integral::integ Interface Reference

Integration of scalar functions. More...

Collaboration diagram for integral::integ:

Private Member Functions
real(rp) function	integ_scal_func (u, qdm)
	Returns \( \int_O u(x) \dx \). More...
real(rp) function	integ_scal_fe (E, u, uh, X_h, qdm)
	Returns \( \int_O E(x, u(x), u_h(x)) \dx \). More...
real(rp) function	integ_scal_fe_grad (E, phi, uh, X_h, qdm)
	Returns \( \int_O E(x, \phi(x), \nabla u_h(x)) \dx \). More...
real(rp) function	integ_scal_fe_grad_2 (E, uh1, uh2, X_h, qdm)
	Returns \( \int_O E(x, \nabla u1_h(x), \nabla u2_h(x)) \dx \). More...

Detailed Description

Integration of scalar functions.

Definition at line 54 of file integral.F90.

Member Function/Subroutine Documentation

integ_scal_fe()

real(rp) function integral::integ::integ_scal_fe ( procedure(r3xrxrtor)  E, procedure(r3tor)  u, real(rp), dimension(:), intent(in)  uh, type(fespace), intent(in)  X_h, type(quadmesh), intent(in)  qdm  )

private

Returns \( \int_O E(x, u(x), u_h(x)) \dx \).

• \( E~: \R^3 \times \R \times \R \mapsto \R \)

• \(u~: \R^3 \mapsto \R \) is a scalar function,

• \( u_h~: \Omega \mapsto \R\) is a scalar finite element function in the finite element space \( X_h \)
  (associated to a mesh \( \T \) with domain \( \Omega \)),

• 'qdm' = integration method on the mesh \( \T \),

• \( O \) is the integration domain, see quadmesh_mod for a definition.

Definition at line 193 of file integral.F90.

integ_scal_fe_grad()

real(rp) function integral::integ::integ_scal_fe_grad ( procedure(r3xr3xr3tor)  E, procedure(r3tor3)  phi, real(rp), dimension(:), intent(in)  uh, type(fespace), intent(in)  X_h, type(quadmesh), intent(in)  qdm  )

private

Returns \( \int_O E(x, \phi(x), \nabla u_h(x)) \dx \).

• \( E~: \R^3 \times \R^3 \times \R^3 \mapsto \R \)

• \(\phi~: \R^3 \mapsto \R^3 \) is a vector function,

• \( u_h~: \Omega \mapsto \R\) is a scalar finite element function in the finite element space \( X_h \)
  (associated to a mesh \( \T \) with domain \( \Omega \)),

• 'qdm' = integration method on the mesh \( \T \),

• \( O \) is the integration domain, see quadmesh_mod for a definition.

Definition at line 345 of file integral.F90.

integ_scal_fe_grad_2()

real(rp) function integral::integ::integ_scal_fe_grad_2 ( procedure(r3xr3xr3tor)  E, real(rp), dimension(:), intent(in)  uh1, real(rp), dimension(:), intent(in)  uh2, type(fespace), intent(in)  X_h, type(quadmesh), intent(in)  qdm  )

private

Returns \( \int_O E(x, \nabla u1_h(x), \nabla u2_h(x)) \dx \).

• \( E~: \R^3 \times \R^3 \times \R^3 \mapsto \R \)

• \( ui_h~: \Omega \mapsto \R\) is a scalar finite element function in the finite element space \( X_h \)
  (associated to a mesh \( \T \) with domain \( \Omega \)),

• 'qdm' = integration method on the mesh \( \T \),

• \( O \) is the integration domain, see quadmesh_mod for a definition.

Definition at line 702 of file integral.F90.

integ_scal_func()

real(rp) function integral::integ::integ_scal_func ( procedure(r3tor)  u, type(quadmesh), intent(in)  qdm  )

private

Returns \( \int_O u(x) \dx \).

• \( u \) = scalar function,
• 'qdm' = integration method on a mesh,
  \( O \) is the integration domain, see quadmesh_mod for a definition.

Definition at line 81 of file integral.F90.

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The documentation for this interface was generated from the following file:

• /home/cpierre1/choral/SRC/integral.F90