oft_h1_operators Module Reference

Detailed Description

Nedelec H1 FE operator definitions.

• 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_h1_cinterp
	Interpolate \( \nabla \times \) of a H1 vector field. More...
type	oft_h1_dinterp
	Interpolate \( \nabla \times \) of a H1 vector field. More...
type	oft_h1_divout
	Clean the divergence from a H1 vector field. More...
type	oft_h1_rinterp
	Interpolate a H1 vector field. More...
type	oft_h1_zerograd
	Orthogonalize a H1 vector field by zeroing the gradient subspace. More...

Functions/Subroutines
subroutine	h1_base_pop (acors, afine)
	Transfer a base level Lagrange scalar field to the next MPI level.
subroutine	h1_base_push (afine, acors)
	Transfer a MPI level Lagrange scalar field to the base level.
subroutine	h1_bmc (a, hcpc, hcpv, new_tol)
	Compute the 0-th order gradient due to a jump plane.
subroutine	h1_cinterp (self, cell, f, gop, val)
	Reconstruct \( \nabla \times \) of a Nedelec H1 vector field.
subroutine	h1_curltp (a, b)
	Apply the curl transpose operator to a H1 field.
subroutine	h1_dinterp (self, cell, f, gop, val)
	Reconstruct \( \nabla \cdot \) of a Nedelec H1 vector field.
subroutine	h1_div (a, b)
	Apply the divergence operator to a H1 field.
subroutine	h1_divout_apply (self, u)
	Remove divergence from a H1 vector field by adding a gradient correction.
subroutine	h1_divout_delete (self)
	Clean-up internal storage for a oft_h1_divout object.
subroutine	h1_divout_setup (self, bc)
	Setup matrix and solver with default.
subroutine	h1_getmop (mat, bc)
	Construct mass matrix for a H1 representation.
subroutine	h1_getmop_pre (pre, mats, level, nlevels)
	Compute eigenvalues and smoothing coefficients for the operator H1::MOP.
subroutine	h1_grad (a, b, keep_boundary)
	Add the gradient of a H0 scalar field to a H1 vector field.
subroutine	h1_gradtp (a, b)
	Apply the transposed gradient operator to a Nedelec H1 vector field.
subroutine	h1_inject (afine, acors)
	Inject a fine level Lagrange scalar field to the next coarsest level.
subroutine	h1_interp (acors, afine)
	Interpolate a coarse level Lagrange scalar field to the next finest level.
real(r8) function	h1_jump_error (u, quad_order)
	Evaluate the jump error in a field over internal faces.
subroutine	h1_mc (a, hcpc, hcpv, new_tol)
	Compute the 0-th order gradient due to a jump plane.
subroutine	h1_mloptions
	Read-in options for the basic Nedelec H1(Curl) ML preconditioners.
subroutine	h1_mop_eigs (minlev)
	Compute eigenvalues and smoothing coefficients for the operator H1::MOP.
subroutine	h1_rinterp (self, cell, f, gop, val)
	Reconstruct a Nedelec H1 vector field.
subroutine	h1_rinterp_delete (self)
	Destroy temporary internal storage.
subroutine	h1_rinterp_setup (self)
	Setup interpolator for H1 vector fields.
subroutine	h1_setup_interp (create_full)
	Construct interpolation matrices on each MG level.
subroutine	h1_zerob (a)
	Zero a Nedelec H1 vector field at all boundary nodes.
subroutine	h1_zerograd_apply (self, u)
subroutine	h1_zerograd_delete (self)
subroutine	h1_zeroi (a)
	Zero a Nedelec H1 vector field at all interior nodes.
subroutine	h1curl_zerob (a)
	Zero the curl components of a Nedelec H1 vector field at all boundary nodes.
subroutine	h1grad_zerop (a)
	Zero the gradient components of a Nedelec H1 vector field at all boundary nodes.
subroutine	hgrad_ginterpmatrix (mat)
	Construct interpolation matrix for polynomial levels.
subroutine	oft_h1_bproject (field, x)
	Boundary projection of a vector field onto a H1 basis.
subroutine	oft_h1_project (field, x)
	Project a vector field onto a H1 basis.

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

Function/Subroutine Documentation

h1_base_pop()

subroutine h1_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

h1_base_push()

subroutine h1_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

h1_bmc()

subroutine h1_bmc	(	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]

h1_cinterp()

subroutine h1_cinterp	(	class(oft_h1_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 Nedelec H1 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]

h1_curltp()

subroutine h1_curltp	(	class(oft_vector), intent(inout)	a,
		class(oft_vector), intent(inout)	b
	)

Apply the curl transpose operator to a H1 field.

h1_dinterp()

subroutine h1_dinterp	(	class(oft_h1_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 Nedelec H1 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 [1]

h1_div()

subroutine h1_div	(	class(oft_vector), intent(inout)	a,
		class(oft_vector), intent(inout)	b
	)

Apply the divergence operator to a H1 field.

h1_divout_apply()

subroutine h1_divout_apply	(	class(oft_h1_divout), intent(inout)	self,
		class(oft_vector), intent(inout)	u
	)

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

Note

Should only be used via class oft_h1_divout

Parameters

[in,out]

u

Field for divergence cleaning

h1_divout_delete()

subroutine h1_divout_delete

(

class(oft_h1_divout), intent(inout)

self

)

Clean-up internal storage for a oft_h1_divout object.

Note

Should only be used via class oft_h1_divout

h1_divout_setup()

subroutine h1_divout_setup	(	class(oft_h1_divout), intent(inout)	self,
		character(len=*), intent(in)	bc
	)

Setup matrix and solver with default.

Note

Should only be used via class oft_h1_divout

Parameters

[in]

bc

Boundary condition

h1_getmop()

subroutine h1_getmop	(	class(oft_matrix), intent(inout), pointer	mat,
		character(len=*), intent(in)	bc
	)

Construct mass matrix for a H1 representation.

Supported boundary conditions

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

Parameters

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

h1_getmop_pre()

subroutine h1_getmop_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
	)

Compute eigenvalues and smoothing coefficients for the operator H1::MOP.

h1_grad()

subroutine h1_grad	(	class(oft_vector), intent(inout)	a,
		class(oft_vector), intent(inout)	b,
		logical, intent(in), optional	keep_boundary
	)

Add the gradient of a H0 scalar field to a H1 vector field.

Note

By default the 0-th order gradient subspace is represented on the H1(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)

h1_gradtp()

subroutine h1_gradtp	(	class(oft_vector), intent(inout)	a,
		class(oft_vector), intent(inout)	b
	)

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

Parameters

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

h1_inject()

subroutine h1_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

h1_interp()

subroutine h1_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

h1_jump_error()

real(r8) function h1_jump_error	(	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.

Parameters

[in,out]	u	H1 vector field to evaluate
[in]	quad_order	Desired quadrature order for integration

Returns

Jump error metric

h1_mc()

subroutine h1_mc	(	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]

h1_mloptions()

subroutine h1_mloptions

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

h1_mop_eigs()

subroutine h1_mop_eigs

(

integer(i4), intent(in)

minlev

)

Compute eigenvalues and smoothing coefficients for the operator H1::MOP.

h1_rinterp()

subroutine h1_rinterp	(	class(oft_h1_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 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]

h1_rinterp_delete()

subroutine h1_rinterp_delete

(

class(oft_h1_rinterp), intent(inout)

self

)

Destroy temporary internal storage.

Note

Should only be used via class oft_h1_rinterp or children

h1_rinterp_setup()

subroutine h1_rinterp_setup

(

class(oft_h1_rinterp), intent(inout)

self

)

Setup interpolator for H1 vector fields.

Fetches local representation used for interpolation from vector object

Note

Should only be used via class oft_h1_rinterp or children

h1_setup_interp()

subroutine h1_setup_interp

(

logical, intent(in), optional

create_full

)

Construct interpolation matrices on each MG level.

h1_zerob()

subroutine h1_zerob

(

class(oft_vector), intent(inout)

a

)

Zero a Nedelec H1 vector field at all boundary nodes.

Parameters

[in,out]

a

Field to be zeroed

h1_zerograd_apply()

subroutine h1_zerograd_apply	(	class(oft_h1_zerograd), intent(inout)	self,
		class(oft_vector), intent(inout)	u
	)

h1_zerograd_delete()

subroutine h1_zerograd_delete

(

class(oft_h1_zerograd), intent(inout)

self

)

h1_zeroi()

subroutine h1_zeroi

(

class(oft_vector), intent(inout)

a

)

Zero a Nedelec H1 vector field at all interior nodes.

Parameters

[in,out]

a

Field to be zeroed

h1curl_zerob()

subroutine h1curl_zerob

(

class(oft_vector), intent(inout)

a

)

Zero the curl components of a Nedelec H1 vector field at all boundary nodes.

Parameters

[in,out]

a

Field to be zeroed

h1grad_zerop()

subroutine h1grad_zerop

(

class(oft_vector), intent(inout)

a

)

Zero the gradient components of a Nedelec H1 vector field at all boundary nodes.

Parameters

[in,out]

a

Field to be zeroed

hgrad_ginterpmatrix()

subroutine hgrad_ginterpmatrix

(

class(oft_matrix), intent(inout), pointer

mat

)

Construct interpolation matrix for polynomial levels.

oft_h1_bproject()

subroutine oft_h1_bproject	(	class(fem_interp), intent(inout)	field,
		class(oft_vector), intent(inout)	x
	)

Boundary projection of a vector field onto a H1 basis.

Note

This subroutine only performs the integration of the field with boundary test functions for a H1 basis.

Parameters

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

oft_h1_project()

subroutine oft_h1_project	(	class(fem_interp), intent(inout)	field,
		class(oft_vector), intent(inout)	x
	)

Project a vector field onto a H1 basis.

Note

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

Parameters

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

Variable Documentation

df_mop

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

private

nu_mop

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

private