oft_hcurl_operators Module Reference

Detailed Description

Nedelec H1(Curl) FE operator definitions.

• Operator construction
  • MOP: mass matrix \( \int \left( u^T \cdot v \right) dV \)
  • KOP: helicity matrix \( \int \left( \nabla \times u^T \cdot v \right) dV \)
  • WOP: energy matrix \( \int \left( \nabla \times u^T \cdot \nabla \times v \right) dV \)
• Interpolation classes
• Explicit operators
  • Gradient
  • Divergence
  • GradT
  • MC gradient
  • Divergence cleaning
• Boundary conditions
• Multi-Grid setup and operators
• Default preconditioner setup
  • Optimal smoother calculation

Authors

Chris Hansen

Date

August 2011

Data Types
type	oft_hcurl_cinterp
	Interpolate \( \nabla \times \) of a H1(Curl) field. More...
type	oft_hcurl_divout
	Clean the divergence from a H1(Curl) vector field. More...
type	oft_hcurl_orthog
	Orthogonalize a H1(Curl) vector against a library of given modes. More...
type	oft_hcurl_rinterp
	Interpolate a H1(Curl) field. More...

Functions/Subroutines
subroutine	hcurl_base_pop (acors, afine)
	Transfer a base level H1(Curl) vector field to the next MPI level.
subroutine	hcurl_base_push (afine, acors)
	Transfer a MPI level H1(Curl) vector field to the base level.
subroutine	hcurl_cinterp (self, cell, f, gop, val)
	Reconstruct the curl of a Nedelec H1(Curl) vector field.
subroutine	hcurl_div (a, b)
	Apply the divergence operator to a H1(Curl) field.
subroutine	hcurl_divout_apply (self, u)
	Remove divergence from a H1(Curl) vector field by adding a gradient correction.
subroutine	hcurl_divout_delete (self)
	Clean-up internal storage for a oft_hcurl_divout object.
subroutine	hcurl_divout_setup (self, bc)
	Setup matrix and solver with default.
subroutine	hcurl_getjmlb_pre (pre, mats, alam, level, nlevels)
	Construct default MG preconditioner for H1(Curl)::JMLB.
subroutine	hcurl_getwop_pre (pre, mats, level, nlevels)
	Construct default MG preconditioner for H1(Curl)::WOP.
subroutine	hcurl_ginterpmatrix (mat)
	Construct interpolation matrix for polynomial levels.
subroutine	hcurl_grad (a, b)
	Add the gradient of a linear Lagrange scalar field to a H1(Curl) field.
subroutine	hcurl_gradtp (a, b)
	Apply the transposed gradient operator to a Nedelec H1(Curl) vector field.
subroutine	hcurl_inject (afine, acors)
	Inject a fine level H1(Curl) vector field to the next coarsest level.
subroutine	hcurl_interp (acors, afine)
	Interpolate a coarse level H1(Curl) vector field to the next finest level.
subroutine	hcurl_mloptions
	Read-in options for the basic Nedelec H1(Curl) ML preconditioners.
subroutine	hcurl_orthog_apply (self, u)
	Orthogonalize a H1(Curl) vector against a library of given modes.
subroutine	hcurl_orthog_delete (self)
	Clean-up internal storage for a oft_hcurl_orthog object.
subroutine	hcurl_pinterpmatrix (mat)
	Construct interpolation matrix for polynomial levels.
subroutine	hcurl_rinterp (self, cell, f, gop, val)
	Reconstruct a Nedelec H1(Curl) vector field.
subroutine	hcurl_rinterp_delete (self)
	Destroy temporary internal storage.
subroutine	hcurl_rinterp_setup (self)
	Setup interpolator for H1(Curl) fields.
subroutine	hcurl_setup_interp
	Construct interpolation matrices on each MG level.
subroutine	hcurl_wop_eigs (minlev)
	Compute eigenvalues and smoothing coefficients for the operator H1(Curl)::WOP.
subroutine	hcurl_zerob (a)
	Zero the tangential component of a Nedelec H1(Curl) vector field on the boundary.
subroutine	oft_hcurl_bcurl (field, x)
	Compute the boundary term for integration by parts of the curl operator using a HCurl basis.
subroutine	oft_hcurl_getjmlb (mat, alam, bc)
	Construct force-free response matrix for a H1(Curl) representation.
subroutine	oft_hcurl_getkop (mat, bc)
	Construct helicity matrix for a H1(Curl) representation.
subroutine	oft_hcurl_getmop (mat, bc)
	Construct mass matrix for a H1(Curl) representation.
subroutine	oft_hcurl_getwop (mat, bc)
	Construct energy matrix for a H1(Curl) representation.
subroutine	oft_hcurl_project (field, x)
	Project a vector field onto a H1(Curl) basis.

Variables
real(r8), dimension(fem_max_levels)	df_wop =-1.d99
integer(i4), dimension(fem_max_levels)	nu_jmlb =20
integer(i4), dimension(fem_max_levels)	nu_wop =0
real(r8), dimension(:,:), pointer	oft_hcurl_cop => NULL()
real(r8), dimension(:,:), pointer	oft_hcurl_rop => NULL()

Function/Subroutine Documentation

hcurl_base_pop()

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

Transfer a base level H1(Curl) vector field to the next MPI level.

Parameters

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

hcurl_base_push()

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

Transfer a MPI level H1(Curl) vector field to the base level.

Parameters

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

hcurl_cinterp()

subroutine hcurl_cinterp	(	class(oft_hcurl_cinterp), 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 Nedelec H1(Curl) vector field.

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]

hcurl_div()

subroutine hcurl_div	(	class(oft_vector), intent(inout)	a,
		class(oft_vector), intent(inout)	b
	)

Apply the divergence operator to a H1(Curl) field.

Note

This subroutine computes the divergence of a H1(Curl) field as projected on to a linear Lagrange scalar basis.

hcurl_divout_apply()

subroutine hcurl_divout_apply	(	class(oft_hcurl_divout), intent(inout)	self,
		class(oft_vector), intent(inout)	u
	)

Remove divergence from a H1(Curl) vector field by adding a gradient correction.

Note

Should only be used via class oft_hcurl_divout

Parameters

[in,out]

u

Field for divergence cleaning

hcurl_divout_delete()

subroutine hcurl_divout_delete

(

class(oft_hcurl_divout), intent(inout)

self

)

Clean-up internal storage for a oft_hcurl_divout object.

Note

Should only be used via class oft_hcurl_divout

hcurl_divout_setup()

subroutine hcurl_divout_setup	(	class(oft_hcurl_divout), intent(inout)	self,
		character(len=*), intent(in)	bc
	)

Setup matrix and solver with default.

Note

Should only be used via class oft_hcurl_divout

Parameters

[in]

bc

Boundary condition

hcurl_getjmlb_pre()

subroutine hcurl_getjmlb_pre	(	class(oft_solver), intent(out), pointer	pre,
		type(oft_matrix_ptr), dimension(:), intent(inout), pointer	mats,
		real(r8), intent(in)	alam,
		integer(i4), intent(in), optional	level,
		integer(i4), intent(in), optional	nlevels
	)

Construct default MG preconditioner for H1(Curl)::JMLB.

hcurl_getwop_pre()

subroutine hcurl_getwop_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 H1(Curl)::WOP.

hcurl_ginterpmatrix()

subroutine hcurl_ginterpmatrix

(

class(oft_matrix), intent(inout), pointer

mat

)

Construct interpolation matrix for polynomial levels.

hcurl_grad()

subroutine hcurl_grad	(	class(oft_vector), intent(inout)	a,
		class(oft_vector), intent(inout)	b
	)

Add the gradient of a linear Lagrange scalar field to a H1(Curl) field.

hcurl_gradtp()

subroutine hcurl_gradtp	(	class(oft_vector), intent(inout)	a,
		class(oft_vector), intent(inout)	b
	)

Apply the transposed gradient operator to a Nedelec H1(Curl) vector field.

Note

Only the 0th order component is computed from the discrete gradient operator

Parameters

[in,out]	a	Input field
[in,out]	b	\( G^{T} a \)

hcurl_inject()

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

Inject a fine level H1(Curl) vector field to the next coarsest level.

Note

The global H1(Curl) level in decremented by one in this subroutine

Parameters

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

hcurl_interp()

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

Interpolate a coarse level H1(Curl) vector field to the next finest level.

Note

The global H1(Curl) level in incremented by one in this subroutine

Parameters

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

hcurl_mloptions()

subroutine hcurl_mloptions

Read-in options for the basic Nedelec H1(Curl) ML preconditioners.

hcurl_orthog_apply()

subroutine hcurl_orthog_apply	(	class(oft_hcurl_orthog), intent(inout)	self,
		class(oft_vector), intent(inout)	u
	)

Orthogonalize a H1(Curl) vector against a library of given modes.

Note

Used as a member function of oft_hcurl_orthog only

Parameters

[in,out]

u

Field to orthogonalize

hcurl_orthog_delete()

subroutine hcurl_orthog_delete

(

class(oft_hcurl_orthog), intent(inout)

self

)

Clean-up internal storage for a oft_hcurl_orthog object.

Note

Used as a member function of oft_hcurl_orthog only

hcurl_pinterpmatrix()

subroutine hcurl_pinterpmatrix

(

class(oft_matrix), intent(inout), pointer

mat

)

Construct interpolation matrix for polynomial levels.

hcurl_rinterp()

subroutine hcurl_rinterp	(	class(oft_hcurl_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 Nedelec H1(Curl) vector field.

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]

hcurl_rinterp_delete()

subroutine hcurl_rinterp_delete

(

class(oft_hcurl_rinterp), intent(inout)

self

)

Destroy temporary internal storage.

Note

Should only be used via class oft_hcurl_rinterp or children

hcurl_rinterp_setup()

subroutine hcurl_rinterp_setup

(

class(oft_hcurl_rinterp), intent(inout)

self

)

Setup interpolator for H1(Curl) fields.

Fetches local representation used for interpolation from vector object

Note

Should only be used via class oft_hcurl_rinterp or children

hcurl_setup_interp()

subroutine hcurl_setup_interp

Construct interpolation matrices on each MG level.

hcurl_wop_eigs()

subroutine hcurl_wop_eigs

(

integer(i4), intent(in)

minlev

)

Compute eigenvalues and smoothing coefficients for the operator H1(Curl)::WOP.

hcurl_zerob()

subroutine hcurl_zerob

(

class(oft_vector), intent(inout)

a

)

Zero the tangential component of a Nedelec H1(Curl) vector field on the boundary.

Parameters

[in,out]

a

Field to be zeroed

oft_hcurl_bcurl()

subroutine oft_hcurl_bcurl	(	class(fem_interp), intent(inout)	field,
		class(oft_vector), intent(inout)	x
	)

Compute the boundary term for integration by parts of the curl operator using a HCurl basis.

Parameters

[in,out]	field	Vector field for projection
[in,out]	x	\( \int \left( \textbf{u}^T \times \textbf{F} \right) \cdot \textbf{dS} \)

oft_hcurl_getjmlb()

subroutine oft_hcurl_getjmlb	(	class(oft_matrix), intent(inout), pointer	mat,
		real(r8), intent(in)	alam,
		character(len=*), intent(in)	bc
	)

Construct force-free response matrix for a H1(Curl) representation.

Supported boundary conditions

• 'none' Full matrix
• 'zerob' Dirichlet for all boundary DOF

Parameters

[in,out]	mat	Matrix object
[in]	alam	Lambda for response
[in]	bc	Boundary condition

oft_hcurl_getkop()

subroutine oft_hcurl_getkop	(	class(oft_matrix), intent(inout), pointer	mat,
		character(len=*), intent(in)	bc
	)

Construct helicity matrix for a H1(Curl) representation.

Supported boundary conditions

• 'none' Full matrix
• 'zerob' Dirichlet for all boundary DOF

Parameters

[in,out]	mat	Matrix object
[in]	bc	Boundary condition

oft_hcurl_getmop()

subroutine oft_hcurl_getmop	(	class(oft_matrix), intent(inout), pointer	mat,
		character(len=*), intent(in)	bc
	)

Construct mass matrix for a H1(Curl) representation.

Supported boundary conditions

• 'none' Full matrix
• 'zerob' Dirichlet for all boundary DOF

Parameters

[in,out]	mat	Matrix object
[in]	bc	Boundary condition

oft_hcurl_getwop()

subroutine oft_hcurl_getwop	(	class(oft_matrix), intent(inout), pointer	mat,
		character(len=*), intent(in)	bc
	)

Construct energy matrix for a H1(Curl) representation.

Supported boundary conditions

• 'none' Full matrix
• 'zerob' Dirichlet for all boundary DOF

Parameters

[in,out]	mat	Matrix object
[in]	bc	Boundary condition

oft_hcurl_project()

subroutine oft_hcurl_project	(	class(fem_interp), intent(inout)	field,
		class(oft_vector), intent(inout)	x
	)

Project a vector field onto a H1(Curl) basis.

Note

This subroutine only performs the integration of the field with test functions for a H1(Curl) basis. To retrieve the correct projection the result must be multiplied by the inverse of H1(Curl)::MOP.

Parameters

[in,out]	field	Vector field for projection
[in,out]	x	Field projected onto H1(Curl) basis

Variable Documentation

df_wop

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

nu_jmlb

integer(i4), dimension(fem_max_levels) nu_jmlb =20

nu_wop

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

oft_hcurl_cop

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

oft_hcurl_rop

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