerob()

subroutine lag_zerob

(

class(oft_vector), intent(inout)

a

)

Zero a Lagrange scalar field at all boundary nodes.

Parameters

[in,out]

a

Field to be zeroed

lag_zerogrnd()

subroutine lag_zerogrnd

(

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

oft_lag_getlop()

subroutine oft_lag_getlop	(	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_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_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(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(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_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(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

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()