Choral
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COMPUTATION OF INTEGRALS using a quadrature methods on a mesh. More...
Data Types | |
interface | integ |
Integration of scalar functions. More... | |
interface | l2_dist |
integral L2 distance More... | |
interface | l2_dist_grad |
Functions/Subroutines | |
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, public | integ_scal_fe_grad_proj (E, phi, uh, X_h, qdm) |
Returns \( \int_O E(x, \phi_T(x), \nabla u_h(x)) \dx \). 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... | |
real(rp) function | e_l2 (x, u1, u2) |
\( (x-y)^2 \) More... | |
real(rp) function | e_l2_vect (x, p1, p2) |
\( (p-q)^2 \) More... | |
real(rp) function | l2_dist_scalfe (u, uh, X_h, qdm) |
Returns \( \int_O \vert u - u_h \vert^2 \dx \). More... | |
real(rp) function | l2_dist_grad_scalfe (phi, uh, X_h, qdm) |
Returns \( \int_O \vert \phi - \nabla u_h \vert^2 \dx \). More... | |
real(rp) function, public | l2_dist_grad_proj (phi, uh, X_h, qdm) |
Returns \( \int_O \vert \phi_T - \nabla u_h \vert^2 \dx \). More... | |
real(rp) function, public | l2_dist_vect (phi, phi_h, X_h, qdm) |
Returns \( \int_O \vert \phi - \phi_h \vert^2 \dx \). More... | |
COMPUTATION OF INTEGRALS using a quadrature methods on a mesh.
Given:
This module proposes various computation of integrals with an integration domain composed of cells of the mesh \( \mathcal{T} \).
Integration domain: see quadmesh_mod mreamble for a definition.
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\( (x-y)^2 \)
Definition at line 875 of file integral.F90.
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\( (p-q)^2 \)
Definition at line 884 of file integral.F90.
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Returns \( \int_O E(x, u(x), u_h(x)) \dx \).
Definition at line 193 of file integral.F90.
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Returns \( \int_O E(x, \phi(x), \nabla u_h(x)) \dx \).
Definition at line 345 of file integral.F90.
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Returns \( \int_O E(x, \nabla u1_h(x), \nabla u2_h(x)) \dx \).
Definition at line 702 of file integral.F90.
real(rp) function, public integral::integ_scal_fe_grad_proj | ( | procedure(r3xr3xr3tor) | E, |
procedure(r3tor3) | phi, | ||
real(rp), dimension(:), intent(in) | uh, | ||
type(fespace), intent(in) | X_h, | ||
type(quadmesh), intent(in) | qdm | ||
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Returns \( \int_O E(x, \phi_T(x), \nabla u_h(x)) \dx \).
same as integral::integ_scal_fe_grad BUT :
\( \phi_T \): tangent component of \( \phi\) in the tangent space to any cell in the integration domain O
Definition at line 511 of file integral.F90.
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Returns \( \int_O u(x) \dx \).
Definition at line 81 of file integral.F90.
real(rp) function, public integral::l2_dist_grad_proj | ( | procedure(r3tor3) | phi, |
real(rp), dimension(:), intent(in) | uh, | ||
type(fespace), intent(in) | X_h, | ||
type(quadmesh), intent(in) | qdm | ||
) |
Returns \( \int_O \vert \phi_T - \nabla u_h \vert^2 \dx \).
same as integral::l2_dist_grad BUT :
\( \phi_T \): tangent component of \( \phi\) in the tangent space to any cell in the integration domain O
Definition at line 956 of file integral.F90.
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Returns \( \int_O \vert \phi - \nabla u_h \vert^2 \dx \).
Definition at line 934 of file integral.F90.
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Returns \( \int_O \vert u - u_h \vert^2 \dx \).
Definition at line 905 of file integral.F90.
real(rp) function, public integral::l2_dist_vect | ( | procedure(r3tor3) | phi, |
real(rp), dimension(:), intent(in) | phi_h, | ||
type(fespace), intent(in) | X_h, | ||
type(quadmesh), intent(in) | qdm | ||
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Returns \( \int_O \vert \phi - \phi_h \vert^2 \dx \).
Definition at line 986 of file integral.F90.