// Stiffness and RHS assembly
// Equation references are from Samanta and Zabaras, 2005
void EnergySystem :: assemble(){
// GENERAL VARIABLES
// Get a constant reference to the mesh object.
const MeshBase& mesh = this->get_mesh();
// The dimension that we are running
const unsigned int dim = this->ndim();
// FEM THERMODYNAMIC RELATIONSHIPS (ThermoEq Class)
// Determine the FEM type (should be same for all ThermoEq variables)
FEType fe_type_thermo = thermo->variable_type(0);
// Build FE object; accessed via a pointer
AutoPtr<FEBase> fe_thermo(FEBase::build(dim, fe_type_thermo));
// Setup a quadrature rule
QGauss qrule_thermo(dim, fe_type_thermo.default_quadrature_order());
// Link FE and Quadrature
fe_thermo->attach_quadrature_rule(&qrule_thermo);
// References to shape functions and derivatives
const vector<std::vector<Real> >& N_thermo = fe_thermo->get_phi();
const vector<std::vector<RealGradient> >& B_thermo = fe_thermo->get_dphi();
// Setup a DOF map
const DofMap& dof_map_thermo = thermo->get_dof_map();
// FEM MOMENTUM EQUATION
// Determine the FEM type
FEType fe_type_momentum = momentum->variable_type(0);
// Build FE object; accessed via a pointer
AutoPtr<FEBase> fe_momentum(FEBase::build(dim, fe_type_momentum));
// Setup a quadrature rule
QGauss qrule_momentum(dim, fe_type_momentum.default_quadrature_order());
// Link FE and Quadrature
fe_momentum->attach_quadrature_rule(&qrule_momentum);
// References to shape functions and derivatives
const vector<std::vector<Real> >& N_momentum = fe_momentum->get_phi();
// Setup a DOF map
const DofMap& dof_map_momentum = momentum->get_dof_map();
// FEM ENERGY EQ. RELATIONSHIPS
// Get a constant reference to the Finite Element type
// for the first (and only) variable in the system.
FEType fe_type = this->variable_type(0);
// Build a Finite Element object of the specified type
AutoPtr<FEBase> fe (FEBase::build(dim, fe_type));
AutoPtr<FEBase> fe_face (FEBase::build(dim, fe_type));
// A Gauss quadrature rule for numerical integration.
// Let the \p FEType object decide what order rule is appropriate.
QGauss qrule (dim, fe_type.default_quadrature_order());
QGauss qface (dim-1, fe_type.default_quadrature_order());
// Tell the finite element object to use our quadrature rule.
fe->attach_quadrature_rule(&qrule);
fe_face->attach_quadrature_rule(&qface);
// Here we define some references to cell-specific data that
// will be used to assemble the linear system. We will start
// with the element Jacobian * quadrature weight at each integration point.
const vector<Real>& JxW = fe->get_JxW();
const vector<Real>& JxW_face = fe_face->get_JxW();
// The element shape functions evaluated at the quadrature points.
const vector<std::vector<Real> >& N = fe->get_phi();
const vector<std::vector<Real> >& N_face = fe_face->get_phi();
// Element shape function gradients evaluated at quadrature points
const vector<std::vector<RealGradient> >& B = fe->get_dphi();
// The XY locations of the quadrature points used for face integration
const vector<Point>& qface_points = fe_face->get_xyz();
// A reference to the \p DofMap objects
const DofMap& dof_map = this->get_dof_map(); // this system
// DEFINE VECTOR AND MATRIX VARIABLES
// Define data structures to contain the element matrix
// and right-hand-side vector contribution (Eq. 107)
DenseMatrix<Number> Me; // [\hat{M} + \hat{M}_{\delta}]
DenseMatrix<Number> Ne; // [\hat{N} + \hat{N}_{\delta}]
DenseMatrix<Number> Ke; // [\hat{K} + \hat{K}_{\delta}]
DenseVector<Number> Fe; // [\hat{F} + \hat{F}_{\delta}]
//DenseVector<Number> Fe_old; // element force vector (previous time)
DenseVector<Number> h; // element enthalpy vector (previous time)
DenseVector<Number> h_dot;
//DenseVector<Number> delta_h_dot;
DenseMatrix<Number> Mstar; // general time integration stiffness matrix (Eq. 125)
DenseVector<Number> R; // general time integration force vector (Eq. 126)
// Storage vectors for the degree of freedom indices
std::vector<unsigned int> dof_indices; // this system (h)
// std::vector<unsigned int> dof_indices_hdot;
// std::vector<unsigned int> dof_indices_deltahdot;
std::vector<unsigned int> dof_indices_velocity; // this system
std::vector<unsigned int> dof_indices_rho; // ThermoEq density
std::vector<unsigned int> dof_indices_tmp; // ThermoEq temperature
std::vector<unsigned int> dof_indices_f; // ThermoEq liquid fraction
std::vector<unsigned int> dof_indices_eps; // ThermoEq epsilon
// Define the necessary constants
const Number gamma = get_constant<Number>("gamma");
const Number dt = get_constant<Number>("dt"); // time step
Real time = this->time; // current time
const Number ks = thermo->get_constant<Number>("conductivity_solid");
const Number kf = thermo->get_constant<Number>("conductivity_fluid");
const Number cs = thermo->get_constant<Number>("specific_heat_solid");
const Number cf = thermo->get_constant<Number>("specific_heat_fluid");
const Number Te = thermo->get_constant<Number>("eutectic_temperature");
const Number hf = thermo->get_constant<Number>("latent_heat");
// Index of density variable in ThermoEq system
const unsigned int rho_idx = thermo->variable_number("density");
const unsigned int tmp_idx = thermo->variable_number("temperature");
const unsigned int f_idx = thermo->variable_number("liquid_mass_fraction");
const unsigned int eps_idx = thermo->variable_number("epsilon");
// Loop over all the elements in the mesh that are on local processor
MeshBase::const_element_iterator el = mesh.active_local_elements_begin();
const MeshBase::const_element_iterator end_el = mesh.active_local_elements_end();
for ( ; el != end_el; ++el){
// Pointer to the element current element
const Elem* elem = *el;
// Get the degree of freedom indices for the current element
dof_map.dof_indices(elem, dof_indices, 0);
//dof_map.dof_indices(elem, dof_indices_hdot, 1);
//dof_map.dof_indices(elem, dof_indices_deltahdot, 2);
dof_map_momentum.dof_indices(elem, dof_indices_velocity);
dof_map_thermo.dof_indices(elem, dof_indices_rho, rho_idx);
dof_map_thermo.dof_indices(elem, dof_indices_tmp, tmp_idx);
dof_map_thermo.dof_indices(elem, dof_indices_f, f_idx);
dof_map_thermo.dof_indices(elem, dof_indices_eps, eps_idx);
// Compute the element-specific data for the current element
fe->reinit (elem);
fe_thermo->reinit(elem);
fe_momentum->reinit(elem);
// Zero the element matrices and vectors
Me.resize (dof_indices.size(), dof_indices.size()); // [\hat{M} + \hat{M}_{\delta}]
Ne.resize (dof_indices.size(), dof_indices.size()); //
Ke.resize (dof_indices.size(), dof_indices.size());
Fe.resize (dof_indices.size());
// Extract a vector of quadrature x,y,z coordinates
const vector<Point> qp_vec = fe->get_xyz();
// Compute the element length, h
Number elem_length = thermo->element_length(elem);
// Compute the RHS and mass and stiffness matrix for this element (Me)
for (unsigned int qp = 0; qp < qrule.n_points(); qp++){
// Get the velocity vector at this point (old value)
VectorValue<Number> v;
for (unsigned int i = 0; i < N_momentum.size(); i++){
for (unsigned int j = 0; j < dim; j++){
v(j) += N_momentum[i][qp] * momentum->old_solution(dof_indices_velocity[2*i+j]);
}
}
// Compute ThermoEq variables; must be mapped from node to quadrature points
Number T = 0;
Gradient grad_T;
Number f = 0;
Gradient grad_f;
Number rho = 0;
Number rho_old = 0;
Number eps = 0;
for (unsigned int i = 0; i < N_thermo.size(); i++){
T += N_thermo[i][qp] * thermo->current_solution(dof_indices_tmp[i]);
grad_T.add_scaled(B_thermo[i][qp], thermo->current_solution(dof_indices_tmp[i]));
f += N_thermo[i][qp] * thermo->current_solution(dof_indices_f[i]);
grad_f.add_scaled(B_thermo[i][qp], thermo->current_solution(dof_indices_f[i]));
rho += N_thermo[i][qp] * thermo->current_solution(dof_indices_rho[i]);
rho_old += N_thermo[i][qp] * thermo->old_solution(dof_indices_rho[i]);
eps += N_thermo[i][qp] * thermo->current_solution(dof_indices_eps[i]);
}
// Compute EnergySystem variables
Gradient grad_h;
for (unsigned int i = 0; i < B.size(); i++){
grad_h.add_scaled(B[i][qp], this->current_solution(dof_indices[i]));
}
// Compute T_{,k}^h v_k^h and f_{,k} v_k^h summation terms for F
Number Tv = 0;
Number fv = 0;
for (unsigned int i = 0; i < dim; i++){
Tv += grad_T(i) * v(i);
fv += grad_f(i) * v(i);
}
// Compute the time derivative of density
const Number drho_dt = (rho - rho_old)/dt;
// Compute alpha term of Eq. 69
const Number alpha = this->alpha(grad_T, grad_h, f);
// Extract tau_1 stabilization term
const Number tau_1 = thermo->tau_1(qp_vec[qp], elem_length);
// Loop through the components and construct matrices
for (unsigned int i = 0; i < N.size(); i++){
// Compute advective stabilization term (Eq. A, p. 1777)
const Number d = tau_1 * v * B[i][qp] / f - tau_1 * 1/rho * drho_dt * (1-f)/f * N[i][qp];
// Force vector, Eq. 77
Number F1 = JxW[qp] * (N[i][qp] + d) * rho * (1 - f) * (cf - cs) * Tv;
Number F2 = JxW[qp] * (N[i][qp] + d) * rho * fv * ((cf - cs) * (T - Te) + hf);
Number F3 = JxW[qp] * (N[i][qp] + d) * drho_dt * (1 - f) * ((cf - cs) * (T - Te) + hf);
Fe(i) += F1 + F2 + F3;
// Build the stiffness matrices
for (unsigned int j = 0; j < N.size(); j++){
// Mass matrix, Eq. 108
Me(i,j) += JxW[qp] * rho * ((N[i][qp] + d) * N[j][qp]);
// Stiffness matrix one, Ne, Eq. 109
Ne(i,j) += JxW[qp] * rho * ((N[i][qp] + d) * (v * B[j][qp]));
// Stiffness matrix two, Ke, Eq. 110
Ke(i,j) += JxW[qp]*((eps*kf + (1 - eps)*ks) * alpha * B[i][qp] * B[j][qp]);
}
}
}
printf("Me:\n");
Me.print(std::cout);
printf("\nNe:\n");
Ne.print(std::cout);
printf("\nKe:\n");
Ke.print(std::cout);
printf("\nFe:\n");
Fe.print(std::cout);
h.resize(dof_indices.size());
h_dot.resize(dof_indices.size());
// delta_h_dot.resize(dof_indices_deltahdot.size());
for (unsigned int i = 0; i < dof_indices.size(); i++){
h(i) = this->old_solution(dof_indices[i]);
h_dot(i) = this->get_vector("h_dot")(dof_indices[i]);
// delta_h_dot(i) = this->old_solution(dof_indices_deltahdot[i]);
}
this->get_matrix("M").add_matrix(Me, dof_indices);
this->get_matrix("N").add_matrix(Ne, dof_indices);
this->get_matrix("K").add_matrix(Ke, dof_indices);
this->get_vector("F").add_vector(Fe, dof_indices);
Mstar.resize(dof_indices.size(), dof_indices.size());
R.resize(dof_indices.size());
// Me + gamma*dt*(Ke + Ne);
Mstar.add(1,Me);
Mstar.add(gamma*dt,Ke);
Mstar.add(gamma*dt,Ne);
this->matrix->add_matrix(Mstar, dof_indices);
R.add(1,Fe);
DenseVector<Number> a(dof_indices.size());
Me.vector_mult(a, h_dot);
R.add(-1, a);
DenseMatrix<Number> B(dof_indices.size(), dof_indices.size());
DenseVector<Number> b(dof_indices.size());
B.add(1,Ne);
B.add(1,Ke);
B.vector_mult(b, h);
R.add(-1,b);
this->rhs->add_vector(R, dof_indices);
/*
// BOUNDARY CONDITIONS
// Loop through each side of the element for applying boundary conditions
for (unsigned int s = 0; s < elem->n_sides(); s++){
// Only consider the side if it does not have a neighbor
if (elem->neighbor(s) == NULL){
// Pointer to current element side
const AutoPtr<Elem> side = elem->side(s);
// Boundary ID of the current side
int boundary_id = (mesh.boundary_info)->boundary_id(elem, s);
// Get index of the boundary class with the same id
// this vector is empty if there is no match and only
// contains a single value if there is a match
std::vector<int> idx = get_boundary_index(boundary_id);
// Continue of there is a match
if(!idx.empty()){
// Compute the shape function values on the element face
fe_face->reinit(elem, s);
// Create a shared pointer to the boundary class
boost::shared_ptr<HeatEqBoundaryBase> ptr = bc_ptrs[idx[0]];
// Determine the type of boundary considered
std::string type = ptr->type;
// Loop through quadrature points
for (unsigned int qp = 0; qp < qface.n_points(); qp++){
// DIRICHLET (libMesh version; handled at initialization)
if(type.compare("dirichlet") == 0){
// The dirichlet conditions are handled at initlization
// but I don't want to throw an error if they are
// encountered, so just do nothing
// NEUMANN condition
} else if(type.compare("neumann") == 0){
// Current and past flux values
const Number q = ptr->q(qface_points[qp], time);
const Number q_old = ptr->q(qface_points[qp], time - dt);
// Add values to Fe
for (unsigned int i = 0; i < psi.size(); i++){
Fe(i) += JxW_face[qp] * q * psi[i][qp];
Fe_old(i) += JxW_face[qp] * q_old * psi[i][qp];
}
// CONVECTION boundary
} else if(type.compare("convection") == 0){
// Current and past h and T_inf
const Number h = ptr->h(qface_points[qp], time);
const Number h_old = ptr->h(qface_points[qp], time - dt);
const Number Tinf = ptr->Tinf(qface_points[qp], time);
const Number Tinf_old = ptr->Tinf(qface_points[qp], time - dt);
// Add values to Ke and Fe
for (unsigned int i = 0; i < psi.size(); i++){
Fe(i) += (1) * JxW_face[qp] * h * Tinf * psi[i][qp];
Fe_old(i) += (1) * JxW_face[qp] * h_old * Tinf_old * psi[i][qp];
for (unsigned int j = 0; j < psi.size(); j++){
Ke(i,j) += JxW_face[qp] * psi[i][qp] * h * psi[j][qp];
}
}
// Un-registerd type
} else {
printf("WARNING! The boundary type, %s, was not understood!\n", type.c_str());
} // (end) type.compare(...) statemenst
} //(end) for (int qp = 0; qp < qface.n_points(); qp++)
} // (end) if(!idx.empty)
} // (end) if (elem->neighbor(s) == NULL){
} // (end) for (int s = 0; s < elem->n_sides(); s++)
// Zero the pervious time-step temperature vector for this element
u_old.resize(dof_indices.size());
// Gather the temperatures at the nodes
for (unsigned int i = 0; i < psi.size(); i++){
u_old(i) = this->old_solution(dof_indices[i]);
}
// Build K_hat and F_hat (appends existing)
K_hat.resize(dof_indices.size(), dof_indices.size());
F_hat.resize(dof_indices.size());
build_stiffness_and_rhs(K_hat, F_hat, Me, Ke, Fe_old, Fe, u_old, dt, theta);
// Applies the dirichlet constraints to K_hat and F_hat
dof_map.heterogenously_constrain_element_matrix_and_vector(K_hat, F_hat, dof_indices);
// Apply the local components to the global K and F
this->matrix->add_matrix(K_hat, dof_indices);
this->rhs->add_vector(F_hat, dof_indices);
*/
} // (end) for ( ; el != end_el; ++el)
//update_rhs();
} // (end) assemble()
// The matrix assembly function to be called at each time step to
// prepare for the linear solve.
void assemble_solid (EquationSystems& es,
const std::string& system_name)
{
//es.print_info();
#if LOG_ASSEMBLE_PERFORMANCE
PerfLog perf_log("Assemble");
perf_log.push("assemble stiffness");
#endif
// Get a reference to the auxiliary system
//TransientExplicitSystem& aux_system = es.get_system<TransientExplicitSystem>("Newton-update");
// It is a good idea to make sure we are assembling
// the proper system.
libmesh_assert (system_name == "Newton-update");
// Get a constant reference to the mesh object.
const MeshBase& mesh = es.get_mesh();
// The dimension that we are running
const unsigned int dim = mesh.mesh_dimension();
// Get a reference to the Stokes system object.
TransientLinearImplicitSystem & newton_update =
es.get_system<TransientLinearImplicitSystem> ("Newton-update");
// New
TransientLinearImplicitSystem & last_non_linear_soln =
es.get_system<TransientLinearImplicitSystem> ("Last-non-linear-soln");
TransientLinearImplicitSystem & fluid_system_vel =
es.get_system<TransientLinearImplicitSystem> ("fluid-system-vel");
#if VELOCITY
TransientLinearImplicitSystem& velocity = es.get_system<TransientLinearImplicitSystem>("velocity-system");
#endif
#if UN_MINUS_ONE
TransientLinearImplicitSystem & unm1 =
es.get_system<TransientLinearImplicitSystem> ("unm1-system");
#endif
test(62);
const System & ref_sys = es.get_system("Reference-Configuration");
test(63);
// Numeric ids corresponding to each variable in the system
const unsigned int u_var = last_non_linear_soln .variable_number ("u");
const unsigned int v_var = last_non_linear_soln .variable_number ("v");
const unsigned int w_var = last_non_linear_soln .variable_number ("w");
#if INCOMPRESSIBLE
const unsigned int p_var = last_non_linear_soln .variable_number ("p");
#endif
#if FLUID_P_CONST
const unsigned int m_var = fluid_system_vel.variable_number ("fluid_M");
std::vector<unsigned int> dof_indices_m;
#endif
// Get the Finite Element type for "u". Note this will be
// the same as the type for "v".
FEType fe_vel_type = last_non_linear_soln.variable_type(u_var);
test(64);
#if INCOMPRESSIBLE
// Get the Finite Element type for "p".
FEType fe_pres_type = last_non_linear_soln .variable_type(p_var);
#endif
// Build a Finite Element object of the specified type for
// the velocity variables.
AutoPtr<FEBase> fe_vel (FEBase::build(dim, fe_vel_type));
#if INCOMPRESSIBLE
// Build a Finite Element object of the specified type for
// the pressure variables.
AutoPtr<FEBase> fe_pres (FEBase::build(dim, fe_pres_type));
#endif
// A Gauss quadrature rule for numerical integration.
// Let the \p FEType object decide what order rule is appropriate.
QGauss qrule (dim, fe_vel_type.default_quadrature_order());
// Tell the finite element objects to use our quadrature rule.
fe_vel->attach_quadrature_rule (&qrule);
test(65);
// AutoPtr<QBase> qrule2(fe_vel_type.default_quadrature_rule(dim));
// fe_vel->attach_quadrature_rule (qrule2.get());
#if INCOMPRESSIBLE
fe_pres->attach_quadrature_rule (&qrule);
#endif
// The element Jacobian * quadrature weight at each integration point.
const std::vector<Real>& JxW = fe_vel->get_JxW();
// The element shape functions evaluated at the quadrature points.
const std::vector<std::vector<Real> >& phi = fe_vel->get_phi();
// The element shape function gradients for the velocity
// variables evaluated at the quadrature points.
const std::vector<std::vector<RealGradient> >& dphi = fe_vel->get_dphi();
test(66);
#if INCOMPRESSIBLE
// The element shape functions for the pressure variable
// evaluated at the quadrature points.
const std::vector<std::vector<Real> >& psi = fe_pres->get_phi();
#endif
const std::vector<Point>& coords = fe_vel->get_xyz();
// A reference to the \p DofMap object for this system. The \p DofMap
// object handles the index translation from node and element numbers
// to degree of freedom numbers. We will talk more about the \p DofMap
// in future examples.
const DofMap & dof_map = last_non_linear_soln .get_dof_map();
#if FLUID_P_CONST
const DofMap & dof_map_fluid = fluid_system_vel .get_dof_map();
#endif
// K will be the jacobian
// F will be the Residual
DenseMatrix<Number> Ke;
DenseVector<Number> Fe;
DenseSubMatrix<Number>
Kuu(Ke), Kuv(Ke), Kuw(Ke),
Kvu(Ke), Kvv(Ke), Kvw(Ke),
Kwu(Ke), Kwv(Ke), Kww(Ke);
#if INCOMPRESSIBLE
DenseSubMatrix<Number> Kup(Ke),Kvp(Ke),Kwp(Ke), Kpu(Ke), Kpv(Ke), Kpw(Ke), Kpp(Ke);
#endif;
DenseSubVector<Number>
Fu(Fe), Fv(Fe), Fw(Fe);
#if INCOMPRESSIBLE
DenseSubVector<Number> Fp(Fe);
#endif
// This vector will hold the degree of freedom indices for
// the element. These define where in the global system
// the element degrees of freedom get mapped.
std::vector<unsigned int> dof_indices;
std::vector<unsigned int> dof_indices_u;
std::vector<unsigned int> dof_indices_v;
std::vector<unsigned int> dof_indices_w;
#if INCOMPRESSIBLE
std::vector<unsigned int> dof_indices_p;
#endif
#if INERTIA
test(67);
const unsigned int a_var = last_non_linear_soln.variable_number ("a");
const unsigned int b_var = last_non_linear_soln.variable_number ("b");
const unsigned int c_var = last_non_linear_soln.variable_number ("c");
//B block
DenseSubMatrix<Number>
Kua(Ke), Kub(Ke), Kuc(Ke),
Kva(Ke), Kvb(Ke), Kvc(Ke),
Kwa(Ke), Kwb(Ke), Kwc(Ke);
//C block
DenseSubMatrix<Number>
Kau(Ke), Kav(Ke), Kaw(Ke),
Kbu(Ke), Kbv(Ke), Kbw(Ke),
Kcu(Ke), Kcv(Ke), Kcw(Ke);
//D block
DenseSubMatrix<Number>
Kaa(Ke), Kab(Ke), Kac(Ke),
Kba(Ke), Kbb(Ke), Kbc(Ke),
Kca(Ke), Kcb(Ke), Kcc(Ke);
DenseSubVector<Number>
Fa(Fe), Fb(Fe), Fc(Fe);
std::vector<unsigned int> dof_indices_a;
std::vector<unsigned int> dof_indices_b;
std::vector<unsigned int> dof_indices_c;
test(68);
#endif
DenseMatrix<Real> stiff;
DenseVector<Real> res;
VectorValue<Gradient> grad_u_mat;
VectorValue<Gradient> grad_u_mat_old;
const Real dt = es.parameters.get<Real>("dt");
const Real progress = es.parameters.get<Real>("progress");
#if PORO
DenseVector<Real> p_stiff;
DenseVector<Real> p_res;
PoroelasticConfig material(dphi,psi);
#endif
// Just calculate jacobian contribution when we need to
material.calculate_linearized_stiffness = true;
MeshBase::const_element_iterator el = mesh.active_local_elements_begin();
const MeshBase::const_element_iterator end_el = mesh.active_local_elements_end();
for ( ; el != end_el; ++el)
{
test(69);
const Elem* elem = *el;
dof_map.dof_indices (elem, dof_indices);
dof_map.dof_indices (elem, dof_indices_u, u_var);
dof_map.dof_indices (elem, dof_indices_v, v_var);
dof_map.dof_indices (elem, dof_indices_w, w_var);
#if INCOMPRESSIBLE
dof_map.dof_indices (elem, dof_indices_p, p_var);
#endif
const unsigned int n_dofs = dof_indices.size();
const unsigned int n_u_dofs = dof_indices_u.size();
const unsigned int n_v_dofs = dof_indices_v.size();
const unsigned int n_w_dofs = dof_indices_w.size();
#if INCOMPRESSIBLE
const unsigned int n_p_dofs = dof_indices_p.size();
#endif
#if FLUID_P_CONST
dof_map_fluid.dof_indices (elem, dof_indices_m, m_var);
#endif
//elem->print_info();
fe_vel->reinit (elem);
#if INCOMPRESSIBLE
fe_pres->reinit (elem);
#endif
Ke.resize (n_dofs, n_dofs);
Fe.resize (n_dofs);
Kuu.reposition (u_var*n_u_dofs, u_var*n_u_dofs, n_u_dofs, n_u_dofs);
Kuv.reposition (u_var*n_u_dofs, v_var*n_u_dofs, n_u_dofs, n_v_dofs);
Kuw.reposition (u_var*n_u_dofs, w_var*n_u_dofs, n_u_dofs, n_w_dofs);
#if INCOMPRESSIBLE
Kup.reposition (u_var*n_u_dofs, p_var*n_u_dofs, n_u_dofs, n_p_dofs);
#endif
Kvu.reposition (v_var*n_v_dofs, u_var*n_v_dofs, n_v_dofs, n_u_dofs);
Kvv.reposition (v_var*n_v_dofs, v_var*n_v_dofs, n_v_dofs, n_v_dofs);
Kvw.reposition (v_var*n_v_dofs, w_var*n_v_dofs, n_v_dofs, n_w_dofs);
#if INCOMPRESSIBLE
Kvp.reposition (v_var*n_v_dofs, p_var*n_v_dofs, n_v_dofs, n_p_dofs);
#endif
Kwu.reposition (w_var*n_w_dofs, u_var*n_w_dofs, n_w_dofs, n_u_dofs);
Kwv.reposition (w_var*n_w_dofs, v_var*n_w_dofs, n_w_dofs, n_v_dofs);
Kww.reposition (w_var*n_w_dofs, w_var*n_w_dofs, n_w_dofs, n_w_dofs);
#if INCOMPRESSIBLE
Kwp.reposition (w_var*n_w_dofs, p_var*n_w_dofs, n_w_dofs, n_p_dofs);
Kpu.reposition (p_var*n_u_dofs, u_var*n_u_dofs, n_p_dofs, n_u_dofs);
Kpv.reposition (p_var*n_u_dofs, v_var*n_u_dofs, n_p_dofs, n_v_dofs);
Kpw.reposition (p_var*n_u_dofs, w_var*n_u_dofs, n_p_dofs, n_w_dofs);
Kpp.reposition (p_var*n_u_dofs, p_var*n_u_dofs, n_p_dofs, n_p_dofs);
#endif
Fu.reposition (u_var*n_u_dofs, n_u_dofs);
Fv.reposition (v_var*n_u_dofs, n_v_dofs);
Fw.reposition (w_var*n_u_dofs, n_w_dofs);
#if INCOMPRESSIBLE
Fp.reposition (p_var*n_u_dofs, n_p_dofs);
#endif
#if INERTIA
//B block
Kua.reposition (u_var*n_u_dofs, 3*n_u_dofs + n_p_dofs, n_u_dofs, n_u_dofs);
Kub.reposition (u_var*n_u_dofs, 4*n_u_dofs + n_p_dofs, n_u_dofs, n_v_dofs);
Kuc.reposition (u_var*n_u_dofs, 5*n_u_dofs + n_p_dofs, n_u_dofs, n_w_dofs);
Kva.reposition (v_var*n_v_dofs, 3*n_u_dofs + n_p_dofs, n_v_dofs, n_u_dofs);
Kvb.reposition (v_var*n_v_dofs, 4*n_u_dofs + n_p_dofs, n_v_dofs, n_v_dofs);
Kvc.reposition (v_var*n_v_dofs, 5*n_u_dofs + n_p_dofs, n_v_dofs, n_w_dofs);
Kwa.reposition (w_var*n_w_dofs, 3*n_u_dofs + n_p_dofs, n_w_dofs, n_u_dofs);
Kwb.reposition (w_var*n_w_dofs, 4*n_u_dofs + n_p_dofs, n_w_dofs, n_v_dofs);
Kwc.reposition (w_var*n_w_dofs, 5*n_u_dofs + n_p_dofs, n_w_dofs, n_w_dofs);
test(701);
//C block
Kau.reposition (3*n_u_dofs + n_p_dofs, u_var*n_u_dofs, n_u_dofs, n_u_dofs);
Kav.reposition (3*n_u_dofs + n_p_dofs, v_var*n_u_dofs, n_u_dofs, n_v_dofs);
Kaw.reposition (3*n_u_dofs + n_p_dofs, w_var*n_u_dofs, n_u_dofs, n_w_dofs);
Kbu.reposition (4*n_u_dofs + n_p_dofs, u_var*n_v_dofs, n_v_dofs, n_u_dofs);
Kbv.reposition (4*n_u_dofs + n_p_dofs, v_var*n_v_dofs, n_v_dofs, n_v_dofs);
Kbw.reposition (4*n_u_dofs + n_p_dofs, w_var*n_v_dofs, n_v_dofs, n_w_dofs);
Kcu.reposition (5*n_u_dofs + n_p_dofs, u_var*n_w_dofs, n_w_dofs, n_u_dofs);
Kcv.reposition (5*n_u_dofs + n_p_dofs, v_var*n_w_dofs, n_w_dofs, n_v_dofs);
Kcw.reposition (5*n_u_dofs + n_p_dofs, w_var*n_w_dofs, n_w_dofs, n_w_dofs);
//D block
Kaa.reposition (3*n_u_dofs + n_p_dofs, 3*n_u_dofs + n_p_dofs, n_u_dofs, n_u_dofs);
Kab.reposition (3*n_u_dofs + n_p_dofs, 4*n_u_dofs + n_p_dofs, n_u_dofs, n_v_dofs);
Kac.reposition (3*n_u_dofs + n_p_dofs, 5*n_u_dofs + n_p_dofs, n_u_dofs, n_w_dofs);
Kba.reposition (4*n_u_dofs + n_p_dofs, 3*n_u_dofs + n_p_dofs, n_v_dofs, n_u_dofs);
Kbb.reposition (4*n_u_dofs + n_p_dofs, 4*n_u_dofs + n_p_dofs, n_v_dofs, n_v_dofs);
Kbc.reposition (4*n_u_dofs + n_p_dofs, 5*n_u_dofs + n_p_dofs, n_v_dofs, n_w_dofs);
Kca.reposition (5*n_u_dofs + n_p_dofs, 3*n_u_dofs + n_p_dofs, n_w_dofs, n_u_dofs);
Kcb.reposition (5*n_u_dofs + n_p_dofs, 4*n_u_dofs + n_p_dofs, n_w_dofs, n_v_dofs);
Kcc.reposition (5*n_u_dofs + n_p_dofs, 5*n_u_dofs + n_p_dofs, n_w_dofs, n_w_dofs);
Fa.reposition (3*n_u_dofs + n_p_dofs, n_u_dofs);
Fb.reposition (4*n_u_dofs + n_p_dofs, n_v_dofs);
Fc.reposition (5*n_u_dofs + n_p_dofs, n_w_dofs);
dof_map.dof_indices (elem, dof_indices_a, a_var);
dof_map.dof_indices (elem, dof_indices_b, b_var);
dof_map.dof_indices (elem, dof_indices_c, c_var);
test(71);
#endif
System& aux_system = es.get_system<System>("Reference-Configuration");
std::vector<unsigned int> undefo_index;
std::vector<unsigned int> vel_index;
for (unsigned int qp=0; qp<qrule.n_points(); qp++)
{
Point rX;
for (unsigned int l=0; l<n_u_dofs; l++)
{
rX(0) += phi[l][qp]*ref_sys.current_local_solution->el(dof_indices_u[l]);
rX(1) += phi[l][qp]*ref_sys.current_local_solution->el(dof_indices_v[l]);
rX(2) += phi[l][qp]*ref_sys.current_local_solution->el(dof_indices_w[l]);
}
#if INERTIA || DT
test(72);
Real rho_s=15;
Point current_x;
for (unsigned int l=0; l<n_u_dofs; l++)
{
current_x(0) += phi[l][qp]*last_non_linear_soln.current_local_solution->el(dof_indices_u[l]);
current_x(1) += phi[l][qp]*last_non_linear_soln.current_local_solution->el(dof_indices_v[l]);
current_x(2) += phi[l][qp]*last_non_linear_soln.current_local_solution->el(dof_indices_w[l]);
}
Point old_x;
for (unsigned int l=0; l<n_u_dofs; l++)
{
old_x(0) += phi[l][qp]*last_non_linear_soln.old_local_solution->el(dof_indices_u[l]);
old_x(1) += phi[l][qp]*last_non_linear_soln.old_local_solution->el(dof_indices_v[l]);
old_x(2) += phi[l][qp]*last_non_linear_soln.old_local_solution->el(dof_indices_w[l]);
}
#if INERTIA
Point old_vel;
for (unsigned int l=0; l<n_u_dofs; l++)
{
old_vel(0) += phi[l][qp]*last_non_linear_soln.old_local_solution->el(dof_indices_a[l]);
old_vel(1) += phi[l][qp]*last_non_linear_soln.old_local_solution->el(dof_indices_b[l]);
old_vel(2) += phi[l][qp]*last_non_linear_soln.old_local_solution->el(dof_indices_c[l]);
}
Point current_vel;
for (unsigned int l=0; l<n_u_dofs; l++)
{
current_vel(0) += phi[l][qp]*last_non_linear_soln.current_local_solution->el(dof_indices_a[l]);
current_vel(1) += phi[l][qp]*last_non_linear_soln.current_local_solution->el(dof_indices_b[l]);
current_vel(2) += phi[l][qp]*last_non_linear_soln.current_local_solution->el(dof_indices_c[l]);
}
#endif
#if UN_MINUS_ONE
Point unm1_x;
for (unsigned int l=0; l<n_u_dofs; l++)
{
unm1_x(0) += phi[l][qp]*unm1.old_local_solution->el(dof_indices_u[l]);
unm1_x(1) += phi[l][qp]*unm1.old_local_solution->el(dof_indices_v[l]);
unm1_x(2) += phi[l][qp]*unm1.old_local_solution->el(dof_indices_w[l]);
}
#endif
Point value_acc;
Point value_acc_alt;
#if DT
for (unsigned int d = 0; d < dim; ++d) {
value_acc_alt(d) = (rho_s)*( ((current_x(d)-rX(d))-(old_x(d)-rX(d)))-((old_x(d)-rX(d))- (unm1_x(d)-rX(d))) );
value_acc(d) = (rho_s)*((current_x(d))-2*(old_x(d))+ (unm1_x(d)));
value_acc(d) = (rho_s)*((current_x(d))-(old_x(d)));
}
#endif
Point res_1;
Point res_2;
#if INERTIA
for (unsigned int d = 0; d < dim; ++d) {
res_1(d) = (rho_s)*((current_vel(d))-(old_vel(d)));
res_2(d) = current_x(d)-dt*current_vel(d)-old_x(d);
}
/*
std::cout<<" current_vel "<<current_vel<<std::endl;
std::cout<<" res_1 "<<res_1<<std::endl;
std::cout<<" res_2 "<<res_2<<std::endl;
*/
#endif
test(73);
#endif
Number p_solid = 0.;
#if MOVING_MESH
grad_u_mat(0) = grad_u_mat(1) = grad_u_mat(2) = 0;
for (unsigned int d = 0; d < dim; ++d) {
std::vector<Number> u_undefo;
//Fills the vector di with the global degree of freedom indices for the element. :dof_indicies
aux_system.get_dof_map().dof_indices(elem, undefo_index,d);
aux_system.current_local_solution->get(undefo_index, u_undefo);
for (unsigned int l = 0; l != n_u_dofs; l++)
grad_u_mat(d).add_scaled(dphi[l][qp], u_undefo[l]);
}
#endif
//#include "fixed_mesh_in_solid_assemble_code.txt"
#if INCOMPRESSIBLE
for (unsigned int l=0; l<n_p_dofs; l++)
{
p_solid += psi[l][qp]*last_non_linear_soln.current_local_solution->el(dof_indices_p[l]);
}
#endif
#if INCOMPRESSIBLE
Real m=0;
Real p_fluid=0;
#if FLUID_VEL
for (unsigned int l=0; l<n_p_dofs; l++)
{
p_fluid += psi[l][qp]*fluid_system_vel.current_local_solution->el(dof_indices_p[l]);
}
//As outlined in Chappel p=(p_curr-p_old)/2
Real p_fluid_old=0;
for (unsigned int l=0; l<n_p_dofs; l++)
{
p_fluid_old += psi[l][qp]*fluid_system_vel.old_local_solution->el(dof_indices_p[l]);
}
p_fluid=0.5*p_fluid+0.5*p_fluid_old;
Real m_old=0;
#if FLUID_P_CONST
for (unsigned int l=0; l<n_p_dofs; l++)
{
m += psi[l][qp]*fluid_system_vel.current_local_solution->el(dof_indices_m[l]);
}
for (unsigned int l=0; l<n_p_dofs; l++)
{
m_old += psi[l][qp]*fluid_system_vel.old_local_solution->el(dof_indices_m[l]);
}
#endif
material.init_for_qp(grad_u_mat, p_solid, qp, 1.0*m+0.0*m_old, p_fluid);
#endif
#endif //#if INCOMPRESSIBLE
#if INCOMPRESSIBLE && ! PORO
material.init_for_qp(grad_u_mat, p_solid, qp);
#endif
for (unsigned int i=0; i<n_u_dofs; i++)
{
res.resize(dim);
material.get_residual(res, i);
res.scale(JxW[qp]);
#if INERTIA
res.scale(dt);
#endif
#if DT
res.scale(dt);
#endif
//std::cout<< "res "<<res<<std::endl;
Fu(i) += res(0);
Fv(i) += res(1) ;
Fw(i) += res(2);
#if GRAVITY
Real grav=0.0;
Fu(i) += progress*grav*JxW[qp]*phi[i][qp];
#endif
#if INERTIA
Fu(i) += JxW[qp]*phi[i][qp]*res_1(0);
Fv(i) += JxW[qp]*phi[i][qp]*res_1(1);
Fw(i) += JxW[qp]*phi[i][qp]*res_1(2);
Fa(i) += JxW[qp]*phi[i][qp]*res_2(0);
Fb(i) += JxW[qp]*phi[i][qp]*res_2(1);
Fc(i) += JxW[qp]*phi[i][qp]*res_2(2);
#endif
// Matrix contributions for the uu and vv couplings.
for (unsigned int j=0; j<n_u_dofs; j++)
{
material.get_linearized_stiffness(stiff, i, j);
stiff.scale(JxW[qp]);
#if DT
res.scale(dt);
#endif
#if INERTIA
stiff.scale(dt);
Kua(i,j)+= rho_s*JxW[qp]*phi[i][qp]*phi[j][qp];
Kvb(i,j)+= rho_s*JxW[qp]*phi[i][qp]*phi[j][qp];
Kwc(i,j)+= rho_s*JxW[qp]*phi[i][qp]*phi[j][qp];
Kau(i,j)+= JxW[qp]*phi[i][qp]*phi[j][qp];
Kbv(i,j)+= JxW[qp]*phi[i][qp]*phi[j][qp];
Kcw(i,j)+= JxW[qp]*phi[i][qp]*phi[j][qp];
Kaa(i,j)+= -dt*JxW[qp]*phi[i][qp]*phi[j][qp];
Kbb(i,j)+= -dt*JxW[qp]*phi[i][qp]*phi[j][qp];
Kcc(i,j)+= -dt*JxW[qp]*phi[i][qp]*phi[j][qp];
#endif
Kuu(i,j)+= stiff(u_var, u_var);
Kuv(i,j)+= stiff(u_var, v_var);
Kuw(i,j)+= stiff(u_var, w_var);
Kvu(i,j)+= stiff(v_var, u_var);
Kvv(i,j)+= stiff(v_var, v_var);
Kvw(i,j)+= stiff(v_var, w_var);
Kwu(i,j)+= stiff(w_var, u_var);
Kwv(i,j)+= stiff(w_var, v_var);
Kww(i,j)+= stiff(w_var, w_var);
#if GRAVITY
Kuu(i,j)+= 1*JxW[qp]*phi[i][qp]*phi[j][qp];
#endif
}
}
#if INCOMPRESSIBLE && FLUID_P_CONST
for (unsigned int i = 0; i < n_p_dofs; i++) {
material.get_p_residual(p_res, i);
p_res.scale(JxW[qp]);
Fp(i) += p_res(0);
}
for (unsigned int i = 0; i < n_u_dofs; i++) {
for (unsigned int j = 0; j < n_p_dofs; j++) {
material.get_linearized_uvw_p_stiffness(p_stiff, i, j);
p_stiff.scale(JxW[qp]);
Kup(i, j) += p_stiff(0);
Kvp(i, j) += p_stiff(1);
Kwp(i, j) += p_stiff(2);
}
}
for (unsigned int i = 0; i < n_p_dofs; i++) {
for (unsigned int j = 0; j < n_u_dofs; j++) {
material.get_linearized_p_uvw_stiffness(p_stiff, i, j);
p_stiff.scale(JxW[qp]);
Kpu(i, j) += p_stiff(0);
Kpv(i, j) += p_stiff(1);
Kpw(i, j) += p_stiff(2);
}
}
#endif
#if CHAP && ! FLUID_P_CONST
for (unsigned int i = 0; i < n_p_dofs; i++) {
Fp(i) += 0*JxW[qp]*psi[i][qp];
}
for (unsigned int i = 0; i < n_p_dofs; i++) {
for (unsigned int j = 0; j < n_p_dofs; j++) {
Kpp(i, j) += 1*JxW[qp]*psi[i][qp]*psi[j][qp];
}
}
#endif
}//end of qp loop
newton_update.matrix->add_matrix (Ke, dof_indices);
newton_update.rhs->add_vector (Fe, dof_indices);
} // end of element loop
// dof_map.constrain_element_matrix_and_vector (Ke, Fe, dof_indices);
newton_update.rhs->close();
newton_update.matrix->close();
#if LOG_ASSEMBLE_PERFORMANCE
perf_log.pop("assemble stiffness");
#endif
#if LOG_ASSEMBLE_PERFORMANCE
perf_log.push("assemble bcs");
#endif
//Assemble the boundary conditions.
assemble_bcs(es);
#if LOG_ASSEMBLE_PERFORMANCE
perf_log.pop("assemble bcs");
#endif
std::ofstream lhs_out("lhsoutS3.dat");
Ke.print(lhs_out);
lhs_out.close();
return;
}