Miscelleanous assembly routines for common terms. Use the low-level generic assembly. Prefer the high-level one. More...

#include "getfem_assembling_tensors.h"
#include "getfem_generic_assembly.h"

Namespaces
	getfem
	GEneric Tool for Finite Element Methods.

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 >
void	getfem::asm_mass_matrix (const MAT &M, const mesh_im &mim, const mesh_fem &mf1, const mesh_fem &mf2, const mesh_region &rg=mesh_region::all_convexes())
	generic mass matrix assembly (on the whole mesh or on the specified 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_from_consistent (const MAT &M)
	lumped mass matrix assembly from consistent mass matrix

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_laplacian_componentwise (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())
	The same as getfem::asm_stiffness_matrix_for_laplacian , but on each component of mf when mf has a qdim > 1.

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_stiffness_matrix_for_homogeneous_scalar_elliptic (MAT &M, const mesh_im &mim, const mesh_fem &mf, const VECT &A, const mesh_region &rg=mesh_region::all_convexes())
	The same but with a constant matrix.

template<typename MAT , typename VECT >
void	getfem::asm_stiffness_matrix_for_scalar_elliptic_componentwise (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())
	The same but on each component of mf when mf has a qdim > 1.

template<typename MAT , typename VECT >
void	getfem::asm_stiffness_matrix_for_homogeneous_scalar_elliptic_componentwise (MAT &M, const mesh_im &mim, const mesh_fem &mf, const VECT &A, const mesh_region &rg=mesh_region::all_convexes())
	The same but with a constant matrix.

template<typename MAT , typename VECT >
void	getfem::asm_stiffness_matrix_for_vector_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 NxNxQxQ (symmetric positive definite) tensor defined on mf_data.

template<typename MAT , typename VECT >
void	getfem::asm_stiffness_matrix_for_homogeneous_vector_elliptic (MAT &M, const mesh_im &mim, const mesh_fem &mf, const VECT &A, const mesh_region &rg=mesh_region::all_convexes())
	Assembly of $\int_\Omega A(x)\nabla u.\nabla v$ , where is a NxNxQxQ (symmetric positive definite) constant tensor.

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...