DERIVED TYPE feSpace: finite element spaces More...

Data Types
interface	assemble

interface	clear

interface	fespace
	Derived type feSpace: finite element space on a mesh. More...

interface	interp_vect_func

interface	print
	print a short description More...

interface	set

interface	valid

interface	write
	write a finite element space to a file More...

Functions/Subroutines
subroutine	fespace_clear (X_h)
	Destructor for feSpace type. More...

type(fespace) function	fespace_create (m)
	Constructor for the type feSpace More...

subroutine	fespace_set (X_h, ft)
	Apply the finite element method 'ft' to all cells with comptible geometry. More...

subroutine	fespace_print (X_h)
	Print a short description. More...

logical function	fespace_valid (X_h)
	Check if the structure content is correct. More...

subroutine	fespace_write (X_h, fileName, fileFormat)
	Write feSpace to file 'fileName' with format 'fileFormat'. More...

subroutine	gmsh_write (X_h, fileName)
	Write feSpace m to file 'fileName' gmsh ASCII format. More...

subroutine, public	gmsh_addview (X_h, v, fileName, vname, time, idx)
	add a view to X_h output file gmesh file format More...

subroutine, public	interp_scal_fe (u2, X_h2, u1, X_h1)
	Interpolate a scalar finite element function u1 on a second finite element space X_h2. More...

subroutine, public	eval_scal_fe_at_points (val, P, u, X_h)
	u is a finite element function on the finite element space X_h More...

subroutine	locate_nodes (T, P, X_h, ndToNd)
	Locate each point P(:,i) inside a cell of X_hmesh associated to a non void finite element. More...

integer function	closest_cell (x, X_h)
	finds the cell in X_h with non void feType the closest from node x More...

subroutine	fespace_assemble (X_h)
	sets cell dof local indexing –> global dof indexing connectivity More...

subroutine	x_h_dofcoord (X_h)

subroutine	initialise_doftab (dofTab, cl_row, X_h)

subroutine	scan_dof (dofTab, X_h, wdt)
	Checks every local dof to say wether it is equal to dof 'dof2' of cell 'cl2' for cl2 < cell. More...

subroutine	build_cltodof (dofTab, cl_row, X_h)

subroutine	get_perm_3 (p, t1, t2)
	t2 is a permutation of t1 More...

subroutine	get_perm_2 (p, t1, t2)
	t2 is a permutation of t1 More...

subroutine, public	interp_scal_func (uh, u, X_h)
	Interpolation of a scalar function to a scalar finite element function. More...

subroutine	fespace_interp_vect_func (phi_h, phi, X_h)
	Interp : vector function case. More...

subroutine, public	flag_x_h_dof (dof_flag, X_h, dim, f)
	OUTPUT: flag(:) array of logical with size X_hnbDof. More...

Detailed Description

DERIVED TYPE feSpace: finite element spaces

Given a mesh \( \mathcal{T}\) of a domain \( \Omega \):

the derived type feSpace defines a finite element space \( X_h \) on \( \mathcal{T}\) such as:
- \( X_h = P^k(\mathcal{T})\) (Lagrange finite element space for scalar functions)( {T})
- \( X_h = RT^k(\mathcal{T})\) (Raviart Thomas finite element space for vector functions).

a finite element spae is a mesh whose cells are associated to finite element methods.
- each cell has its own finite element method: various finite element methods can be considered on a single mesh,
- by default a cell is associated to a void finite element method,
- see fe_mod for the definition of finite element method.

Let 'X_h' of type feSpace:

The construction of 'X_h' consists in:
1. defining its degrees of freedom (dof),
2. defining the cell to dof connectivity graph 'X_h%ClToDof'.

It is done in 3 steps:
1. x_h = fespace(msh)
  associates 'X_h' with the mesh 'msh'.
2. call set(X_h, ...)
  associate the mesh cells to finite element methods (default is void).
  This can be done in more than one step to define different finite element methods on different mesh subdomains.
3. call assemble(Xh)
  ends up the construction.

Tutorial examples:

feSpace_visu.f90: assembling of a finite element space in 2D, interpolation of a function on this space + visualisation.
poisson_2d.f90: assembling of a finite element space to solve a Poisson problem in 2D.

Author: Charles Pierre

Function/Subroutine Documentation

◆ build_cltodof()

subroutine fespace_mod::build_cltodof	(	integer, dimension(:,:), intent(inout)	dofTab,
		integer, dimension(:), intent(in)	cl_row,
		type(fespace), intent(inout)	X_h
	)

private

Definition at line 1507 of file feSpace_mod.F90.

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◆ closest_cell()

integer function fespace_mod::closest_cell	(	real(rp), dimension(3), intent(in)	x,
		type(fespace), intent(in)	X_h
	)

private

finds the cell in X_h with non void feType the closest from node x

distance = sum_i^nbVtx |x-Ai|_1/nbVtx, A_i vertex of cell cl

Definition at line 902 of file feSpace_mod.F90.

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◆ eval_scal_fe_at_points()

subroutine, public fespace_mod::eval_scal_fe_at_points	(	real(rp), dimension(:), allocatable	val,
		real(rp), dimension(:,:), intent(in)	P,
		real(rp), dimension(:), intent(in)	u,
		type(fespace), intent(in)	X_h
	)

u is a finite element function on the finite element space X_h

P is a set of points

OUTPUT : val = values of the function u at the points P: val(i) = u( P(:,i))

INPUT : u = finite element function X_h = finite element space for u1 P = set of points

It is assumed the points in P are in the mesh domain !

Definition at line 605 of file feSpace_mod.F90.

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◆ fespace_assemble()

subroutine fespace_mod::fespace_assemble ( type(fespace), intent(inout) X_h )

private

sets cell dof local indexing –> global dof indexing connectivity

Definition at line 952 of file feSpace_mod.F90.

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◆ fespace_clear()

subroutine fespace_mod::fespace_clear ( type(fespace), intent(inout) X_h )

private

Destructor for feSpace type.

Definition at line 180 of file feSpace_mod.F90.

◆ fespace_create()

type(fespace) function fespace_mod::fespace_create ( type(mesh), target m )

private

Constructor for the type feSpace

OUTPUT:
- X_h = feSpace, finite element space

INPUT:
- m = mesh

Definition at line 206 of file feSpace_mod.F90.

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◆ fespace_interp_vect_func()

subroutine fespace_mod::fespace_interp_vect_func	(	real(rp), dimension(:), allocatable	phi_h,
		procedure(r3tor3)	phi,
		type(fespace), intent(in)	X_h
	)

private

Interp : vector function case.

To be reconsidered

Definition at line 1675 of file feSpace_mod.F90.

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◆ fespace_print()

subroutine fespace_mod::fespace_print ( type(fespace), intent(in) X_h )

private

Print a short description.

Definition at line 256 of file feSpace_mod.F90.

◆ fespace_set()

subroutine fespace_mod::fespace_set	(	type(fespace), intent(inout)	X_h,
		integer, intent(in)	ft
	)

private

Apply the finite element method 'ft' to all cells with comptible geometry.

Definition at line 225 of file feSpace_mod.F90.

◆ fespace_valid()

logical function fespace_mod::fespace_valid ( type (fespace), intent(in) X_h )

private

Check if the structure content is correct.

Definition at line 286 of file feSpace_mod.F90.

◆ fespace_write()

subroutine fespace_mod::fespace_write	(	type(fespace), intent(in)	X_h,
		character(len=*), intent(in)	fileName,
		character(len=*), intent(in)	fileFormat
	)

private

Write feSpace to file 'fileName' with format 'fileFormat'.

Definition at line 308 of file feSpace_mod.F90.

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◆ flag_x_h_dof()

subroutine, public fespace_mod::flag_x_h_dof	(	logical, dimension(:), allocatable	dof_flag,
		type(fespace), intent(in)	X_h,
		integer, intent(in)	dim,
		procedure(r3tor), optional	f
	)

OUTPUT: flag(:) array of logical with size X_hnbDof.

for the dof 'i' in the finire element space 'X_h':
flag(i) = .TRUE. iif:

the dof 'i' belongs to a cell 'cl' of dimension 'dim' in the mesh 'X_hmesh'
f(x) >=0 at all node 'x' of the cell (if the argument 'f' is provided)

Definition at line 1840 of file feSpace_mod.F90.

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◆ get_perm_2()

subroutine fespace_mod::get_perm_2	(	integer, intent(out)	p,
		integer, dimension(2), intent(in)	t1,
		integer, dimension(2), intent(in)	t2
	)

private

t2 is a permutation of t1

returns p such that :

t1(1) = t2( p )

Definition at line 1624 of file feSpace_mod.F90.

◆ get_perm_3()

subroutine fespace_mod::get_perm_3	(	integer, dimension(2), intent(out)	p,
		integer, dimension(3), intent(in)	t1,
		integer, dimension(3), intent(in)	t2
	)

private

t2 is a permutation of t1

returns p(:) such that :

t1(i) = t2( p(i) ) for i=1 .. 2

Definition at line 1586 of file feSpace_mod.F90.

◆ gmsh_addview()

subroutine, public fespace_mod::gmsh_addview	(	type(fespace), intent(in)	X_h,
		real(rp), dimension(:), intent(in)	v,
		character(len=*), intent(in)	fileName,
		character(len=*), intent(in)	vname,
		real(rp), intent(in)	time,
		integer, intent(in)	idx
	)

add a view to X_h output file gmesh file format

Definition at line 412 of file feSpace_mod.F90.

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◆ gmsh_write()

subroutine fespace_mod::gmsh_write	(	type(fespace), intent(in)	X_h,
		character(len=*), intent(in)	fileName
	)

private

Write feSpace m to file 'fileName' gmsh ASCII format.

Definition at line 328 of file feSpace_mod.F90.

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◆ initialise_doftab()

subroutine fespace_mod::initialise_doftab	(	integer, dimension(:,:), intent(inout), allocatable	dofTab,
		integer, dimension(:), intent(out)	cl_row,
		type(fespace), intent(inout)	X_h
	)

private

Definition at line 1044 of file feSpace_mod.F90.

◆ interp_scal_fe()

subroutine, public fespace_mod::interp_scal_fe	(	real(rp), dimension(:), intent(out)	u2,
		type(fespace), intent(in)	X_h2,
		real(rp), dimension(:), intent(in)	u1,
		type(fespace), intent(in)	X_h1
	)

Interpolate a scalar finite element function u1 on a second finite element space X_h2.

OUTPUT : u2 = finite element function on the finite element space X_h2

INPUT : X_h1 = finite element space u1 = finite element function on X_h1 X_h = second finite element space

OUTPUT: u2 = finite element function on X_h2 interpolant of u1 at the dof of X_h2

It is assumed that X_h1 and X_h2 are Lagrangian spaces here. Consequently, u2 is given by the values of u1 at the nodes of X_h2.

Definition at line 468 of file feSpace_mod.F90.

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◆ interp_scal_func()

subroutine, public fespace_mod::interp_scal_func	(	real(rp), dimension(:), allocatable	uh,
		procedure(r3tor)	u,
		type(fespace), intent(in)	X_h
	)

Interpolation of a scalar function to a scalar finite element function.

Definition at line 1641 of file feSpace_mod.F90.

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◆ locate_nodes()

subroutine fespace_mod::locate_nodes	(	integer, dimension(:), intent(inout)	T,
		real(rp), dimension(:,:), intent(in)	P,
		type(fespace), intent(in)	X_h,
		type(graph), intent(in)	ndToNd
	)

private

Locate each point P(:,i) inside a cell of X_hmesh associated to a non void finite element.

initially, T(ii) is the closest node of X_hmesh obtained with :

call closest_node(T, dist, P, X_hmesh, ndToNd)

Input = ndToNd = node to node connectivity of the mesh X_hmesh

Definition at line 732 of file feSpace_mod.F90.

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◆ scan_dof()

subroutine fespace_mod::scan_dof	(	integer, dimension(:,:), intent(inout)	dofTab,
		type(fespace), intent(inout)	X_h,
		integer, intent(in)	wdt
	)

private

Checks every local dof to say wether it is equal to dof 'dof2' of cell 'cl2' for cl2 < cell.

In that case dofTab(1:2, dof) = (/cl2, dof2/)

Definition at line 1091 of file feSpace_mod.F90.

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◆ x_h_dofcoord()

subroutine fespace_mod::x_h_dofcoord ( type(fespace), intent(inout) X_h )

private

Definition at line 990 of file feSpace_mod.F90.

Data Types

Functions/Subroutines

Detailed Description

Function/Subroutine Documentation

◆ build_cltodof()

◆ closest_cell()

◆ eval_scal_fe_at_points()

◆ fespace_assemble()

◆ fespace_clear()

◆ fespace_create()

◆ fespace_interp_vect_func()

◆ fespace_print()

◆ fespace_set()

◆ fespace_valid()

◆ fespace_write()

◆ flag_x_h_dof()

◆ get_perm_2()

◆ get_perm_3()

◆ gmsh_addview()

◆ gmsh_write()

◆ initialise_doftab()

◆ interp_scal_fe()

◆ interp_scal_func()

◆ locate_nodes()

◆ scan_dof()

◆ x_h_dofcoord()