quadmesh_mod Module Reference

DERIVED TYPE quadMesh: integration methods on meshes More...

Data Types
interface	assemble
interface	clear
interface	print
interface	quadmesh
	The type quadMesh defines integration methods on meshes. More...
interface	set
	Sets an integration method quadMesh. More...
interface	valid

Functions/Subroutines
subroutine	quadmesh_clear (qdm)
	Destructor for quadMesh type. More...
type(quadmesh) function	quadmesh_create (m)
	Constructor for the type quadMesh More...
subroutine	quadmesh_set (qdm, quadType, f)
	Sets an integration method quadMesh More...
subroutine	set_flagged_cells (qdm, cpt, quadType, flag)
	Set the integration method 'qdm' to 'quadType' on all cells 'cl' of compatible geometry that moreover satisfy flag(cl)==.TRUE. More...
subroutine	quadmesh_assemble (qdm)
	Sets mdim, qdmquad_count. More...
subroutine	quadmesh_print (qdm)
	number of cells per fe type More...
logical function	quadmesh_valid (qdm)
	Check if assembling is correct. More...

Detailed Description

DERIVED TYPE quadMesh: integration methods on meshes

Given a mesh of a domain \( \Omega \),

• the derived type quadMesh defines an integration method on a subdomain of \( \Omega \)

• a quadMesh is a mesh whose cells are associated to quadrature rules,
  • each cell has its own quadrature rule: various quadrature rules can be considered on a single mesh,
  • by default a cell is associated to a void quadrature rule (no integration will be performed on that cell),
  • see quad_mod for the definition of quadrature rules.

• With a quadMesh of a domain \( \Omega \), integration can be performed on a subdomain of \(\Omega\)
  • the integration domain is the union of all mesh cell with non void quadrature rule,
  • the integration domain can be
    • \( \Omega \),
    • \(\partial \Omega \),
    • \( \Omega \) or of \( \partial \Omega \),
    • a 1D line \( \gamma \subset \Omega \) or \( \gamma \subset \partial \Omega \) made of edges. ...

A quadMesh 'qdm' is defined in three steps

1. qdm = quadmesh(msh) 

   associates 'qdm' with the mesh 'msh',

2. call set(qdm, ...)

   associate the mesh cells to quadrature rules, see set documentation
   This can be done in more than one step to define different quadrature rules on different mesh subdomains.

3. call assemble(qdm) 

   ends up the construction.

Example: quadmesh_integral.f90
Consider a triangle mesh 'msh' of \( \Omega=[0,1]\times[0,1]\) including edge cells that mesh \( \partial \Omega \).

• Integration domain = mesh domain (2D)

  qdm = quadmesh(msh)
  call set(qdm, quad_gauss_trg_3)
  call assemble(qdm)

  defines qdm \(= \int_\Omega ~~ {\rm d}x \):
  all the mesh triangles are associated to the 3 point Gaussian quadrature rule on triangles.

• Integration domain = mesh boundary (1D)

  qdm = quadmesh(msh)
  call set(qdm, quad_gauss_edg_3)
  call assemble(qdm)

  defines qdm \(= \int_{\partial\Omega} ~~ {\rm d}l \):
  all the mesh edges are associated to the 3 point Gaussian quadrature rule on edges.

• Integration domain defined with a signed function,

    qdm = quadmesh(msh)
    call set(qdm, quad_gauss_edg_3, x_ge_1)
    call assemble(qdm)
  
  contains
  
    function x_ge_1(x)  result(r)
      real(RP)                           :: r
      real(RP), dimension(3), intent(in) :: x
      r = x(1) - 1.0_rp
    end function x_ge_1

  defines qdm \(= \int_{\{1\}\times[0,1]} ~~ {\rm d}l \):
  only the mesh cells where the function 'x_ge_1 \(\ge 0\)' will be considered,
  the resulting integration domain is \( \partial\Omega \cap \{x\ge 1\} = \{1\}\times[0,1] \).

• Composite integration domain:

  qdm = quadmesh(msh)
  call set(qdm, quad_gauss_edg_3, x_ge_1)
  call set(qdm, quad_gauss_trg_3)
  call assemble(qdm)

  definess qdm \(= \int_{\Omega} ~~ {\rm d}x ~+~ \int_{\{1\}\times[0,1]} ~~ {\rm d}l \).

Author

Charles Pierre

Function/Subroutine Documentation

quadmesh_assemble()

subroutine quadmesh_mod::quadmesh_assemble ( type(quadmesh), intent(inout)  qdm )

private

Sets mdim, qdmquad_count.

Definition at line 333 of file quadMesh_mod.f90.

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quadmesh_clear()

subroutine quadmesh_mod::quadmesh_clear ( type(quadmesh), intent(inout)  qdm )

private

Destructor for quadMesh type.

Definition at line 201 of file quadMesh_mod.f90.

quadmesh_create()

type(quadmesh) function quadmesh_mod::quadmesh_create ( type(mesh), target  m )

private

Constructor for the type quadMesh

• OUTPUT:
  • qdm = quadMesh

• INPUT:
  • m = mesh

Definition at line 220 of file quadMesh_mod.f90.

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quadmesh_print()

subroutine quadmesh_mod::quadmesh_print ( type(quadmesh), intent(in)  qdm )

private

number of cells per fe type

Definition at line 361 of file quadMesh_mod.f90.

quadmesh_set()

subroutine quadmesh_mod::quadmesh_set ( type(quadmesh), intent(inout)  qdm, integer, intent(in)  quadType, procedure(r3tor), optional  f  )

private

Sets an integration method quadMesh

Given a quadrature rule 'quadType' with reference czell \(K_{\rm ref}\),

1. select all the mesh cells associated to the same reference cell,
2. optionnally (if 'f' is given) select among these cells those where \( f \ge 0 \),
3. set on these cells the quadrature rule to 'quadType'.

• OUTPUT:
  • qdm = quadMesh

• INPUT:
  • quadType = a quadrature rule
  Optional:
  • f = a scalar function \( \R^3 \rightarrow \R \)

Definition at line 265 of file quadMesh_mod.f90.

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quadmesh_valid()

logical function quadmesh_mod::quadmesh_valid ( type (quadmesh), intent(in)  qdm )

private

Check if assembling is correct.

Definition at line 382 of file quadMesh_mod.f90.

set_flagged_cells()

subroutine quadmesh_mod::set_flagged_cells ( type(quadmesh), intent(inout)  qdm, integer, intent(out)  cpt, integer, intent(in)  quadType, logical, dimension(:), intent(in)  flag  )

private

Set the integration method 'qdm' to 'quadType' on all cells 'cl' of compatible geometry that moreover satisfy flag(cl)==.TRUE.

Returns cpt = number of cells that have been set to 'quadType'

Definition at line 298 of file quadMesh_mod.f90.

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