oft_h1_operators Module Reference

Detailed Description

H^1 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_h1_ginterp
	Interpolate \( \nabla \) of a H^1 field. More...
type	oft_h1_rinterp
	Interpolate a H^1 field. More...
type	oft_h1_zerob
	Needs docs. More...
type	oft_h1_zerogrnd
	Needs docs. More...
type	oft_h1_zeroi
	Needs docs. More...

Functions/Subroutines
subroutine	ginterp_apply (self, cell, f, gop, val)
	Reconstruct the gradient of a H^1 scalar field.
subroutine	h1_base_pop (self, acors, afine)
	Transfer a base level H^1 scalar field to the next MPI level.
subroutine	h1_base_push (self, afine, acors)
	Transfer a MPI level H^1 scalar field to the base level.
subroutine	h1_getlop_pre (ml_h1_rep, pre, mats, bc_type, level, nlevels)
	Compute eigenvalues and smoothing coefficients for the operator H^1::LOP.
subroutine	h1_lop_eigs (ml_h1_rep, minlev)
	Compute eigenvalues and smoothing coefficients for the operator H^1::LOP.
subroutine	h1_mloptions
	Read-in options for the basic H^1 ML preconditioners.
subroutine	h1_setup_interp (ml_h1_rep)
	Construct interpolation matrices for transfer between H^1 finite element spaces.
subroutine	oft_h1_getlop (fe_rep, mat, bc)
	Construct laplacian matrix for H^1 scalar representation.
subroutine	oft_h1_getmop (fe_rep, mat, bc)
	Construct mass matrix for H^1 scalar representation.
subroutine	oft_h1_project (fe_rep, field, x)
	Project a scalar field onto a H^1 basis.
subroutine	rinterp_apply (self, cell, f, gop, val)
	Reconstruct a H^1 scalar field.
subroutine	rinterp_delete (self)
	Destroy temporary internal storage.
subroutine	rinterp_setup (self, h1_rep)
	Setup interpolator for H^1 scalar fields.
subroutine	zerob_apply (self, a)
	Zero a H^1 scalar field at all boundary nodes.
subroutine	zerob_delete (self)
	Zero a H^1 scalar field at all boundary nodes.
subroutine	zerogrnd_apply (self, a)
	Zero a H^1 scalar field at the global grounding node.
subroutine	zeroi_apply (self, a)
	Zero a H^1 scalar field at all interior nodes.

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_h1_gop => NULL()
real(r8), dimension(:), pointer	oft_h1_rop => NULL()

Function/Subroutine Documentation

ginterp_apply()

subroutine ginterp_apply	(	class(oft_h1_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 H^1 scalar 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]

h1_base_pop()

subroutine h1_base_pop	(	class(oft_ml_fe_vecspace), intent(inout)	self,
		class(oft_vector), intent(inout)	acors,
		class(oft_vector), intent(inout)	afine
	)

Transfer a base level H^1 scalar field to the next MPI level.

Parameters

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

h1_base_push()

subroutine h1_base_push	(	class(oft_ml_fe_vecspace), intent(inout)	self,
		class(oft_vector), intent(inout)	afine,
		class(oft_vector), intent(inout)	acors
	)

Transfer a MPI level H^1 scalar field to the base level.

Parameters

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

h1_getlop_pre()

subroutine h1_getlop_pre	(	type(oft_ml_fem_type), intent(inout), target	ml_h1_rep,
		class(oft_solver), intent(out), pointer	pre,
		type(oft_matrix_ptr), dimension(:), intent(inout), pointer	mats,
		character(len=*), intent(in)	bc_type,
		integer(i4), intent(in), optional	level,
		integer(i4), intent(in), optional	nlevels
	)

Compute eigenvalues and smoothing coefficients for the operator H^1::LOP.

Parameters

[in]

bc_type

Boundary condition

h1_lop_eigs()

subroutine h1_lop_eigs	(	type(oft_ml_fem_type), intent(inout), target	ml_h1_rep,
		integer(i4), intent(in)	minlev
	)

Compute eigenvalues and smoothing coefficients for the operator H^1::LOP.

h1_mloptions()

subroutine h1_mloptions

Read-in options for the basic H^1 ML preconditioners.

h1_setup_interp()

subroutine h1_setup_interp

(

class(oft_ml_fem_type), intent(inout)

ml_h1_rep

)

Construct interpolation matrices for transfer between H^1 finite element spaces.

oft_h1_getlop()

subroutine oft_h1_getlop	(	class(oft_afem_type), intent(inout), target	fe_rep,
		class(oft_matrix), intent(inout), pointer	mat,
		character(len=*), intent(in)	bc
	)

Construct laplacian matrix for H^1 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_h1_getmop()

subroutine oft_h1_getmop	(	class(oft_afem_type), intent(inout), target	fe_rep,
		class(oft_matrix), intent(inout), pointer	mat,
		character(len=*), intent(in)	bc
	)

Construct mass matrix for H^1 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_h1_project()

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

Project a scalar field onto a H^1 basis.

Note

This subroutine only performs the integration of the field with test functions for a H^1 basis. To retrieve the correct projection the result must be multiplied by the inverse of H^1::MOP.

Parameters

[in,out]	field	Vector field for projection
[in,out]	x	Field projected onto H^1 basis

rinterp_apply()

subroutine rinterp_apply	(	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 H^1 scalar 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]

rinterp_delete()

subroutine rinterp_delete

(

class(oft_h1_rinterp), intent(inout)

self

)

Destroy temporary internal storage.

rinterp_setup()

subroutine rinterp_setup	(	class(oft_h1_rinterp), intent(inout)	self,
		class(oft_afem_type), intent(inout), target	h1_rep
	)

Setup interpolator for H^1 scalar fields.

Fetches local representation used for interpolation from vector object

zerob_apply()

subroutine zerob_apply	(	class(oft_h1_zerob), intent(inout)	self,
		class(oft_vector), intent(inout)	a
	)

Zero a H^1 scalar field at all boundary nodes.

Parameters

[in,out]

a

Field to be zeroed

zerob_delete()

subroutine zerob_delete

(

class(oft_h1_zerob), intent(inout)

self

)

Zero a H^1 scalar field at all boundary nodes.

zerogrnd_apply()

subroutine zerogrnd_apply	(	class(oft_h1_zerogrnd), intent(inout)	self,
		class(oft_vector), intent(inout)	a
	)

Zero a H^1 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

zeroi_apply()

subroutine zeroi_apply	(	class(oft_h1_zeroi), intent(inout)	self,
		class(oft_vector), intent(inout)	a
	)

Zero a H^1 scalar field at all interior nodes.

Parameters

[in,out]

a

Field to be zeroed

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_h1_gop

real(r8), dimension(:,:), pointer oft_h1_gop => NULL()

oft_h1_rop

real(r8), dimension(:), pointer oft_h1_rop => NULL()