GetFEM  5.4.2
Functions
Assembly routines

Functions

template<typename VEC >
scalar_type getfem::asm_L2_norm (const mesh_im &mim, const mesh_fem &mf, const VEC &U, const mesh_region &rg=mesh_region::all_convexes())
 compute $ \|U\|_2 $, U might be real or complex
 
template<typename VEC1 , typename VEC2 >
scalar_type getfem::asm_L2_dist (const mesh_im &mim, const mesh_fem &mf1, const VEC1 &U1, const mesh_fem &mf2, const VEC2 &U2, mesh_region rg=mesh_region::all_convexes())
 Compute the distance between U1 and U2, defined on two different mesh_fems (but sharing the same mesh), without interpolating U1 on mf2.
 
template<typename VEC >
scalar_type getfem::asm_H1_semi_norm (const mesh_im &mim, const mesh_fem &mf, const VEC &U, const mesh_region &rg=mesh_region::all_convexes())
 compute $\|\nabla U\|_2$, U might be real or complex
 
template<typename VEC1 , typename VEC2 >
scalar_type getfem::asm_H1_semi_dist (const mesh_im &mim, const mesh_fem &mf1, const VEC1 &U1, const mesh_fem &mf2, const VEC2 &U2, mesh_region rg=mesh_region::all_convexes())
 Compute the H1 semi-distance between U1 and U2, defined on two different mesh_fems (but sharing the same mesh), without interpolating U1 on mf2.
 
template<typename VEC >
scalar_type getfem::asm_H1_norm (const mesh_im &mim, const mesh_fem &mf, const VEC &U, const mesh_region &rg=mesh_region::all_convexes())
 compute the H1 norm of U. More...
 
template<typename VEC1 , typename VEC2 >
scalar_type getfem::asm_H1_dist (const mesh_im &mim, const mesh_fem &mf1, const VEC1 &U1, const mesh_fem &mf2, const VEC2 &U2, mesh_region rg=mesh_region::all_convexes())
 Compute the H1 distance between U1 and U2.
 
template<typename VEC >
scalar_type getfem::asm_H2_semi_norm (const mesh_im &mim, const mesh_fem &mf, const VEC &U, const mesh_region &rg=mesh_region::all_convexes())
 compute $\|Hess U\|_2$, U might be real or complex. More...
 
template<typename VEC >
scalar_type getfem::asm_H2_norm (const mesh_im &mim, const mesh_fem &mf, const VEC &U, const mesh_region &rg=mesh_region::all_convexes())
 compute the H2 norm of U (for C^1 elements).
 
template<typename VEC1 , typename VEC2 >
scalar_type getfem::asm_H2_dist (const mesh_im &mim, const mesh_fem &mf1, const VEC1 &U1, const mesh_fem &mf2, const VEC2 &U2, const mesh_region &rg=mesh_region::all_convexes())
 Compute the H2 distance between U1 and U2.
 
template<typename MAT >
void getfem::asm_mass_matrix (const MAT &M, const mesh_im &mim, const mesh_fem &mf1, const mesh_region &rg=mesh_region::all_convexes())
 generic mass matrix assembly (on the whole mesh or on the specified convex set or boundary)
 
template<typename MAT , typename VECT >
void getfem::asm_mass_matrix_param (const MAT &M, const mesh_im &mim, const mesh_fem &mf1, const mesh_fem &mf2, const mesh_fem &mf_data, const VECT &A, const mesh_region &rg=mesh_region::all_convexes())
 generic mass matrix assembly with an additional parameter (on the whole mesh or on the specified boundary)
 
template<typename MAT , typename VECT >
void getfem::asm_mass_matrix_param (MAT &M, const mesh_im &mim, const mesh_fem &mf_u, const mesh_fem &mf_data, const VECT &F, const mesh_region &rg=mesh_region::all_convexes())
 generic mass matrix assembly with an additional parameter (on the whole mesh or on the specified boundary)
 
template<typename MAT , typename VECT >
void getfem::asm_mass_matrix_homogeneous_param (MAT &M, const mesh_im &mim, const mesh_fem &mf_u, const VECT &F, const mesh_region &rg=mesh_region::all_convexes())
 generic mass matrix assembly with an additional constant parameter (on the whole mesh or on the specified boundary)
 
template<typename MAT >
void getfem::asm_lumped_mass_matrix_for_first_order (const MAT &M, const mesh_im &mim, const mesh_fem &mf1, const mesh_region &rg=mesh_region::all_convexes())
 lumped mass matrix assembly (on the whole mesh or on the specified boundary)
 
template<typename MAT , typename VECT >
void getfem::asm_lumped_mass_matrix_for_first_order_param (MAT &M, const mesh_im &mim, const mesh_fem &mf_u, const mesh_fem &mf_data, const VECT &F, const mesh_region &rg=mesh_region::all_convexes())
 lumped mass matrix assembly with an additional parameter (on the whole mesh or on the specified boundary)
 
template<typename VECT1 , typename VECT2 >
void getfem::asm_source_term (const VECT1 &B, const mesh_im &mim, const mesh_fem &mf, const mesh_fem &mf_data, const VECT2 &F, const mesh_region &rg=mesh_region::all_convexes())
 source term (for both volumic sources and boundary (Neumann) sources).
 
template<typename VECT1 , typename VECT2 >
void getfem::asm_homogeneous_source_term (const VECT1 &B, const mesh_im &mim, const mesh_fem &mf, const VECT2 &F, const mesh_region &rg=mesh_region::all_convexes())
 source term (for both volumic sources and boundary (Neumann) sources). More...
 
template<typename VECT1 , typename VECT2 >
void getfem::asm_normal_source_term (VECT1 &B, const mesh_im &mim, const mesh_fem &mf, const mesh_fem &mf_data, const VECT2 &F, const mesh_region &rg)
 Normal source term (for boundary (Neumann) condition).
 
template<typename VECT1 , typename VECT2 >
void getfem::asm_homogeneous_normal_source_term (VECT1 &B, const mesh_im &mim, const mesh_fem &mf, const VECT2 &F, const mesh_region &rg)
 Homogeneous normal source term (for boundary (Neumann) condition).
 
template<typename MAT , typename VECT >
void getfem::asm_qu_term (MAT &M, const mesh_im &mim, const mesh_fem &mf_u, const mesh_fem &mf_d, const VECT &Q, const mesh_region &rg)
 assembly of $\int{qu.v}$ More...
 
template<class MAT , class VECT >
void getfem::asm_stiffness_matrix_for_linear_elasticity (const MAT &M, const mesh_im &mim, const mesh_fem &mf, const mesh_fem &mf_data, const VECT &LAMBDA, const VECT &MU, const mesh_region &rg=mesh_region::all_convexes())
 Stiffness matrix for linear elasticity, with Lamé coefficients.
 
template<class MAT , class VECT >
void getfem::asm_stiffness_matrix_for_homogeneous_linear_elasticity (const MAT &M, const mesh_im &mim, const mesh_fem &mf, const VECT &LAMBDA, const VECT &MU, const mesh_region &rg=mesh_region::all_convexes())
 Stiffness matrix for linear elasticity, with constant Lamé coefficients.
 
template<typename MAT , typename VECT >
void getfem::asm_stiffness_matrix_for_linear_elasticity_Hooke (MAT &RM, const mesh_im &mim, const mesh_fem &mf, const mesh_fem &mf_data, const VECT &H, const mesh_region &rg=mesh_region::all_convexes())
 Stiffness matrix for linear elasticity, with a general Hooke tensor. More...
 
template<typename MAT >
void getfem::asm_stokes_B (const MAT &B, const mesh_im &mim, const mesh_fem &mf_u, const mesh_fem &mf_p, const mesh_region &rg=mesh_region::all_convexes())
 Build the mixed pressure term $ B = - \int p.div u $.
 
template<typename MAT >
void getfem::asm_stiffness_matrix_for_homogeneous_laplacian (const MAT &M, const mesh_im &mim, const mesh_fem &mf, const mesh_region &rg=mesh_region::all_convexes())
 assembly of $\int_\Omega \nabla u.\nabla v$.
 
template<typename MAT >
void getfem::asm_stiffness_matrix_for_homogeneous_laplacian_componentwise (const MAT &M, const mesh_im &mim, const mesh_fem &mf, const mesh_region &rg=mesh_region::all_convexes())
 assembly of $\int_\Omega \nabla u.\nabla v$.
 
template<typename MAT , typename VECT >
void getfem::asm_stiffness_matrix_for_laplacian (MAT &M, const mesh_im &mim, const mesh_fem &mf, const mesh_fem &mf_data, const VECT &A, const mesh_region &rg=mesh_region::all_convexes())
 assembly of $\int_\Omega a(x)\nabla u.\nabla v$ , where $a(x)$ is scalar.
 
template<typename MAT , typename VECT >
void getfem::asm_stiffness_matrix_for_scalar_elliptic (MAT &M, const mesh_im &mim, const mesh_fem &mf, const mesh_fem &mf_data, const VECT &A, const mesh_region &rg=mesh_region::all_convexes())
 assembly of $\int_\Omega A(x)\nabla u.\nabla v$, where $A(x)$ is a (symmetric positive definite) NxN matrix. More...
 
template<typename MAT , typename VECT >
void getfem::asm_Helmholtz (MAT &M, const mesh_im &mim, const mesh_fem &mf_u, const mesh_fem &mf_data, const VECT &K_squared, const mesh_region &rg=mesh_region::all_convexes())
 assembly of the term $\int_\Omega Kuv - \nabla u.\nabla v$, for the helmholtz equation ( $\Delta u + k^2u = 0$, with $K=k^2$). More...
 
template<typename MAT , typename VECT >
void getfem::asm_homogeneous_Helmholtz (MAT &M, const mesh_im &mim, const mesh_fem &mf_u, const VECT &K_squared, const mesh_region &rg=mesh_region::all_convexes())
 assembly of the term $\int_\Omega Kuv - \nabla u.\nabla v$, for the helmholtz equation ( $\Delta u + k^2u = 0$, with $K=k^2$). More...
 
template<typename MAT , typename VECT1 , typename VECT2 >
void getfem::asm_dirichlet_constraints (MAT &H, VECT1 &R, const mesh_im &mim, const mesh_fem &mf_u, const mesh_fem &mf_mult, const mesh_fem &mf_r, const VECT2 &r_data, const mesh_region &region, int version=ASMDIR_BUILDALL)
 Assembly of Dirichlet constraints $ u(x) = r(x) $ in a weak form. More...
 
template<typename MAT , typename VECT1 , typename VECT2 , typename VECT3 >
void getfem::asm_generalized_dirichlet_constraints (MAT &H, VECT1 &R, const mesh_im &mim, const mesh_fem &mf_u, const mesh_fem &mf_h, const mesh_fem &mf_r, const VECT2 &h_data, const VECT3 &r_data, const mesh_region &region, int version=ASMDIR_BUILDALL)
 Assembly of generalized Dirichlet constraints h(x)u(x) = r(x), where h is a QxQ matrix field (Q == mf_u.get_qdim()), outputs a (under-determined) linear system HU=R. More...
 
template<typename MAT1 , typename MAT2 , typename VECT1 , typename VECT2 >
size_type getfem::Dirichlet_nullspace (const MAT1 &H, MAT2 &NS, const VECT1 &R, VECT2 &U0)
 Build an orthogonal basis of the kernel of H in NS, gives the solution of minimal norm of H*U = R in U0 and return the dimension of the kernel. More...
 
template<typename MAT , typename VECT >
void getfem::asm_stiffness_matrix_for_bilaplacian (const MAT &M, const mesh_im &mim, const mesh_fem &mf, const mesh_fem &mf_data, const VECT &A, const mesh_region &rg=mesh_region::all_convexes())
 assembly of $\int_\Omega \Delta u \Delta v$.
 
template<typename VECT1 , typename VECT2 >
void getfem::asm_normal_derivative_source_term (VECT1 &B, const mesh_im &mim, const mesh_fem &mf, const mesh_fem &mf_data, const VECT2 &F, const mesh_region &rg)
 assembly of $\int_\Gamma{\partial_n u f}$.
 
template<typename MAT , typename VECT1 , typename VECT2 >
void getfem::asm_normal_derivative_dirichlet_constraints (MAT &H, VECT1 &R, const mesh_im &mim, const mesh_fem &mf_u, const mesh_fem &mf_mult, const mesh_fem &mf_r, const VECT2 &r_data, const mesh_region &rg, bool R_must_be_derivated, int version)
 Assembly of normal derivative Dirichlet constraints $ \partial_n u(x) = r(x) $ in a weak form. More...
 
template<typename MAT , typename VECT >
void getfem::asm_navier_stokes_tgm (const MAT &M, const mesh_im &mim, const mesh_fem &mf, const VECT &U, const mesh_region &rg=mesh_region::all_convexes())
 assembly of Tangent matrix for Navier-Stokes.
 
template<typename VECT1 , typename VECT2 >
void getfem::asm_navier_stokes_rhs (const VECT1 &V, const mesh_im &mim, const mesh_fem &mf, const VECT2 &U, const mesh_region &rg=mesh_region::all_convexes())
 assembly of right hand side for Navier-Stokes.
 
template<typename MAT , typename VECT1 , typename VECT2 >
void getfem::asm_nonlinear_elasticity_tangent_matrix (const MAT &K_, const mesh_im &mim, const getfem::mesh_fem &mf, const VECT1 &U, const getfem::mesh_fem *mf_data, const VECT2 &PARAMS, const abstract_hyperelastic_law &AHL, const mesh_region &rg=mesh_region::all_convexes())
 Tangent matrix for the non-linear elasticity.
 

Detailed Description

Function Documentation

◆ asm_H1_norm()

template<typename VEC >
scalar_type getfem::asm_H1_norm ( const mesh_im &  mim,
const mesh_fem &  mf,
const VEC &  U,
const mesh_region &  rg = mesh_region::all_convexes() 
)

compute the H1 norm of U.

compute $\|\nabla U\|_2$, U might be real or complex

Definition at line 302 of file getfem_assembling.h.

◆ asm_H2_semi_norm()

template<typename VEC >
scalar_type getfem::asm_H2_semi_norm ( const mesh_im &  mim,
const mesh_fem &  mf,
const VEC &  U,
const mesh_region &  rg = mesh_region::all_convexes() 
)

compute $\|Hess U\|_2$, U might be real or complex.

For C^1 elements

Definition at line 422 of file getfem_assembling.h.

◆ asm_homogeneous_source_term()

template<typename VECT1 , typename VECT2 >
void getfem::asm_homogeneous_source_term ( const VECT1 &  B,
const mesh_im &  mim,
const mesh_fem &  mf,
const VECT2 &  F,
const mesh_region &  rg = mesh_region::all_convexes() 
)

source term (for both volumic sources and boundary (Neumann) sources).

For an homogeneous term.

Definition at line 893 of file getfem_assembling.h.

◆ asm_qu_term()

template<typename MAT , typename VECT >
void getfem::asm_qu_term ( MAT &  M,
const mesh_im &  mim,
const mesh_fem &  mf_u,
const mesh_fem &  mf_d,
const VECT &  Q,
const mesh_region &  rg 
)

assembly of $\int{qu.v}$

(if $u$ is a vector field of size $N$, $q$ is a square matrix $N\times N$ used by assem_general_boundary_conditions

convention: Q is of the form Q1_11 Q2_11 ..... Qn_11 Q1_21 Q2_21 ..... Qn_21 Q1_12 Q2_12 ..... Qn_12 Q1_22 Q2_22 ..... Qn_22 if N = 2, and mf_d has n/N degree of freedom

Q is a vector, so the matrix is assumed to be stored by columns (fortran style)

Works for both volumic assembly and boundary assembly

Definition at line 944 of file getfem_assembling.h.

◆ asm_stiffness_matrix_for_linear_elasticity_Hooke()

template<typename MAT , typename VECT >
void getfem::asm_stiffness_matrix_for_linear_elasticity_Hooke ( MAT &  RM,
const mesh_im &  mim,
const mesh_fem &  mf,
const mesh_fem &  mf_data,
const VECT &  H,
const mesh_region &  rg = mesh_region::all_convexes() 
)

Stiffness matrix for linear elasticity, with a general Hooke tensor.

This is more a demonstration of generic assembly than something useful !

Note that this function is just an alias for asm_stiffness_matrix_for_vector_elliptic.

Definition at line 1063 of file getfem_assembling.h.

◆ asm_stiffness_matrix_for_scalar_elliptic()

template<typename MAT , typename VECT >
void getfem::asm_stiffness_matrix_for_scalar_elliptic ( MAT &  M,
const mesh_im &  mim,
const mesh_fem &  mf,
const mesh_fem &  mf_data,
const VECT &  A,
const mesh_region &  rg = mesh_region::all_convexes() 
)

assembly of $\int_\Omega A(x)\nabla u.\nabla v$, where $A(x)$ is a (symmetric positive definite) NxN matrix.

Arguments:

Parameters
Ma sparse matrix of dimensions mf.nb_dof() x mf.nb_dof()
mimthe mesh_im.
mf: the mesh_fem that describes the solution, with mf.get_qdim() == N.
mf_datathe mesh_fem that describes the coefficients of A (mf_data.get_qdim() == 1).
Aa (very large) vector, which is a flattened (n x n x mf_data.nb_dof()) 3D array. For each dof of mf_data, it contains the n x n coefficients of $A$. As usual, the order is the "fortran-order", i.e. A = [A_11(dof1) A_21(dof1) A_31(dof1) A_12(dof1) A_22(dof1) ... A_33(dof) A_11(dof2) .... A_33(lastdof)]

Definition at line 1195 of file getfem_assembling.h.

◆ asm_Helmholtz()

template<typename MAT , typename VECT >
void getfem::asm_Helmholtz ( MAT &  M,
const mesh_im &  mim,
const mesh_fem &  mf_u,
const mesh_fem &  mf_data,
const VECT &  K_squared,
const mesh_region &  rg = mesh_region::all_convexes() 
)

assembly of the term $\int_\Omega Kuv - \nabla u.\nabla v$, for the helmholtz equation ( $\Delta u + k^2u = 0$, with $K=k^2$).

The argument K_squared may be a real or a complex-valued vector.

Definition at line 1274 of file getfem_assembling.h.

◆ asm_homogeneous_Helmholtz()

template<typename MAT , typename VECT >
void getfem::asm_homogeneous_Helmholtz ( MAT &  M,
const mesh_im &  mim,
const mesh_fem &  mf_u,
const VECT &  K_squared,
const mesh_region &  rg = mesh_region::all_convexes() 
)

assembly of the term $\int_\Omega Kuv - \nabla u.\nabla v$, for the helmholtz equation ( $\Delta u + k^2u = 0$, with $K=k^2$).

The argument K_squared may be a real or a complex-valued scalar.

Definition at line 1344 of file getfem_assembling.h.

◆ asm_dirichlet_constraints()

template<typename MAT , typename VECT1 , typename VECT2 >
void getfem::asm_dirichlet_constraints ( MAT &  H,
VECT1 &  R,
const mesh_im &  mim,
const mesh_fem &  mf_u,
const mesh_fem &  mf_mult,
const mesh_fem &  mf_r,
const VECT2 &  r_data,
const mesh_region &  region,
int  version = ASMDIR_BUILDALL 
)

Assembly of Dirichlet constraints $ u(x) = r(x) $ in a weak form.

\[ \int_{\Gamma} u(x)v(x) = \int_{\Gamma} r(x)v(x) \forall v\]

, where $ v $ is in the space of multipliers corresponding to mf_mult.

size(r_data) = Q * nb_dof(mf_rh);

A simplification can be done when the fem for u and r are the same and when the fem for the multipliers is of same dimension as the one for u. version = |ASMDIR_BUILDH : build H |ASMDIR_BUILDR : build R |ASMDIR_SIMPLIFY : simplify |ASMDIR_BUILDALL : do everything.

Definition at line 1373 of file getfem_assembling.h.

◆ asm_generalized_dirichlet_constraints()

template<typename MAT , typename VECT1 , typename VECT2 , typename VECT3 >
void getfem::asm_generalized_dirichlet_constraints ( MAT &  H,
VECT1 &  R,
const mesh_im &  mim,
const mesh_fem &  mf_u,
const mesh_fem &  mf_h,
const mesh_fem &  mf_r,
const VECT2 &  h_data,
const VECT3 &  r_data,
const mesh_region &  region,
int  version = ASMDIR_BUILDALL 
)

Assembly of generalized Dirichlet constraints h(x)u(x) = r(x), where h is a QxQ matrix field (Q == mf_u.get_qdim()), outputs a (under-determined) linear system HU=R.

size(h_data) = Q^2 * nb_dof(mf_rh); size(r_data) = Q * nb_dof(mf_rh);

This function tries hard to make H diagonal or mostly diagonal: this function is able to "simplify" the dirichlet constraints (see below) version = |ASMDIR_BUILDH : build H |ASMDIR_BUILDR : build R |ASMDIR_SIMPLIFY : simplify |ASMDIR_BUILDALL : do everything.

Definition at line 1550 of file getfem_assembling.h.

◆ Dirichlet_nullspace()

template<typename MAT1 , typename MAT2 , typename VECT1 , typename VECT2 >
size_type getfem::Dirichlet_nullspace ( const MAT1 &  H,
MAT2 &  NS,
const VECT1 &  R,
VECT2 &  U0 
)

Build an orthogonal basis of the kernel of H in NS, gives the solution of minimal norm of H*U = R in U0 and return the dimension of the kernel.

The function is based on a Gramm-Schmidt algorithm.

Definition at line 1656 of file getfem_assembling.h.

◆ asm_normal_derivative_dirichlet_constraints()

template<typename MAT , typename VECT1 , typename VECT2 >
void getfem::asm_normal_derivative_dirichlet_constraints ( MAT &  H,
VECT1 &  R,
const mesh_im &  mim,
const mesh_fem &  mf_u,
const mesh_fem &  mf_mult,
const mesh_fem &  mf_r,
const VECT2 &  r_data,
const mesh_region &  rg,
bool  R_must_be_derivated,
int  version 
)

Assembly of normal derivative Dirichlet constraints $ \partial_n u(x) = r(x) $ in a weak form.

\[ \int_{\Gamma} \partial_n u(x)v(x)=\int_{\Gamma} r(x)v(x) \forall v\]

, where $ v $ is in the space of multipliers corresponding to mf_mult.

size(r_data) = Q * nb_dof(mf_rh);

version = |ASMDIR_BUILDH : build H |ASMDIR_BUILDR : build R |ASMDIR_BUILDALL : do everything.

Definition at line 352 of file getfem_fourth_order.h.

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