oft_h0_operators Module Reference

Detailed Description

Nedelec H0 FE operator definitions.

• Operator construction
  • MOP: mass matrix \( \int \left( u^T v \right) dV \)
  • LOP: laplacian matrix \( \int \left( \nabla u^T \cdot \nabla v \right) dV \)
• Interpolation classes
• Boundary conditions
• Multi-Grid setup and operators
• Default preconditioner setup
  • Optimal smoother calculation

Authors

Chris Hansen

Date

August 2011

Data Types
type	oft_h0_ginterp
	Interpolate \( \nabla \) of a H0 field. More...
type	oft_h0_rinterp
	Interpolate a H0 field. More...

Functions/Subroutines
subroutine	h0_base_pop (acors, afine)
	Transfer a base level H0 scalar field to the next MPI level.
subroutine	h0_base_push (afine, acors)
	Transfer a MPI level H0 scalar field to the base level.
subroutine	h0_getlop_pre (pre, mats, level, nlevels)
	Compute eigenvalues and smoothing coefficients for the operator H0::LOP.
subroutine	h0_ginterp_apply (self, cell, f, gop, val)
	Reconstruct the gradient of a Nedelec H0 scalar field.
subroutine	h0_ginterpmatrix (mat)
	Construct interpolation matrix for transfer between geometric levels of H0 finite element space.
subroutine	h0_inject (afine, acors)
	Inject a fine level H0 scalar field to the next coarsest level.
subroutine	h0_interp (acors, afine)
	Interpolate a coarse level H0 scalar field to the next finest level.
subroutine	h0_lop_eigs (minlev)
	Compute eigenvalues and smoothing coefficients for the operator H0::LOP.
subroutine	h0_mloptions
	Read-in options for the basic Nedelec H0 ML preconditioners.
subroutine	h0_pinterpmatrix (mat)
	Construct interpolation matrix for transfer between polynomial levels of H0 finite element space.
subroutine	h0_rinterp (self, cell, f, gop, val)
	Reconstruct a Nedelec H0 scalar field.
subroutine	h0_rinterp_delete (self)
	Destroy temporary internal storage.
subroutine	h0_rinterp_setup (self)
	Setup interpolator for H0 scalar fields.
subroutine	h0_setup_interp
	Construct interpolation matrices for transfer between H0 finite element spaces.
subroutine	h0_zerob (a)
	Zero a Nedelec H0 scalar field at all boundary nodes.
subroutine	h0_zerogrnd (a)
	Zero a Nedelec H0 scalar field at the global grounding node.
subroutine	h0_zeroi (a)
	Zero a Nedelec H0 scalar field at all interior nodes.
subroutine	oft_h0_getlop (mat, bc)
	Construct laplacian matrix for H0 scalar representation.
subroutine	oft_h0_getmop (mat, bc)
	Construct mass matrix for H0 scalar representation.
subroutine	oft_h0_project (field, x)
	Project a scalar field onto a H0 basis.

Variables
real(r8), dimension(fem_max_levels)	df_lop =-1.d99
integer(i4), dimension(fem_max_levels)	nu_lop =0
real(r8), dimension(:,:), pointer	oft_h0_gop => NULL()
real(r8), dimension(:), pointer	oft_h0_rop => NULL()

Function/Subroutine Documentation

h0_base_pop()

subroutine h0_base_pop	(	class(oft_vector), intent(inout)	acors,
		class(oft_vector), intent(inout)	afine
	)

Transfer a base level H0 scalar field to the next MPI level.

Parameters

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

h0_base_push()

subroutine h0_base_push	(	class(oft_vector), intent(inout)	afine,
		class(oft_vector), intent(inout)	acors
	)

Transfer a MPI level H0 scalar field to the base level.

Parameters

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

h0_getlop_pre()

subroutine h0_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
	)

Compute eigenvalues and smoothing coefficients for the operator H0::LOP.

h0_ginterp_apply()

subroutine h0_ginterp_apply	(	class(oft_h0_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 Nedelec H0 scalar 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]

h0_ginterpmatrix()

subroutine h0_ginterpmatrix

(

class(oft_matrix), intent(inout), pointer

mat

)

Construct interpolation matrix for transfer between geometric levels of H0 finite element space.

h0_inject()

subroutine h0_inject	(	class(oft_vector), intent(inout)	afine,
		class(oft_vector), intent(inout)	acors
	)

Inject a fine level H0 scalar field to the next coarsest level.

Note

The global H0 level in decremented by one in this subroutine

Parameters

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

h0_interp()

subroutine h0_interp	(	class(oft_vector), intent(inout)	acors,
		class(oft_vector), intent(inout)	afine
	)

Interpolate a coarse level H0 scalar field to the next finest level.

Note

The global H0 level in incremented by one in this subroutine

Parameters

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

h0_lop_eigs()

subroutine h0_lop_eigs

(

integer(i4), intent(in)

minlev

)

Compute eigenvalues and smoothing coefficients for the operator H0::LOP.

h0_mloptions()

subroutine h0_mloptions

Read-in options for the basic Nedelec H0 ML preconditioners.

h0_pinterpmatrix()

subroutine h0_pinterpmatrix

(

class(oft_matrix), intent(inout), pointer

mat

)

Construct interpolation matrix for transfer between polynomial levels of H0 finite element space.

h0_rinterp()

subroutine h0_rinterp	(	class(oft_h0_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 H0 scalar 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]

h0_rinterp_delete()

subroutine h0_rinterp_delete

(

class(oft_h0_rinterp), intent(inout)

self

)

Destroy temporary internal storage.

Note

Should only be used via class oft_h0_rinterp or children

h0_rinterp_setup()

subroutine h0_rinterp_setup

(

class(oft_h0_rinterp), intent(inout)

self

)

Setup interpolator for H0 scalar fields.

Fetches local representation used for interpolation from vector object

Note

Should only be used via class oft_h0_rinterp or children

h0_setup_interp()

subroutine h0_setup_interp

Construct interpolation matrices for transfer between H0 finite element spaces.

h0_zerob()

subroutine h0_zerob

(

class(oft_vector), intent(inout)

a

)

Zero a Nedelec H0 scalar field at all boundary nodes.

Parameters

[in,out]

a

Field to be zeroed

h0_zerogrnd()

subroutine h0_zerogrnd

(

class(oft_vector), intent(inout)

a

)

Zero a Nedelec H0 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

h0_zeroi()

subroutine h0_zeroi

(

class(oft_vector), intent(inout)

a

)

Zero a Nedelec H0 scalar field at all interior nodes.

Parameters

[in,out]

a

Field to be zeroed

oft_h0_getlop()

subroutine oft_h0_getlop	(	class(oft_matrix), intent(inout), pointer	mat,
		character(len=*), intent(in)	bc
	)

Construct laplacian matrix for H0 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_h0_getmop()

subroutine oft_h0_getmop	(	class(oft_matrix), intent(inout), pointer	mat,
		character(len=*), intent(in)	bc
	)

Construct mass matrix for H0 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_h0_project()

subroutine oft_h0_project	(	class(fem_interp), intent(inout)	field,
		class(oft_vector), intent(inout)	x
	)

Project a scalar field onto a H0 basis.

Note

This subroutine only performs the integration of the field with test functions for a H0 basis. To retrieve the correct projection the result must be multiplied by the inverse of H0::MOP.

Parameters

[in,out]	field	Vector field for projection
[in,out]	x	Field projected onto H0 basis

Variable Documentation

df_lop

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

nu_lop

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

oft_h0_gop

real(r8), dimension(:,:), pointer oft_h0_gop => NULL()

oft_h0_rop

real(r8), dimension(:), pointer oft_h0_rop => NULL()