oft_hcurl_grad_operators Module Reference

Detailed Description

FE operators for full H(Curl) + Grad(H^1) space.

• Operator construction
  • MOP: mass matrix \( \int \left( u^T \cdot v \right) dV \)
• 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_grad_cinterp
	Interpolate \( \nabla \times \) of a H(Curl) + Grad(H^1) vector field. More...
type	oft_hcurl_grad_czerob
	Needs docs. More...
type	oft_hcurl_grad_dinterp
	Interpolate \( \nabla \times \) of a H(Curl) + Grad(H^1) vector field. More...
type	oft_hcurl_grad_divout
	Clean the divergence from a H(Curl) + Grad(H^1) vector field. More...
type	oft_hcurl_grad_gzero
	Orthogonalize a H(Curl) + Grad(H^1) vector field by zeroing the gradient subspace. More...
type	oft_hcurl_grad_gzerop
	Needs docs. More...
type	oft_hcurl_grad_rinterp
	Interpolate a H(Curl) + Grad(H^1) vector field. More...
type	oft_hcurl_grad_zerob
	Needs docs. More...
type	oft_hcurl_grad_zeroi
	Needs docs. More...
type	oft_ml_hcurl_grad_vecspace
	Needs docs. More...

Functions/Subroutines
subroutine	base_pop (self, acors, afine)
	Transfer a base level Lagrange scalar field to the next MPI level.
subroutine	base_push (self, afine, acors)
	Transfer a MPI level Lagrange scalar field to the base level.
subroutine	cinterp_apply (self, cell, f, gop, val)
	Reconstruct \( \nabla \times \) of a H(Curl) + Grad(H^1) vector field.
subroutine	curl_zerob_apply (self, a)
	Zero the curl components of a H(Curl) + Grad(H^1) vector field at all boundary nodes.
subroutine	dinterp_apply (self, cell, f, gop, val)
	Reconstruct \( \nabla \cdot \) of a H(Curl) + Grad(H^1) vector field.
subroutine	divout_apply (self, a)
	Remove divergence from a H(Curl) + Grad(H^1) vector field by adding a gradient correction.
subroutine	divout_delete (self)
	Clean-up internal storage for a oft_hcurl_grad_divout object.
subroutine	divout_setup (self, ml_hcurl_grad_rep, bc, solver)
	Setup matrix and solver with default.
subroutine	grad_zerop_apply (self, a)
	Zero the gradient components of a H(Curl) + Grad(H^1) vector field at all boundary nodes.
subroutine	hcurl_grad_bmc (mesh, a, hcpc, hcpv, new_tol)
	Compute the 0-th order gradient due to a jump plane.
subroutine	hcurl_grad_curltp (hcurl_grad_fe, a, b)
	Apply the curl transpose operator to a H(Curl) + Grad(H^1) field.
subroutine	hcurl_grad_div (hcurl_grad_fe, a, b)
	Apply the divergence operator to a H(Curl) + Grad(H^1) field.
subroutine	hcurl_grad_getmop (hcurl_grad_rep, mat, bc)
	Construct mass matrix for a H(Curl) + Grad(H^1) representation.
subroutine	hcurl_grad_getmop_pre (ml_hcurl_aug_obj, pre, mats, level, nlevels)
	Compute eigenvalues and smoothing coefficients for the operator H(Curl) + Grad(H^1) mass matrix.
subroutine	hcurl_grad_grad (hcurl_grad_fe, a, b, keep_boundary)
	Add the gradient of a H^1 scalar field to a H(Curl) + Grad(H^1) vector field.
subroutine	hcurl_grad_gradtp (h1_fe, a, b)
	Apply the transposed gradient operator to a H(Curl) + Grad(H^1) vector field.
real(r8) function	hcurl_grad_jump_error (hcurl_grad_fe, u, quad_order)
	Evaluate the jump error in a field over internal faces.
subroutine	hcurl_grad_mc (mesh, a, hcpc, hcpv, new_tol)
	Compute the 0-th order gradient due to a jump plane.
subroutine	hcurl_grad_mloptions
	Read-in options for the basic H(Curl) + Grad(H^1) space ML preconditioners.
subroutine	hcurl_grad_mop_eigs (ml_hcurl_aug_obj, minlev)
	Compute eigenvalues and smoothing coefficients for the mass matrix.
subroutine	hcurl_grad_setup_interp (ml_hcurl_aug_rep, ml_h1_rep, create_full)
	Construct interpolation matrices on each MG level.
subroutine	ml_vecspace_inject (self, afine, acors)
	Interpolate a coarse level Lagrange scalar field to the next finest level.
subroutine	ml_vecspace_interp (self, acors, afine)
	Interpolate a coarse level Lagrange scalar field to the next finest level.
subroutine	oft_hcurl_grad_bproject (hcurl_grad_rep, field, x)
	Boundary projection of a vector field onto a H(Curl) + Grad(H^1) basis.
subroutine	oft_hcurl_grad_project (hcurl_grad_rep, field, x)
	Project a vector field onto a H(Curl) + Grad(H^1) basis.
subroutine	rinterp_apply (self, cell, f, gop, val)
	Reconstruct a H(Curl) + Grad(H^1) vector field.
subroutine	rinterp_delete (self)
	Destroy temporary internal storage.
subroutine	rinterp_setup1 (self, hcurl_grad_rep)
	Setup interpolator for H(Curl) + Grad(H^1) vector fields.
subroutine	rinterp_setup2 (self, hcurl_rep, hgrad_rep)
	Setup interpolator for H(Curl) + Grad(H^1) vector fields.
subroutine	zerob_apply (self, a)
	Zero a H(Curl) + Grad(H^1) vector field at all boundary nodes.
subroutine	zerob_delete (self)
	Zero a H(Curl) + Grad(H^1) vector field at all boundary nodes.
subroutine	zerograd_apply (self, a)
	Needs docs.
subroutine	zerograd_delete (self)
	Needs docs.
subroutine	zeroi_apply (self, a)
	Zero a H(Curl) + Grad(H^1) vector field at all interior nodes.

Variables
real(r8), dimension(fem_max_levels), private	df_mop =-1.d99
	Needs Docs.
integer(i4), dimension(fem_max_levels), private	nu_mop =0
	Needs Docs.

Function/Subroutine Documentation

base_pop()

subroutine base_pop	(	class(oft_ml_fe_comp_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

base_push()

subroutine base_push	(	class(oft_ml_fe_comp_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	Vector to transfer
[in,out]	acors	Fine vector from transfer

cinterp_apply()

subroutine cinterp_apply	(	class(oft_hcurl_grad_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 \( \nabla \times \) of a H(Curl) + Grad(H^1) 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]

curl_zerob_apply()

subroutine curl_zerob_apply	(	class(oft_hcurl_grad_czerob), intent(inout)	self,
		class(oft_vector), intent(inout)	a
	)

Zero the curl components of a H(Curl) + Grad(H^1) vector field at all boundary nodes.

Parameters

[in,out]

a

Field to be zeroed

dinterp_apply()

subroutine dinterp_apply	(	class(oft_hcurl_grad_dinterp), 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 \( \nabla \cdot \) of a H(Curl) + Grad(H^1) 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 [1]

divout_apply()

subroutine divout_apply	(	class(oft_hcurl_grad_divout), intent(inout)	self,
		class(oft_vector), intent(inout)	a
	)

Remove divergence from a H(Curl) + Grad(H^1) vector field by adding a gradient correction.

Parameters

[in,out]

a

Field for divergence cleaning

divout_delete()

subroutine divout_delete

(

class(oft_hcurl_grad_divout), intent(inout)

self

)

Clean-up internal storage for a oft_hcurl_grad_divout object.

divout_setup()

subroutine divout_setup	(	class(oft_hcurl_grad_divout), intent(inout)	self,
		class(oft_ml_fem_comp_type), intent(inout), target	ml_hcurl_grad_rep,
		character(len=*), intent(in)	bc,
		class(oft_solver), intent(in), optional, target	solver
	)

Setup matrix and solver with default.

Parameters

[in]

bc

Boundary condition

grad_zerop_apply()

subroutine grad_zerop_apply	(	class(oft_hcurl_grad_gzerop), intent(inout)	self,
		class(oft_vector), intent(inout)	a
	)

Zero the gradient components of a H(Curl) + Grad(H^1) vector field at all boundary nodes.

Parameters

[in,out]

a

Field to be zeroed

hcurl_grad_bmc()

subroutine hcurl_grad_bmc	(	class(oft_mesh), intent(inout)	mesh,
		class(oft_vector), intent(inout)	a,
		real(r8), dimension(3), intent(in)	hcpc,
		real(r8), dimension(3), intent(in)	hcpv,
		real(r8), intent(in), optional	new_tol
	)

Compute the 0-th order gradient due to a jump plane.

The jump is represented as a circular surface defined by a center possition and surface normal. This method requires that the mesh contain a matching internal surface, such that no edge crosses the jump plane.

Note

The radius of the surface is represented by \( \left| hcpv \right| \)

Parameters

[in,out]	a	Jump field
[in]	hcpc	Jump plane center possition [3]
[in]	hcpv	Jump plane normal vector [3]

hcurl_grad_curltp()

subroutine hcurl_grad_curltp	(	class(oft_fem_comp_type), intent(inout)	hcurl_grad_fe,
		class(oft_vector), intent(inout)	a,
		class(oft_vector), intent(inout)	b
	)

Apply the curl transpose operator to a H(Curl) + Grad(H^1) field.

Parameters

[in,out]	a	Needs docs
[in,out]	b	Needs docs

hcurl_grad_div()

subroutine hcurl_grad_div	(	class(oft_fem_comp_type), intent(inout)	hcurl_grad_fe,
		class(oft_vector), intent(inout)	a,
		class(oft_vector), intent(inout)	b
	)

Apply the divergence operator to a H(Curl) + Grad(H^1) field.

Parameters

[in,out]	a	Needs docs
[in,out]	b	Needs docs

hcurl_grad_getmop()

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

Construct mass matrix for a H(Curl) + Grad(H^1) representation.

Supported boundary conditions

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

  Parameters

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

hcurl_grad_getmop_pre()

subroutine hcurl_grad_getmop_pre	(	type(oft_ml_fem_comp_type), intent(inout), target	ml_hcurl_aug_obj,
		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
	)

Compute eigenvalues and smoothing coefficients for the operator H(Curl) + Grad(H^1) mass matrix.

hcurl_grad_grad()

subroutine hcurl_grad_grad	(	class(oft_fem_comp_type), intent(inout)	hcurl_grad_fe,
		class(oft_vector), intent(inout)	a,
		class(oft_vector), intent(inout)	b,
		logical, intent(in), optional	keep_boundary
	)

Add the gradient of a H^1 scalar field to a H(Curl) + Grad(H^1) vector field.

Note

By default the 0-th order gradient subspace is represented on the H(Curl) DOF, use the keep_boundary flag otherwise

Parameters

[in,out]	a	Scalar field
[in,out]	b	Vector field for gradient
[in]	keep_boundary	Flag to keep 0-th order boundary component (optional)

hcurl_grad_gradtp()

subroutine hcurl_grad_gradtp	(	class(oft_afem_type), intent(inout)	h1_fe,
		class(oft_vector), intent(inout)	a,
		class(oft_vector), intent(inout)	b
	)

Apply the transposed gradient operator to a H(Curl) + Grad(H^1) vector field.

Parameters

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

hcurl_grad_jump_error()

real(r8) function hcurl_grad_jump_error	(	class(oft_fem_comp_type), intent(inout)	hcurl_grad_fe,
		class(oft_vector), intent(inout)	u,
		integer(i4), intent(in)	quad_order
	)

Evaluate the jump error in a field over internal faces.

Note

Currently faces on domain boundaries are skipped, this is due to the fact that evaluting the error would require costly communication.

Returns

Jump error metric

Parameters

[in,out]	u	H(Curl) + Grad(H^1) vector field to evaluate
[in]	quad_order	Desired quadrature order for integration

hcurl_grad_mc()

subroutine hcurl_grad_mc	(	class(oft_mesh), intent(inout)	mesh,
		class(oft_vector), intent(inout)	a,
		real(r8), dimension(3), intent(in)	hcpc,
		real(r8), dimension(3), intent(in)	hcpv,
		real(r8), intent(in), optional	new_tol
	)

Compute the 0-th order gradient due to a jump plane.

The jump is represented as a circular surface defined by a center possition and surface normal. This method requires that the mesh contain a matching internal surface, such that no edge crosses the jump plane.

Note

The radius of the surface is represented by \( \left| hcpv \right| \)

Parameters

[in,out]	a	Jump field
[in]	hcpc	Jump plane center possition [3]
[in]	hcpv	Jump plane normal vector [3]

hcurl_grad_mloptions()

subroutine hcurl_grad_mloptions

Read-in options for the basic H(Curl) + Grad(H^1) space ML preconditioners.

hcurl_grad_mop_eigs()

subroutine hcurl_grad_mop_eigs	(	type(oft_ml_fem_comp_type), intent(inout), target	ml_hcurl_aug_obj,
		integer(i4), intent(in)	minlev
	)

Compute eigenvalues and smoothing coefficients for the mass matrix.

hcurl_grad_setup_interp()

subroutine hcurl_grad_setup_interp	(	class(oft_ml_fem_comp_type), intent(inout)	ml_hcurl_aug_rep,
		class(oft_ml_fem_type), intent(inout)	ml_h1_rep,
		logical, intent(in), optional	create_full
	)

Construct interpolation matrices on each MG level.

ml_vecspace_inject()

subroutine ml_vecspace_inject	(	class(oft_ml_hcurl_grad_vecspace), intent(inout)	self,
		class(oft_vector), intent(inout)	afine,
		class(oft_vector), intent(inout)	acors
	)

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

ml_vecspace_interp()

subroutine ml_vecspace_interp	(	class(oft_ml_hcurl_grad_vecspace), intent(inout)	self,
		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,out]	acors	Vector to interpolate
[in,out]	afine	Fine vector from interpolation

oft_hcurl_grad_bproject()

subroutine oft_hcurl_grad_bproject	(	class(oft_fem_comp_type), intent(inout)	hcurl_grad_rep,
		class(fem_interp), intent(inout)	field,
		class(oft_vector), intent(inout)	x
	)

Boundary projection of a vector field onto a H(Curl) + Grad(H^1) basis.

Note

This subroutine only performs the integration of the field with boundary test functions for a H(Curl) + Grad(H^1) basis

Parameters

[in,out]	field	Vector field for projection
[in,out]	x	Field projected onto H(Curl) + Grad(H^1) basis

oft_hcurl_grad_project()

subroutine oft_hcurl_grad_project	(	class(oft_fem_comp_type), intent(inout)	hcurl_grad_rep,
		class(fem_interp), intent(inout)	field,
		class(oft_vector), intent(inout)	x
	)

Project a vector field onto a H(Curl) + Grad(H^1) basis.

Note

This subroutine only performs the integration of the field with test functions for a H(Curl) + Grad(H^1) basis. To retrieve the correct projection the result must be multiplied by the inverse of the mass matrix

Parameters

[in,out]	field	Vector field for projection
[in,out]	x	Field projected onto H(Curl) + Grad(H^1) basis

rinterp_apply()

subroutine rinterp_apply	(	class(oft_hcurl_grad_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 H(Curl) + Grad(H^1) 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]

rinterp_delete()

subroutine rinterp_delete

(

class(oft_hcurl_grad_rinterp), intent(inout)

self

)

Destroy temporary internal storage.

rinterp_setup1()

subroutine rinterp_setup1	(	class(oft_hcurl_grad_rinterp), intent(inout)	self,
		class(oft_fem_comp_type), intent(inout), target	hcurl_grad_rep
	)

Setup interpolator for H(Curl) + Grad(H^1) vector fields.

Fetches local representation used for interpolation from vector object

rinterp_setup2()

subroutine rinterp_setup2	(	class(oft_hcurl_grad_rinterp), intent(inout)	self,
		class(oft_afem_type), intent(inout), target	hcurl_rep,
		class(oft_afem_type), intent(inout), target	hgrad_rep
	)

Setup interpolator for H(Curl) + Grad(H^1) vector fields.

Fetches local representation used for interpolation from vector object

zerob_apply()

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

Zero a H(Curl) + Grad(H^1) vector field at all boundary nodes.

Parameters

[in,out]

a

Field to be zeroed

zerob_delete()

subroutine zerob_delete

(

class(oft_hcurl_grad_zerob), intent(inout)

self

)

Zero a H(Curl) + Grad(H^1) vector field at all boundary nodes.

zerograd_apply()

subroutine zerograd_apply	(	class(oft_hcurl_grad_gzero), intent(inout)	self,
		class(oft_vector), intent(inout)	a
	)

Needs docs.

zerograd_delete()

subroutine zerograd_delete

(

class(oft_hcurl_grad_gzero), intent(inout)

self

)

Needs docs.

zeroi_apply()

subroutine zeroi_apply	(	class(oft_hcurl_grad_zeroi), intent(inout)	self,
		class(oft_vector), intent(inout)	a
	)

Zero a H(Curl) + Grad(H^1) vector field at all interior nodes.

Parameters

[in,out]

a

Field to be zeroed

Variable Documentation

df_mop

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

private

Needs Docs.

nu_mop

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

private

Needs Docs.