DERIVED TYPE feSpacexk: define \( Y = [ X_h ]^k \) for \( X_h \) a finite element space. More...
Data Types | |
| interface | clear |
| destructor More... | |
| interface | fespacexk |
| The type feSpacexk defines \( Y = [ X_h ]^k \) for \( X_h \) a finite element space. More... | |
| interface | interp_vect_func |
| interface | l2_dist |
| integral L2 distance More... | |
| interface | l2_dist_grad |
| interface | |
| print a short description More... | |
| interface | valid |
Functions/Subroutines | |
| subroutine | fespacexk_clear (Y) |
| Destructor for feSpacexk type. More... | |
| type(fespacexk) function | fespacexk_create (X_h, k) |
| Constructor for the type feSpacexk More... | |
| logical function | fespacexk_valid (Y) |
| Check if the structure content is correct. More... | |
| subroutine | fespacexk_interp_vect_func (u_h, Y, u_1, u_2, u_3) |
| Interpolate a function u : R^3 –> R^d given by its components u_1, u_2 and u_3 on Y = [X_h]^d. More... | |
| subroutine | fespacexk_print (Y) |
| Print a short description. More... | |
| subroutine, public | extract_component (u_c, u, Y, c) |
| Extract the component \( c \) of a finite element function \( u \in Y = [X_h]^k \). More... | |
| real(rp) function | l2_dist_2 (uh, Y, qdm, u_1, u_2, u_3) |
| Returns \( \left( \int_O \vert u - u_h \vert^2 \dx \right) ^{1/2} \). More... | |
| real(rp) function | l2_dist_grad_2 (uh, Y, qdm, grad_u1, grad_u2, grad_u3) |
| Returns \( \left( \int_O \vert \nabla u - \nabla u_h \vert^2 dx \right)^{1/2} \). More... | |
Detailed Description
DERIVED TYPE feSpacexk: define \( Y = [ X_h ]^k \) for \( X_h \) a finite element space.
Given a finite element space \( X_h \) of type feSpace:
- \( Y = [ X_h ]^k \) is the Cartesian product \( X_h \times \dots \times X_h \).
- \( Y \) is described with the derived type feSpacexk.
- This module is used in particular in elasticity.F90.
\(Y\) as \(k\) times more degrees of freedom than \(X_h\). They are ordered as follows:
- Dof 1 of \(X_h\) \( \rightarrow \) DOF \(~ 1, \dots, k~~\) of \(Y\)
- \( \dots \)
- Dof \(i\) of \(X_h\) \( \rightarrow \) DOF \(~ k(i-1)+1, \dots, ki~~\) of \(Y\)
Function/Subroutine Documentation
◆ extract_component()
| subroutine, public fespacexk_mod::extract_component | ( | real(rp), dimension(:), allocatable | u_c, |
| real(rp), dimension(:), intent(in) | u, | ||
| type(fespacexk), intent(in) | Y, | ||
| integer, intent(in) | c | ||
| ) |
Extract the component \( c \) of a finite element function \( u \in Y = [X_h]^k \).
INPUT
- \( u = (u_1, \dots, u_k) \in Y = [X_h]^k \) a finite element function given by the vector \( u \) corresponding to its decomposition on the basis of \( Y \)
- \( Y = [X_h]^d \)
- \( c \), the component to be extracted.
OUTPUT:
- \( u_c \in X_h \) the component \( c \) of \( u \). It is also a finite element function given by the vector \( u_c \) corresponding to its decomposition on the basis of \( X_h \)
Definition at line 375 of file feSpacexk_mod.f90.
◆ fespacexk_clear()
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private |
Destructor for feSpacexk type.
Definition at line 163 of file feSpacexk_mod.f90.
◆ fespacexk_create()
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private |
Constructor for the type feSpacexk
- OUTPUT:
- Y = \( [X_h]^k \)
- INPUT:
- X_h = feSpace, finite element space
- k = integer
Definition at line 184 of file feSpacexk_mod.f90.
◆ fespacexk_interp_vect_func()
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private |
Interpolate a function u : R^3 –> R^d given by its components u_1, u_2 and u_3 on Y = [X_h]^d.
If d = 2 : u(x) = [u_1(x), u_2(x)] If d = 3 : u(x) = [u_1(x), u_2(x), u_3(x)]
Definition at line 282 of file feSpacexk_mod.f90.
◆ fespacexk_print()
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private |
Print a short description.
Definition at line 342 of file feSpacexk_mod.f90.
◆ fespacexk_valid()
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private |
Check if the structure content is correct.
Definition at line 257 of file feSpacexk_mod.f90.
◆ l2_dist_2()
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private |
Returns \( \left( \int_O \vert u - u_h \vert^2 \dx \right) ^{1/2} \).
- \( Y = [X_h]^d \) where \( X_h \) is a finite element space on the mesh \( \T \) which is of dimension \( d \).
- \( u~: \R^3 \mapsto \R^d \) is a vector function, given by ite components:
\( u = [u_1, u_2]\) if \( d=2\)
\( u = [u_1, u_2, u_3]\) if \( d=3\)
- \( u_h\in Y^k \), \( u_h~: \Omega \mapsto \R^d\) is a vector finite element function
- 'qdm' = integration method on the mesh \( \T \),
- \( O \) is the integration domain, see quadmesh_mod for a definition.
Definition at line 431 of file feSpacexk_mod.f90.
◆ l2_dist_grad_2()
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private |
Returns \( \left( \int_O \vert \nabla u - \nabla u_h \vert^2 dx \right)^{1/2} \).
- \( Y = [X_h]^d \) where \( X_h \) is a finite element space on the mesh \( \T \) which is of dimension \( d \).
- \( u~: \R^3 \mapsto \R^d \) is a vector function,
- \( \nabla u~: \R^3 \mapsto \R^d \times \R^d\) is a matrix function, given by ite components:
\( \nabla u = [\nabla u_1, \nabla u_2]\) if \( d=2\)
\( \nabla u = (\nabla u_1, \nabla u_2, \nabla u_3]\) if \( d=3\)
where
\( u = [u_1, u_2]\) if \( d=2\)
\( u = [u_1, u_2, u_3]\) if \( d=3\)
- \( u_h\in Y^k \), \( u_h~: \Omega \mapsto \R^d\) is a vector finite element function
- 'qdm' = integration method on the mesh \( \T \),
- \( O \) is the integration domain, see quadmesh_mod for a definition.
Definition at line 514 of file feSpacexk_mod.f90.
