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 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 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 ). 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 ). 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 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

M	a sparse matrix of dimensions mf.nb_dof() x mf.nb_dof()
mim	the mesh_im.
mf	: the mesh_fem that describes the solution, with `mf.get_qdim()` == `N`.
mf_data	the mesh_fem that describes the coefficients of `A` (`mf_data.get_qdim()` == 1).
A	a (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 . 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.

Functions

Detailed Description

Function Documentation

◆ asm_H1_norm()

◆ asm_H2_semi_norm()

◆ asm_homogeneous_source_term()

◆ asm_qu_term()

◆ asm_stiffness_matrix_for_linear_elasticity_Hooke()

◆ asm_stiffness_matrix_for_scalar_elliptic()

◆ asm_Helmholtz()

◆ asm_homogeneous_Helmholtz()

◆ asm_dirichlet_constraints()

◆ asm_generalized_dirichlet_constraints()

◆ Dirichlet_nullspace()

◆ asm_normal_derivative_dirichlet_constraints()