oft_blag_operators Module Reference

Detailed Description

Surface lagrange 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
• Field projection (to plotting mesh)
• Boundary conditions

Authors

Chris Hansen

Date

August 2011

Data Types
type	oft_lag_bg2interp
	Interpolate \( \frac{\partial }{\partial x_i \partial x_j} \) of a Lagrange field. More...
type	oft_lag_bginterp
	Interpolate \( \nabla \) of a Lagrange field. More...
type	oft_lag_brinterp
	Interpolate a surface Lagrange field. More...
type	oft_lag_bvrinterp
	Interpolate a boundary Lagrange vector field. More...

Functions/Subroutines
subroutine	blag_zerob (a)
	Zero a surface Lagrange scalar field at all boundary nodes.
subroutine	blag_zeroe (a)
	Zero a surface Lagrange scalar field at all edge nodes.
subroutine	blag_zerogrnd (a)
	Zero a surface Lagrange scalar field at the mesh "grounding" node.
subroutine	lag_bg2interp (self, cell, f, gop, val)
	Reconstruct the Hessian of a surface Lagrange scalar field.
subroutine	lag_bginterp (self, cell, f, gop, val)
	Reconstruct the gradient of a surface Lagrange scalar field.
subroutine	lag_brinterp (self, cell, f, gop, val)
	Reconstruct a surface Lagrange scalar field.
subroutine	lag_brinterp_delete (self)
	Destroy temporary internal storage.
subroutine	lag_brinterp_setup (self)
	Setup interpolator for boundary Lagrange scalar fields.
subroutine	lag_brinterp_share (self, source_obj)
	Setup interpolator by linking to another interpolator of the same class.
subroutine	lag_bvrinterp (self, cell, f, gop, val)
	Reconstruct a boundary Lagrange vector field.
subroutine	lag_bvrinterp_delete (self)
	Destroy temporary internal storage.
subroutine	lag_bvrinterp_setup (self)
	Setup interpolator for boundary Lagrange vector fields.
subroutine	oft_blag_getlop (mat, bc)
	Construct laplacian matrix for Lagrange scalar representation.
subroutine	oft_blag_getmop (mat, bc)
	Construct mass matrix for a boundary Lagrange scalar representation.
subroutine	oft_blag_nproject (field, x)
	Project the normal component of a vector field onto a boundary Lagrange basis.
subroutine	oft_blag_project (field, x)
	Project a scalar field onto a boundary Lagrange basis.
subroutine	oft_blag_vproject (field, x, y, z)
	Project a vector field onto a boundary Lagrange basis.

Variables
real(r8), dimension(fem_max_levels)	df_lop_surf =-1.d99
integer(i4), dimension(fem_max_levels)	nu_lop_surf =0
real(r8), dimension(:,:), pointer	oft_blag_gop => NULL()
real(r8), dimension(:), pointer	oft_blag_rop => NULL()

Function/Subroutine Documentation

blag_zerob()

subroutine blag_zerob

(

class(oft_vector), intent(inout)

a

)

Zero a surface Lagrange scalar field at all boundary nodes.

Parameters

[in,out]

a

Field to be zeroed

blag_zeroe()

subroutine blag_zeroe

(

class(oft_vector), intent(inout)

a

)

Zero a surface Lagrange scalar field at all edge nodes.

Parameters

[in,out]

a

Field to be zeroed

blag_zerogrnd()

subroutine blag_zerogrnd

(

class(oft_vector), intent(inout)

a

)

Zero a surface Lagrange scalar field at the mesh "grounding" node.

Note

Presently the first boundary node is used as the "grounding" node

Parameters

[in,out]

a

Field to be zeroed

lag_bg2interp()

subroutine lag_bg2interp	(	class(oft_lag_bg2interp), intent(inout)	self,
		integer(i4), intent(in)	cell,
		real(r8), dimension(:), intent(in)	f,
		real(r8), dimension(3,3), intent(in)	gop,
		real(r8), dimension(:), intent(out)	val
	)

Reconstruct the Hessian of a surface Lagrange scalar field.

Note

Should only be used via class oft_lag_bg2interp

Parameters

[in]	cell	Cell for interpolation
[in]	f	Position in cell in logical coord [3]
[in]	gop	Logical gradient vectors at f [3,3]
[out]	val	Reconstructed field at f [6]

lag_bginterp()

subroutine lag_bginterp	(	class(oft_lag_bginterp), intent(inout)	self,
		integer(i4), intent(in)	cell,
		real(r8), dimension(:), intent(in)	f,
		real(r8), dimension(3,3), intent(in)	gop,
		real(r8), dimension(:), intent(out)	val
	)

Reconstruct the gradient of a surface Lagrange scalar field.

Note

Should only be used via class lag_bginterp

Parameters

[in]	cell	Cell for interpolation
[in]	f	Position in cell in logical coord [3]
[in]	gop	Logical gradient vectors at f [3,3]
[out]	val	Reconstructed field at f [3]

lag_brinterp()

subroutine lag_brinterp	(	class(oft_lag_brinterp), intent(inout)	self,
		integer(i4), intent(in)	cell,
		real(r8), dimension(:), intent(in)	f,
		real(r8), dimension(3,3), intent(in)	gop,
		real(r8), dimension(:), intent(out)	val
	)

Reconstruct a surface Lagrange scalar field.

Note

Should only be used via class oft_lag_brinterp

Parameters

[in]	cell	Cell for interpolation
[in]	f	Position in cell in logical coord [3]
[in]	gop	Logical gradient vectors at f [3,3]
[out]	val	Reconstructed field at f [1]

lag_brinterp_delete()

subroutine lag_brinterp_delete

(

class(oft_lag_brinterp), intent(inout)

self

)

Destroy temporary internal storage.

Note

Should only be used via class oft_lag_brinterp or children

lag_brinterp_setup()

subroutine lag_brinterp_setup

(

class(oft_lag_brinterp), intent(inout)

self

)

Setup interpolator for boundary Lagrange scalar fields.

Fetches local representation used for interpolation from solution vector

Note

Should only be used via class oft_lag_brinterp or children

lag_brinterp_share()

subroutine lag_brinterp_share	(	class(oft_lag_brinterp), intent(inout)	self,
		class(oft_lag_brinterp), intent(in)	source_obj
	)

Setup interpolator by linking to another interpolator of the same class.

Note

Should only be used via class oft_lag_brinterp or children

lag_bvrinterp()

subroutine lag_bvrinterp	(	class(oft_lag_bvrinterp), intent(inout)	self,
		integer(i4), intent(in)	cell,
		real(r8), dimension(:), intent(in)	f,
		real(r8), dimension(3,3), intent(in)	gop,
		real(r8), dimension(:), intent(out)	val
	)

Reconstruct a boundary Lagrange vector field.

Note

Should only be used via class oft_lag_bvrinterp

Parameters

[in]	cell	Cell for interpolation
[in]	f	Position in cell in logical coord [3]
[in]	gop	Logical gradient vectors at f [3,3]
[out]	val	Reconstructed field at f [3]

lag_bvrinterp_delete()

subroutine lag_bvrinterp_delete

(

class(oft_lag_bvrinterp), intent(inout)

self

)

Destroy temporary internal storage.

Note

Should only be used via class oft_lag_bvrinterp or children

lag_bvrinterp_setup()

subroutine lag_bvrinterp_setup

(

class(oft_lag_bvrinterp), intent(inout)

self

)

Setup interpolator for boundary Lagrange vector fields.

Fetches local representation used for interpolation from vector object

Note

Should only be used via class oft_lag_bvrinterp or children

oft_blag_getlop()

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

Construct laplacian matrix for Lagrange 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_blag_getmop()

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

Construct mass matrix for a boundary Lagrange 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_blag_nproject()

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

Project the normal component of a vector field onto a boundary Lagrange basis.

Note

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

Parameters

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

oft_blag_project()

subroutine oft_blag_project	(	class(bfem_interp), intent(inout)	field,
		class(oft_vector), intent(inout)	x
	)

Project a scalar field onto a boundary Lagrange basis.

Note

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

Parameters

[in,out]	field	Scalar field for projection
[in,out]	x	Field projected onto boundary Lagrange basis

oft_blag_vproject()

subroutine oft_blag_vproject	(	class(bfem_interp), intent(inout)	field,
		class(oft_vector), intent(inout)	x,
		class(oft_vector), intent(inout)	y,
		class(oft_vector), intent(inout)	z
	)

Project a vector field onto a boundary Lagrange basis.

Note

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

Parameters

[in,out]	field	Vector field for projection
[in,out]	x	Field projected onto boundary Lagrange basis
[in,out]	y	Field projected onto boundary Lagrange basis
[in,out]	z	Field projected onto boundary Lagrange basis

Variable Documentation

df_lop_surf

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

nu_lop_surf

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

oft_blag_gop

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

oft_blag_rop

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