int main(int argc, char * argv[])
{
int * i = &argc;
Fu((*i)).print(); // gets bogus error
Fu((*j));
}
void uhfsolve::setupF(){
//set up the Fock matrix
double Di = 0;
double Ex = 0;
double DiMinusEx = 0;
for(int p=0;p<nStates;p++){
for(int q=0;q<nStates;q++){
//F(p,q) = Bs.h(p,q);
Fu(p,q) = Bs.h(p,q);
Fd(p,q) = Bs.h(p,q);
for(int r=0;r<nStates;r++){
for(int s=0;s<nStates;s++){
//Di = Bs.v(p,r)(q,s);
//Ex = Bs.v(p,r)(s,q);
Di = Bs.v(p,q)(r,s);
Ex = Bs.v(p,s)(r,q);
DiMinusEx = Di-Ex;
//F(p,q) += 0.5*coupledMatrixTilde(p,q,r,s)*P(r,s); //Alt. 2 27/5 2014
Fu(p,q) += Pu(s,r)*(Di-Ex) + Pd(s,r)*Di;
Fd(p,q) += Pd(s,r)*(Di-Ex) + Pu(s,r)*Di;
}
}
}
}
}
void d_toe2full(finteger N,fdouble *to,fdouble *fu,finteger *ld)
/* converts a toeplitz matrix a into a full matrix fu */
{
finteger i;
static finteger inc1=1;
#define Fu(I,J) fu[(I) + (J) * (*ld)]
for(i=0;i<N;i++)
F77CALL (dcopy) (&N,&to[-i],&inc1,&Fu(0,i),&inc1);
#undef Fu
}
bool FEMPhysics::mass_residual (bool request_jacobian,
DiffContext & c)
{
FEMContext & context = cast_ref<FEMContext &>(c);
unsigned int n_qpoints = context.get_element_qrule().n_points();
for (unsigned int var = 0; var != context.n_vars(); ++var)
{
if (!this->is_time_evolving(var))
continue;
FEBase * elem_fe = libmesh_nullptr;
context.get_element_fe( var, elem_fe );
const std::vector<Real> & JxW = elem_fe->get_JxW();
const std::vector<std::vector<Real> > & phi = elem_fe->get_phi();
const unsigned int n_dofs = cast_int<unsigned int>
(context.get_dof_indices(var).size());
DenseSubVector<Number> & Fu = context.get_elem_residual(var);
DenseSubMatrix<Number> & Kuu = context.get_elem_jacobian( var, var );
for (unsigned int qp = 0; qp != n_qpoints; ++qp)
{
Number uprime;
context.interior_rate(var, qp, uprime);
const Number JxWxU = JxW[qp] * uprime;
for (unsigned int i = 0; i != n_dofs; ++i)
{
Fu(i) -= JxWxU * phi[i][qp];
if (request_jacobian && context.elem_solution_rate_derivative)
{
const Number JxWxPhiIxDeriv = JxW[qp] * phi[i][qp] *
context.elem_solution_rate_derivative;
Kuu(i,i) -= JxWxPhiIxDeriv * phi[i][qp];
for (unsigned int j = i+1; j < n_dofs; ++j)
{
const Number Kij = JxWxPhiIxDeriv * phi[j][qp];
Kuu(i,j) -= Kij;
Kuu(j,i) -= Kij;
}
}
}
}
}
return request_jacobian;
}
bool FEMPhysics::mass_residual (bool request_jacobian,
DiffContext &c)
{
FEMContext &context = libmesh_cast_ref<FEMContext&>(c);
unsigned int n_qpoints = (context.get_element_qrule())->n_points();
for (unsigned int var = 0; var != context.n_vars(); ++var)
{
if (!this->is_time_evolving(var))
continue;
const std::vector<Real> &JxW =
context.element_fe_var[var]->get_JxW();
const std::vector<std::vector<Real> > &phi =
context.element_fe_var[var]->get_phi();
const unsigned int n_dofs = context.dof_indices_var[var].size();
DenseSubVector<Number> &Fu = *context.elem_subresiduals[var];
DenseSubMatrix<Number> &Kuu = *context.elem_subjacobians[var][var];
for (unsigned int qp = 0; qp != n_qpoints; ++qp)
{
Number u = context.interior_value(var, qp);
Number JxWxU = JxW[qp] * u;
for (unsigned int i = 0; i != n_dofs; ++i)
{
Fu(i) += JxWxU * phi[i][qp];
if (request_jacobian && context.elem_solution_derivative)
{
libmesh_assert_equal_to (context.elem_solution_derivative, 1.0);
Number JxWxPhiI = JxW[qp] * phi[i][qp];
Kuu(i,i) += JxWxPhiI * phi[i][qp];
for (unsigned int j = i+1; j < n_dofs; ++j)
{
Number Kij = JxWxPhiI * phi[j][qp];
Kuu(i,j) += Kij;
Kuu(j,i) += Kij;
}
}
}
}
}
return request_jacobian;
}
void AveragedTurbine<Mu>::element_time_derivative( bool compute_jacobian,
AssemblyContext& context,
CachedValues& /* cache */ )
{
#ifdef GRINS_USE_GRVY_TIMERS
this->_timer->BeginTimer("AveragedTurbine::element_time_derivative");
#endif
// Element Jacobian * quadrature weights for interior integration
const std::vector<libMesh::Real> &JxW =
context.get_element_fe(this->_flow_vars.u())->get_JxW();
// The shape functions at interior quadrature points.
const std::vector<std::vector<libMesh::Real> >& u_phi =
context.get_element_fe(this->_flow_vars.u())->get_phi();
const std::vector<libMesh::Point>& u_qpoint =
context.get_element_fe(this->_flow_vars.u())->get_xyz();
// The number of local degrees of freedom in each variable
const unsigned int n_u_dofs = context.get_dof_indices(this->_flow_vars.u()).size();
// The subvectors and submatrices we need to fill:
libMesh::DenseSubMatrix<libMesh::Number> &Kuu = context.get_elem_jacobian(this->_flow_vars.u(), this->_flow_vars.u()); // R_{u},{u}
libMesh::DenseSubMatrix<libMesh::Number> &Kuv = context.get_elem_jacobian(this->_flow_vars.u(), this->_flow_vars.v()); // R_{u},{v}
libMesh::DenseSubMatrix<libMesh::Number> &Kvu = context.get_elem_jacobian(this->_flow_vars.v(), this->_flow_vars.u()); // R_{v},{u}
libMesh::DenseSubMatrix<libMesh::Number> &Kvv = context.get_elem_jacobian(this->_flow_vars.v(), this->_flow_vars.v()); // R_{v},{v}
libMesh::DenseSubMatrix<libMesh::Number> &Kus =
context.get_elem_jacobian(this->_flow_vars.u(),
this->fan_speed_var()); // R_{u},{s}
libMesh::DenseSubMatrix<libMesh::Number> &Ksu =
context.get_elem_jacobian(this->fan_speed_var(),
this->_flow_vars.u()); // R_{s},{u}
libMesh::DenseSubMatrix<libMesh::Number> &Kvs =
context.get_elem_jacobian(this->_flow_vars.v(),
this->fan_speed_var()); // R_{v},{s}
libMesh::DenseSubMatrix<libMesh::Number> &Ksv =
context.get_elem_jacobian(this->fan_speed_var(),
this->_flow_vars.v()); // R_{s},{v}
libMesh::DenseSubMatrix<libMesh::Number> &Kss =
context.get_elem_jacobian(this->fan_speed_var(),
this->fan_speed_var()); // R_{s},{s}
libMesh::DenseSubMatrix<libMesh::Number>* Kwu = NULL;
libMesh::DenseSubMatrix<libMesh::Number>* Kwv = NULL;
libMesh::DenseSubMatrix<libMesh::Number>* Kww = NULL;
libMesh::DenseSubMatrix<libMesh::Number>* Kuw = NULL;
libMesh::DenseSubMatrix<libMesh::Number>* Kvw = NULL;
libMesh::DenseSubMatrix<libMesh::Number>* Ksw = NULL;
libMesh::DenseSubMatrix<libMesh::Number>* Kws = NULL;
libMesh::DenseSubVector<libMesh::Number> &Fu = context.get_elem_residual(this->_flow_vars.u()); // R_{u}
libMesh::DenseSubVector<libMesh::Number> &Fv = context.get_elem_residual(this->_flow_vars.v()); // R_{v}
libMesh::DenseSubVector<libMesh::Number>* Fw = NULL;
libMesh::DenseSubVector<libMesh::Number> &Fs = context.get_elem_residual(this->fan_speed_var()); // R_{s}
if( this->mesh_dim(context) == 3 )
{
Kuw = &context.get_elem_jacobian(this->_flow_vars.u(), this->_flow_vars.w()); // R_{u},{w}
Kvw = &context.get_elem_jacobian(this->_flow_vars.v(), this->_flow_vars.w()); // R_{v},{w}
Kwu = &context.get_elem_jacobian(this->_flow_vars.w(), this->_flow_vars.u()); // R_{w},{u}
Kwv = &context.get_elem_jacobian(this->_flow_vars.w(), this->_flow_vars.v()); // R_{w},{v}
Kww = &context.get_elem_jacobian(this->_flow_vars.w(), this->_flow_vars.w()); // R_{w},{w}
Fw = &context.get_elem_residual(this->_flow_vars.w()); // R_{w}
Ksw = &context.get_elem_jacobian(this->fan_speed_var(), this->_flow_vars.w()); // R_{s},{w}
Kws = &context.get_elem_jacobian(this->_flow_vars.w(), this->fan_speed_var()); // R_{w},{s}
Fw = &context.get_elem_residual(this->_flow_vars.w()); // R_{w}
}
unsigned int n_qpoints = context.get_element_qrule().n_points();
for (unsigned int qp=0; qp != n_qpoints; qp++)
{
// Compute the solution at the old Newton iterate.
libMesh::Number u, v, s;
u = context.interior_value(this->_flow_vars.u(), qp);
v = context.interior_value(this->_flow_vars.v(), qp);
s = context.interior_value(this->fan_speed_var(), qp);
libMesh::NumberVectorValue U(u,v);
if (this->mesh_dim(context) == 3)
U(2) = context.interior_value(this->_flow_vars.w(), qp); // w
libMesh::NumberVectorValue U_B_1;
libMesh::NumberVectorValue F;
libMesh::NumberTensorValue dFdU;
libMesh::NumberTensorValue* dFdU_ptr =
compute_jacobian ? &dFdU : NULL;
libMesh::NumberVectorValue dFds;
libMesh::NumberVectorValue* dFds_ptr =
compute_jacobian ? &dFds : NULL;
if (!this->compute_force(u_qpoint[qp], context.time, U, s,
U_B_1, F, dFdU_ptr, dFds_ptr))
continue;
libMesh::Real jac = JxW[qp];
// Using this dot product to derive torque *depends* on s=1
// and U_B_1 corresponding to 1 rad/sec base velocity; this
// means that the length of U_B_1 is equal to radius.
// F is the force on the air, so *negative* F is the force on
// the turbine.
Fs(0) -= U_B_1 * F * jac;
if (compute_jacobian)
{
Kss(0,0) -= U_B_1 * dFds * jac;
for (unsigned int j=0; j != n_u_dofs; j++)
{
libMesh::Real jac_j = JxW[qp] * u_phi[j][qp];
for (unsigned int d=0; d != 3; ++d)
{
Ksu(0,j) -= jac_j * U_B_1(d) * dFdU(d,0);
Ksv(0,j) -= jac_j * U_B_1(d) * dFdU(d,1);
}
if (this->mesh_dim(context) == 3)
{
for (unsigned int d=0; d != 3; ++d)
(*Ksw)(0,j) -= jac_j * U_B_1(d) * dFdU(d,2);
}
} // End j dof loop
}
for (unsigned int i=0; i != n_u_dofs; i++)
{
const libMesh::Number jac_i = jac * u_phi[i][qp];
Fu(i) += F(0)*jac_i;
Fv(i) += F(1)*jac_i;
if( this->mesh_dim(context) == 3 )
(*Fw)(i) += F(2)*jac_i;
if( compute_jacobian )
{
Kus(i,0) += dFds(0) * jac_i;
Kvs(i,0) += dFds(1) * jac_i;
if( this->mesh_dim(context) == 3 )
(*Kws)(i,0) += dFds(2) * jac_i;
for (unsigned int j=0; j != n_u_dofs; j++)
{
const libMesh::Number jac_ij = jac_i * u_phi[j][qp];
Kuu(i,j) += jac_ij * dFdU(0,0);
Kuv(i,j) += jac_ij * dFdU(0,1);
Kvu(i,j) += jac_ij * dFdU(1,0);
Kvv(i,j) += jac_ij * dFdU(1,1);
if( this->mesh_dim(context) == 3 )
{
(*Kuw)(i,j) += jac_ij * dFdU(0,2);
(*Kvw)(i,j) += jac_ij * dFdU(1,2);
(*Kwu)(i,j) += jac_ij * dFdU(2,0);
(*Kwv)(i,j) += jac_ij * dFdU(2,1);
(*Kww)(i,j) += jac_ij * dFdU(2,2);
}
}
}
}
}
#ifdef GRINS_USE_GRVY_TIMERS
this->_timer->EndTimer("AveragedTurbine::element_time_derivative");
#endif
return;
}
void LowMachNavierStokes<Mu,SH,TC>::assemble_momentum_time_deriv( bool /*compute_jacobian*/,
AssemblyContext& context,
CachedValues& cache )
{
// The number of local degrees of freedom in each variable.
const unsigned int n_u_dofs = context.get_dof_indices(this->_u_var).size();
// Check number of dofs is same for _u_var, v_var and w_var.
libmesh_assert (n_u_dofs == context.get_dof_indices(this->_v_var).size());
if (this->_dim == 3)
libmesh_assert (n_u_dofs == context.get_dof_indices(this->_w_var).size());
// Element Jacobian * quadrature weights for interior integration.
const std::vector<libMesh::Real> &JxW =
context.get_element_fe(this->_u_var)->get_JxW();
// The pressure shape functions at interior quadrature points.
const std::vector<std::vector<libMesh::Real> >& u_phi =
context.get_element_fe(this->_u_var)->get_phi();
// The velocity shape function gradients at interior quadrature points.
const std::vector<std::vector<libMesh::RealGradient> >& u_gradphi =
context.get_element_fe(this->_u_var)->get_dphi();
libMesh::DenseSubVector<libMesh::Number> &Fu = context.get_elem_residual(this->_u_var); // R_{u}
libMesh::DenseSubVector<libMesh::Number> &Fv = context.get_elem_residual(this->_v_var); // R_{v}
libMesh::DenseSubVector<libMesh::Number> &Fw = context.get_elem_residual(this->_w_var); // R_{w}
unsigned int n_qpoints = context.get_element_qrule().n_points();
for (unsigned int qp=0; qp != n_qpoints; qp++)
{
libMesh::Number u, v, p, p0, T;
u = cache.get_cached_values(Cache::X_VELOCITY)[qp];
v = cache.get_cached_values(Cache::Y_VELOCITY)[qp];
T = cache.get_cached_values(Cache::TEMPERATURE)[qp];
p = cache.get_cached_values(Cache::PRESSURE)[qp];
p0 = cache.get_cached_values(Cache::THERMO_PRESSURE)[qp];
libMesh::Gradient grad_u = cache.get_cached_gradient_values(Cache::X_VELOCITY_GRAD)[qp];
libMesh::Gradient grad_v = cache.get_cached_gradient_values(Cache::Y_VELOCITY_GRAD)[qp];
libMesh::Gradient grad_w;
if (this->_dim == 3)
grad_w = cache.get_cached_gradient_values(Cache::Z_VELOCITY_GRAD)[qp];
libMesh::NumberVectorValue grad_uT( grad_u(0), grad_v(0) );
libMesh::NumberVectorValue grad_vT( grad_u(1), grad_v(1) );
libMesh::NumberVectorValue grad_wT;
if( this->_dim == 3 )
{
grad_uT(2) = grad_w(0);
grad_vT(2) = grad_w(1);
grad_wT = libMesh::NumberVectorValue( grad_u(2), grad_v(2), grad_w(2) );
}
libMesh::NumberVectorValue U(u,v);
if (this->_dim == 3)
U(2) = cache.get_cached_values(Cache::Z_VELOCITY)[qp]; // w
libMesh::Number divU = grad_u(0) + grad_v(1);
if (this->_dim == 3)
divU += grad_w(2);
libMesh::Number rho = this->rho( T, p0 );
// Now a loop over the pressure degrees of freedom. This
// computes the contributions of the continuity equation.
for (unsigned int i=0; i != n_u_dofs; i++)
{
Fu(i) += ( -rho*U*grad_u*u_phi[i][qp] // convection term
+ p*u_gradphi[i][qp](0) // pressure term
- this->_mu(T)*(u_gradphi[i][qp]*grad_u + u_gradphi[i][qp]*grad_uT
- 2.0/3.0*divU*u_gradphi[i][qp](0) ) // diffusion term
+ rho*this->_g(0)*u_phi[i][qp] // hydrostatic term
)*JxW[qp];
Fv(i) += ( -rho*U*grad_v*u_phi[i][qp] // convection term
+ p*u_gradphi[i][qp](1) // pressure term
- this->_mu(T)*(u_gradphi[i][qp]*grad_v + u_gradphi[i][qp]*grad_vT
- 2.0/3.0*divU*u_gradphi[i][qp](1) ) // diffusion term
+ rho*this->_g(1)*u_phi[i][qp] // hydrostatic term
)*JxW[qp];
if (this->_dim == 3)
{
Fw(i) += ( -rho*U*grad_w*u_phi[i][qp] // convection term
+ p*u_gradphi[i][qp](2) // pressure term
- this->_mu(T)*(u_gradphi[i][qp]*grad_w + u_gradphi[i][qp]*grad_wT
- 2.0/3.0*divU*u_gradphi[i][qp](2) ) // diffusion term
+ rho*this->_g(2)*u_phi[i][qp] // hydrostatic term
)*JxW[qp];
}
/*
if (compute_jacobian && context.get_elem_solution_derivative())
{
libmesh_assert (context.get_elem_solution_derivative() == 1.0);
for (unsigned int j=0; j != n_u_dofs; j++)
{
// TODO: precompute some terms like:
// (Uvec*vel_gblgradphivec[j][qp]),
// vel_phi[i][qp]*vel_phi[j][qp],
// (vel_gblgradphivec[i][qp]*vel_gblgradphivec[j][qp])
Kuu(i,j) += JxW[qp] *
(-_rho*vel_phi[i][qp]*(Uvec*vel_gblgradphivec[j][qp]) // convection term
-_rho*vel_phi[i][qp]*graduvec_x*vel_phi[j][qp] // convection term
-_mu*(vel_gblgradphivec[i][qp]*vel_gblgradphivec[j][qp])); // diffusion term
Kuv(i,j) += JxW[qp] *
(-_rho*vel_phi[i][qp]*graduvec_y*vel_phi[j][qp]); // convection term
Kvv(i,j) += JxW[qp] *
(-_rho*vel_phi[i][qp]*(Uvec*vel_gblgradphivec[j][qp]) // convection term
-_rho*vel_phi[i][qp]*gradvvec_y*vel_phi[j][qp] // convection term
-_mu*(vel_gblgradphivec[i][qp]*vel_gblgradphivec[j][qp])); // diffusion term
Kvu(i,j) += JxW[qp] *
(-_rho*vel_phi[i][qp]*gradvvec_x*vel_phi[j][qp]); // convection term
if (_dim == 3)
{
Kuw(i,j) += JxW[qp] *
(-_rho*vel_phi[i][qp]*graduvec_z*vel_phi[j][qp]); // convection term
Kvw(i,j) += JxW[qp] *
(-_rho*vel_phi[i][qp]*gradvvec_z*vel_phi[j][qp]); // convection term
Kww(i,j) += JxW[qp] *
(-_rho*vel_phi[i][qp]*(Uvec*vel_gblgradphivec[j][qp]) // convection term
-_rho*vel_phi[i][qp]*gradwvec_z*vel_phi[j][qp] // convection term
-_mu*(vel_gblgradphivec[i][qp]*vel_gblgradphivec[j][qp])); // diffusion term
Kwu(i,j) += JxW[qp] *
(-_rho*vel_phi[i][qp]*gradwvec_x*vel_phi[j][qp]); // convection term
Kwv(i,j) += JxW[qp] *
(-_rho*vel_phi[i][qp]*gradwvec_y*vel_phi[j][qp]); // convection term
}
} // end of the inner dof (j) loop
// Matrix contributions for the up, vp and wp couplings
for (unsigned int j=0; j != n_p_dofs; j++)
{
Kup(i,j) += JxW[qp]*vel_gblgradphivec[i][qp](0)*p_phi[j][qp];
Kvp(i,j) += JxW[qp]*vel_gblgradphivec[i][qp](1)*p_phi[j][qp];
if (_dim == 3)
Kwp(i,j) += JxW[qp]*vel_gblgradphivec[i][qp](2)*p_phi[j][qp];
} // end of the inner dof (j) loop
} // end - if (compute_jacobian && context.get_elem_solution_derivative())
} // end of the outer dof (i) loop
} // end of the quadrature point (qp) loop
*/
} // End of DoF loop i
} // End quadrature loop qp
return;
}
bool FEMPhysics::eulerian_residual (bool request_jacobian,
DiffContext &/*c*/)
{
// Only calculate a mesh movement residual if it's necessary
if (!_mesh_sys)
return request_jacobian;
libmesh_not_implemented();
#if 0
FEMContext &context = libmesh_cast_ref<FEMContext&>(c);
// This function only supports fully coupled mesh motion for now
libmesh_assert_equal_to (_mesh_sys, this);
unsigned int n_qpoints = (context.get_element_qrule())->n_points();
const unsigned int n_x_dofs = (_mesh_x_var == libMesh::invalid_uint) ?
0 : context.dof_indices_var[_mesh_x_var].size();
const unsigned int n_y_dofs = (_mesh_y_var == libMesh::invalid_uint) ?
0 : context.dof_indices_var[_mesh_y_var].size();
const unsigned int n_z_dofs = (_mesh_z_var == libMesh::invalid_uint) ?
0 : context.dof_indices_var[_mesh_z_var].size();
const unsigned int mesh_xyz_var = n_x_dofs ? _mesh_x_var :
(n_y_dofs ? _mesh_y_var :
(n_z_dofs ? _mesh_z_var :
libMesh::invalid_uint));
// If we're our own _mesh_sys, we'd better be in charge of
// at least one coordinate, and we'd better have the same
// FE type for all coordinates we are in charge of
libmesh_assert_not_equal_to (mesh_xyz_var, libMesh::invalid_uint);
libmesh_assert(!n_x_dofs || context.element_fe_var[_mesh_x_var] ==
context.element_fe_var[mesh_xyz_var]);
libmesh_assert(!n_y_dofs || context.element_fe_var[_mesh_y_var] ==
context.element_fe_var[mesh_xyz_var]);
libmesh_assert(!n_z_dofs || context.element_fe_var[_mesh_z_var] ==
context.element_fe_var[mesh_xyz_var]);
const std::vector<std::vector<Real> > &psi =
context.element_fe_var[mesh_xyz_var]->get_phi();
for (unsigned int var = 0; var != context.n_vars(); ++var)
{
// Mesh motion only affects time-evolving variables
if (this->is_time_evolving(var))
continue;
// The mesh coordinate variables themselves are Lagrangian,
// not Eulerian, and no convective term is desired.
if (/*_mesh_sys == this && */
(var == _mesh_x_var ||
var == _mesh_y_var ||
var == _mesh_z_var))
continue;
// Some of this code currently relies on the assumption that
// we can pull mesh coordinate data from our own system
if (_mesh_sys != this)
libmesh_not_implemented();
// This residual should only be called by unsteady solvers:
// if the mesh is steady, there's no mesh convection term!
UnsteadySolver *unsteady;
if (this->time_solver->is_steady())
return request_jacobian;
else
unsteady = libmesh_cast_ptr<UnsteadySolver*>(this->time_solver.get());
const std::vector<Real> &JxW =
context.element_fe_var[var]->get_JxW();
const std::vector<std::vector<Real> > &phi =
context.element_fe_var[var]->get_phi();
const std::vector<std::vector<RealGradient> > &dphi =
context.element_fe_var[var]->get_dphi();
const unsigned int n_u_dofs = context.dof_indices_var[var].size();
DenseSubVector<Number> &Fu = *context.elem_subresiduals[var];
DenseSubMatrix<Number> &Kuu = *context.elem_subjacobians[var][var];
DenseSubMatrix<Number> *Kux = n_x_dofs ?
context.elem_subjacobians[var][_mesh_x_var] : NULL;
DenseSubMatrix<Number> *Kuy = n_y_dofs ?
context.elem_subjacobians[var][_mesh_y_var] : NULL;
DenseSubMatrix<Number> *Kuz = n_z_dofs ?
context.elem_subjacobians[var][_mesh_z_var] : NULL;
std::vector<Real> delta_x(n_x_dofs, 0.);
std::vector<Real> delta_y(n_y_dofs, 0.);
std::vector<Real> delta_z(n_z_dofs, 0.);
for (unsigned int i = 0; i != n_x_dofs; ++i)
{
unsigned int j = context.dof_indices_var[_mesh_x_var][i];
delta_x[i] = libmesh_real(this->current_solution(j)) -
libmesh_real(unsteady->old_nonlinear_solution(j));
}
for (unsigned int i = 0; i != n_y_dofs; ++i)
{
unsigned int j = context.dof_indices_var[_mesh_y_var][i];
delta_y[i] = libmesh_real(this->current_solution(j)) -
libmesh_real(unsteady->old_nonlinear_solution(j));
}
for (unsigned int i = 0; i != n_z_dofs; ++i)
{
unsigned int j = context.dof_indices_var[_mesh_z_var][i];
delta_z[i] = libmesh_real(this->current_solution(j)) -
libmesh_real(unsteady->old_nonlinear_solution(j));
}
for (unsigned int qp = 0; qp != n_qpoints; ++qp)
{
Gradient grad_u = context.interior_gradient(var, qp);
RealGradient convection(0.);
for (unsigned int i = 0; i != n_x_dofs; ++i)
convection(0) += delta_x[i] * psi[i][qp];
for (unsigned int i = 0; i != n_y_dofs; ++i)
convection(1) += delta_y[i] * psi[i][qp];
for (unsigned int i = 0; i != n_z_dofs; ++i)
convection(2) += delta_z[i] * psi[i][qp];
for (unsigned int i = 0; i != n_u_dofs; ++i)
{
Number JxWxPhiI = JxW[qp] * phi[i][qp];
Fu(i) += (convection * grad_u) * JxWxPhiI;
if (request_jacobian)
{
Number JxWxPhiI = JxW[qp] * phi[i][qp];
for (unsigned int j = 0; j != n_u_dofs; ++j)
Kuu(i,j) += JxWxPhiI * (convection * dphi[j][qp]);
Number JxWxPhiIoverDT = JxWxPhiI/this->deltat;
Number JxWxPhiIxDUDXoverDT = JxWxPhiIoverDT * grad_u(0);
for (unsigned int j = 0; j != n_x_dofs; ++j)
(*Kux)(i,j) += JxWxPhiIxDUDXoverDT * psi[j][qp];
Number JxWxPhiIxDUDYoverDT = JxWxPhiIoverDT * grad_u(1);
for (unsigned int j = 0; j != n_y_dofs; ++j)
(*Kuy)(i,j) += JxWxPhiIxDUDYoverDT * psi[j][qp];
Number JxWxPhiIxDUDZoverDT = JxWxPhiIoverDT * grad_u(2);
for (unsigned int j = 0; j != n_z_dofs; ++j)
(*Kuz)(i,j) += JxWxPhiIxDUDZoverDT * psi[j][qp];
}
}
}
}
#endif // 0
return request_jacobian;
}
void assemble_postvars_rhs (EquationSystems& es,
const std::string& system_name)
{
const Real E = es.parameters.get<Real>("E");
const Real NU = es.parameters.get<Real>("NU");
const Real KPERM = es.parameters.get<Real>("KPERM");
Real sum_jac_postvars=0;
Real av_pressure=0;
Real total_volume=0;
#include "assemble_preamble_postvars.cpp"
for ( ; el != end_el; ++el)
{
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_p, p_var);
dof_map.dof_indices (elem, dof_indices_x, x_var);
dof_map.dof_indices (elem, dof_indices_y, y_var);
#if THREED
dof_map.dof_indices (elem, dof_indices_w, w_var);
dof_map.dof_indices (elem, dof_indices_z, z_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_p_dofs = dof_indices_p.size();
const unsigned int n_x_dofs = dof_indices_x.size();
const unsigned int n_y_dofs = dof_indices_y.size();
#if THREED
const unsigned int n_w_dofs = dof_indices_w.size();
const unsigned int n_z_dofs = dof_indices_z.size();
#endif
fe_disp->reinit (elem);
fe_vel->reinit (elem);
fe_pres->reinit (elem);
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);
Kup.reposition (u_var*n_u_dofs, p_var*n_u_dofs, n_u_dofs, n_p_dofs);
Kux.reposition (u_var*n_u_dofs, p_var*n_u_dofs + n_p_dofs , n_u_dofs, n_x_dofs);
Kuy.reposition (u_var*n_u_dofs, p_var*n_u_dofs + n_p_dofs+n_x_dofs , n_u_dofs, n_y_dofs);
#if THREED
Kuw.reposition (u_var*n_u_dofs, w_var*n_u_dofs, n_u_dofs, n_w_dofs);
Kuz.reposition (u_var*n_u_dofs, p_var*n_u_dofs + n_p_dofs+2*n_x_dofs , n_u_dofs, n_z_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);
Kvp.reposition (v_var*n_v_dofs, p_var*n_v_dofs, n_v_dofs, n_p_dofs);
Kvx.reposition (v_var*n_v_dofs, p_var*n_u_dofs + n_p_dofs , n_v_dofs, n_x_dofs);
Kvy.reposition (v_var*n_v_dofs, p_var*n_u_dofs + n_p_dofs+n_x_dofs , n_v_dofs, n_y_dofs);
#if THREED
Kvw.reposition (v_var*n_u_dofs, w_var*n_u_dofs, n_v_dofs, n_w_dofs);
Kuz.reposition (v_var*n_u_dofs, p_var*n_u_dofs + n_p_dofs+2*n_x_dofs , n_u_dofs, n_z_dofs);
#endif
#if THREED
Kwu.reposition (w_var*n_w_dofs, u_var*n_v_dofs, n_v_dofs, n_u_dofs);
Kwv.reposition (w_var*n_w_dofs, v_var*n_v_dofs, n_v_dofs, n_v_dofs);
Kwp.reposition (w_var*n_w_dofs, p_var*n_v_dofs, n_v_dofs, n_p_dofs);
Kwx.reposition (w_var*n_w_dofs, p_var*n_u_dofs + n_p_dofs , n_v_dofs, n_x_dofs);
Kwy.reposition (w_var*n_w_dofs, p_var*n_u_dofs + n_p_dofs+n_x_dofs , n_v_dofs, n_y_dofs);
Kww.reposition (w_var*n_w_dofs, w_var*n_u_dofs, n_v_dofs, n_w_dofs);
Kwz.reposition (w_var*n_w_dofs, p_var*n_u_dofs + n_p_dofs+2*n_x_dofs , n_u_dofs, n_z_dofs);
#endif
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);
Kpp.reposition (p_var*n_u_dofs, p_var*n_u_dofs, n_p_dofs, n_p_dofs);
Kpx.reposition (p_var*n_v_dofs, p_var*n_u_dofs + n_p_dofs , n_p_dofs, n_x_dofs);
Kpy.reposition (p_var*n_v_dofs, p_var*n_u_dofs + n_p_dofs+n_x_dofs , n_p_dofs, n_y_dofs);
#if THREED
Kpw.reposition (p_var*n_u_dofs, w_var*n_u_dofs, n_p_dofs, n_w_dofs);
Kpz.reposition (p_var*n_u_dofs, p_var*n_u_dofs + n_p_dofs+2*n_x_dofs , n_p_dofs, n_z_dofs);
#endif
Kxu.reposition (p_var*n_u_dofs + n_p_dofs, u_var*n_u_dofs, n_x_dofs, n_u_dofs);
Kxv.reposition (p_var*n_u_dofs + n_p_dofs, v_var*n_u_dofs, n_x_dofs, n_v_dofs);
Kxp.reposition (p_var*n_u_dofs + n_p_dofs, p_var*n_u_dofs, n_x_dofs, n_p_dofs);
Kxx.reposition (p_var*n_u_dofs + n_p_dofs, p_var*n_u_dofs + n_p_dofs , n_x_dofs, n_x_dofs);
Kxy.reposition (p_var*n_u_dofs + n_p_dofs, p_var*n_u_dofs + n_p_dofs+n_x_dofs , n_x_dofs, n_y_dofs);
#if THREED
Kxw.reposition (p_var*n_u_dofs + n_p_dofs, w_var*n_u_dofs, n_x_dofs, n_w_dofs);
Kxz.reposition (p_var*n_u_dofs + n_p_dofs, p_var*n_u_dofs + n_p_dofs+2*n_x_dofs , n_x_dofs, n_z_dofs);
#endif
Kyu.reposition (p_var*n_u_dofs + n_p_dofs+n_x_dofs, u_var*n_u_dofs, n_y_dofs, n_u_dofs);
Kyv.reposition (p_var*n_u_dofs + n_p_dofs+n_x_dofs, v_var*n_u_dofs, n_y_dofs, n_v_dofs);
Kyp.reposition (p_var*n_u_dofs + n_p_dofs+n_x_dofs, p_var*n_u_dofs, n_y_dofs, n_p_dofs);
Kyx.reposition (p_var*n_u_dofs + n_p_dofs+n_x_dofs, p_var*n_u_dofs + n_p_dofs , n_y_dofs, n_x_dofs);
Kyy.reposition (p_var*n_u_dofs + n_p_dofs+n_x_dofs, p_var*n_u_dofs + n_p_dofs+n_x_dofs , n_y_dofs, n_y_dofs);
#if THREED
Kyw.reposition (p_var*n_u_dofs + n_p_dofs+n_x_dofs, w_var*n_u_dofs, n_x_dofs, n_w_dofs);
Kyz.reposition (p_var*n_u_dofs + n_p_dofs+n_x_dofs, p_var*n_u_dofs + n_p_dofs+2*n_x_dofs , n_x_dofs, n_z_dofs);
#endif
#if THREED
Kzu.reposition (p_var*n_u_dofs + n_p_dofs+2*n_x_dofs, u_var*n_u_dofs, n_y_dofs, n_u_dofs);
Kzv.reposition (p_var*n_u_dofs + n_p_dofs+2*n_x_dofs, v_var*n_u_dofs, n_y_dofs, n_v_dofs);
Kzp.reposition (p_var*n_u_dofs + n_p_dofs+2*n_x_dofs, p_var*n_u_dofs, n_y_dofs, n_p_dofs);
Kzx.reposition (p_var*n_u_dofs + n_p_dofs+2*n_x_dofs, p_var*n_u_dofs + n_p_dofs , n_y_dofs, n_x_dofs);
Kzy.reposition (p_var*n_u_dofs + n_p_dofs+2*n_x_dofs, p_var*n_u_dofs + n_p_dofs+n_x_dofs , n_y_dofs, n_y_dofs);
Kzw.reposition (p_var*n_u_dofs + n_p_dofs+2*n_x_dofs, w_var*n_u_dofs, n_x_dofs, n_w_dofs);
Kzz.reposition (p_var*n_u_dofs + n_p_dofs+2*n_x_dofs, p_var*n_u_dofs + n_p_dofs+2*n_x_dofs , n_x_dofs, n_z_dofs);
#endif
Fu.reposition (u_var*n_u_dofs, n_u_dofs);
Fv.reposition (v_var*n_u_dofs, n_v_dofs);
Fp.reposition (p_var*n_u_dofs, n_p_dofs);
Fx.reposition (p_var*n_u_dofs + n_p_dofs, n_x_dofs);
Fy.reposition (p_var*n_u_dofs + n_p_dofs+n_x_dofs, n_y_dofs);
#if THREED
Fw.reposition (w_var*n_u_dofs, n_w_dofs);
Fz.reposition (p_var*n_u_dofs + n_p_dofs+2*n_x_dofs, n_y_dofs);
#endif
std::vector<unsigned int> undefo_index;
PoroelasticConfig material(dphi,psi);
// Now we will build the element matrix.
for (unsigned int qp=0; qp<qrule.n_points(); qp++)
{
Number p_solid = 0.;
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;
std::vector<Number> u_undefo_ref;
//Fills the vector di with the global degree of freedom indices for the element. :dof_indicies
Last_non_linear_soln.get_dof_map().dof_indices(elem, undefo_index,d);
Last_non_linear_soln.current_local_solution->get(undefo_index, u_undefo);
reference.current_local_solution->get(undefo_index, u_undefo_ref);
for (unsigned int l = 0; l != n_u_dofs; l++){
grad_u_mat(d).add_scaled(dphi[l][qp], u_undefo[l]+u_undefo_ref[l]);
}
}
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]);
}
Point rX;
material.init_for_qp(rX,grad_u_mat, p_solid, qp,0, p_solid,es);
Real J=material.J;
Real I_1=material.I_1;
Real I_2=material.I_2;
Real I_3=material.I_3;
RealTensor sigma=material.sigma;
av_pressure=av_pressure + p_solid*JxW[qp];
/*
std::cout<<"grad_u_mat(0)" << grad_u_mat(0) <<std::endl;
std::cout<<" J " << J <<std::endl;
std::cout<<" sigma " << sigma <<std::endl;
*/
Real sigma_sum_sq=pow(sigma(0,0)*sigma(0,0)+sigma(0,1)*sigma(0,1)+sigma(0,2)*sigma(0,2)+sigma(1,0)*sigma(1,0)+sigma(1,1)*sigma(1,1)+sigma(1,2)*sigma(1,2)+sigma(2,0)*sigma(2,0)+sigma(2,1)*sigma(2,1)+sigma(2,2)*sigma(2,2),0.5);
// std::cout<<" J " << J <<std::endl;
sum_jac_postvars=sum_jac_postvars+JxW[qp];
for (unsigned int i=0; i<n_u_dofs; i++){
Fu(i) += I_1*JxW[qp]*phi[i][qp];
Fv(i) += I_2*JxW[qp]*phi[i][qp];
Fw(i) += I_3*JxW[qp]*phi[i][qp];
Fx(i) += sigma_sum_sq*JxW[qp]*phi[i][qp];
Fy(i) += J*JxW[qp]*phi[i][qp];
Fz(i) += 0*JxW[qp]*phi[i][qp];
}
for (unsigned int i=0; i<n_p_dofs; i++){
Fp(i) += J*JxW[qp]*psi[i][qp];
}
} // end qp
system.rhs->add_vector(Fe, dof_indices);
system.matrix->add_matrix (Ke, dof_indices);
} // end of element loop
system.matrix->close();
system.rhs->close();
std::cout<<"Assemble postvars rhs->l2_norm () "<<system.rhs->l2_norm ()<<std::endl;
std::cout<<"sum_jac "<< sum_jac_postvars <<std::endl;
std::cout<<"av_pressure "<< av_pressure/sum_jac_postvars <<std::endl;
return;
}
void ElasticMembranePressure<PressureType>::element_time_derivative
( bool compute_jacobian, AssemblyContext & context )
{
unsigned int u_var = this->_disp_vars.u();
unsigned int v_var = this->_disp_vars.v();
unsigned int w_var = this->_disp_vars.w();
const unsigned int n_u_dofs = context.get_dof_indices(u_var).size();
const std::vector<libMesh::Real> &JxW =
this->get_fe(context)->get_JxW();
const std::vector<std::vector<libMesh::Real> >& u_phi =
this->get_fe(context)->get_phi();
const MultiphysicsSystem & system = context.get_multiphysics_system();
unsigned int u_dot_var = system.get_second_order_dot_var(u_var);
unsigned int v_dot_var = system.get_second_order_dot_var(v_var);
unsigned int w_dot_var = system.get_second_order_dot_var(w_var);
libMesh::DenseSubVector<libMesh::Number> &Fu = context.get_elem_residual(u_dot_var);
libMesh::DenseSubVector<libMesh::Number> &Fv = context.get_elem_residual(v_dot_var);
libMesh::DenseSubVector<libMesh::Number> &Fw = context.get_elem_residual(w_dot_var);
libMesh::DenseSubMatrix<libMesh::Number>& Kuv = context.get_elem_jacobian(u_dot_var,v_var);
libMesh::DenseSubMatrix<libMesh::Number>& Kuw = context.get_elem_jacobian(u_dot_var,w_var);
libMesh::DenseSubMatrix<libMesh::Number>& Kvu = context.get_elem_jacobian(v_dot_var,u_var);
libMesh::DenseSubMatrix<libMesh::Number>& Kvw = context.get_elem_jacobian(v_dot_var,w_var);
libMesh::DenseSubMatrix<libMesh::Number>& Kwu = context.get_elem_jacobian(w_dot_var,u_var);
libMesh::DenseSubMatrix<libMesh::Number>& Kwv = context.get_elem_jacobian(w_dot_var,v_var);
unsigned int n_qpoints = context.get_element_qrule().n_points();
// All shape function gradients are w.r.t. master element coordinates
const std::vector<std::vector<libMesh::Real> >& dphi_dxi =
this->get_fe(context)->get_dphidxi();
const std::vector<std::vector<libMesh::Real> >& dphi_deta =
this->get_fe(context)->get_dphideta();
const libMesh::DenseSubVector<libMesh::Number>& u_coeffs = context.get_elem_solution( u_var );
const libMesh::DenseSubVector<libMesh::Number>& v_coeffs = context.get_elem_solution( v_var );
const libMesh::DenseSubVector<libMesh::Number>& w_coeffs = context.get_elem_solution( w_var );
const std::vector<libMesh::RealGradient>& dxdxi = this->get_fe(context)->get_dxyzdxi();
const std::vector<libMesh::RealGradient>& dxdeta = this->get_fe(context)->get_dxyzdeta();
for (unsigned int qp=0; qp != n_qpoints; qp++)
{
// sqrt(det(a_cov)), a_cov being the covariant metric tensor of undeformed body
libMesh::Real sqrt_a = sqrt( dxdxi[qp]*dxdxi[qp]*dxdeta[qp]*dxdeta[qp]
- dxdxi[qp]*dxdeta[qp]*dxdeta[qp]*dxdxi[qp] );
// Gradients are w.r.t. master element coordinates
libMesh::Gradient grad_u, grad_v, grad_w;
for( unsigned int d = 0; d < n_u_dofs; d++ )
{
libMesh::RealGradient u_gradphi( dphi_dxi[d][qp], dphi_deta[d][qp] );
grad_u += u_coeffs(d)*u_gradphi;
grad_v += v_coeffs(d)*u_gradphi;
grad_w += w_coeffs(d)*u_gradphi;
}
libMesh::RealGradient dudxi( grad_u(0), grad_v(0), grad_w(0) );
libMesh::RealGradient dudeta( grad_u(1), grad_v(1), grad_w(1) );
libMesh::RealGradient A_1 = dxdxi[qp] + dudxi;
libMesh::RealGradient A_2 = dxdeta[qp] + dudeta;
libMesh::RealGradient A_3 = A_1.cross(A_2);
// Compute pressure at this quadrature point
libMesh::Real press = (*_pressure)(context,qp);
// Small optimization
libMesh::Real p_over_sa = press/sqrt_a;
/* The formula here is actually
P*\sqrt{\frac{A}{a}}*A_3, where A_3 is a unit vector
But, |A_3| = \sqrt{A} so the normalizing part kills
the \sqrt{A} in the numerator, so we can leave it out
and *not* normalize A_3.
*/
libMesh::RealGradient traction = p_over_sa*A_3;
for (unsigned int i=0; i != n_u_dofs; i++)
{
// Small optimization
libMesh::Real phi_times_jac = u_phi[i][qp]*JxW[qp];
Fu(i) -= traction(0)*phi_times_jac;
Fv(i) -= traction(1)*phi_times_jac;
Fw(i) -= traction(2)*phi_times_jac;
if( compute_jacobian )
{
for (unsigned int j=0; j != n_u_dofs; j++)
{
libMesh::RealGradient u_gradphi( dphi_dxi[j][qp], dphi_deta[j][qp] );
const libMesh::Real dt0_dv = p_over_sa*(u_gradphi(0)*A_2(2) - A_1(2)*u_gradphi(1));
const libMesh::Real dt0_dw = p_over_sa*(A_1(1)*u_gradphi(1) - u_gradphi(0)*A_2(1));
const libMesh::Real dt1_du = p_over_sa*(A_1(2)*u_gradphi(1) - u_gradphi(0)*A_2(2));
const libMesh::Real dt1_dw = p_over_sa*(u_gradphi(0)*A_2(0) - A_1(0)*u_gradphi(1));
const libMesh::Real dt2_du = p_over_sa*(u_gradphi(0)*A_2(1) - A_1(1)*u_gradphi(1));
const libMesh::Real dt2_dv = p_over_sa*(A_1(0)*u_gradphi(1) - u_gradphi(0)*A_2(0));
Kuv(i,j) -= dt0_dv*phi_times_jac;
Kuw(i,j) -= dt0_dw*phi_times_jac;
Kvu(i,j) -= dt1_du*phi_times_jac;
Kvw(i,j) -= dt1_dw*phi_times_jac;
Kwu(i,j) -= dt2_du*phi_times_jac;
Kwv(i,j) -= dt2_dv*phi_times_jac;
}
}
}
}
}
void VelocityPenalty<Mu>::element_time_derivative( bool compute_jacobian,
AssemblyContext& context,
CachedValues& /* cache */ )
{
#ifdef GRINS_USE_GRVY_TIMERS
this->_timer->BeginTimer("VelocityPenalty::element_time_derivative");
#endif
// Element Jacobian * quadrature weights for interior integration
const std::vector<libMesh::Real> &JxW =
context.get_element_fe(this->_flow_vars.u_var())->get_JxW();
// The shape functions at interior quadrature points.
const std::vector<std::vector<libMesh::Real> >& u_phi =
context.get_element_fe(this->_flow_vars.u_var())->get_phi();
const std::vector<libMesh::Point>& u_qpoint =
context.get_element_fe(this->_flow_vars.u_var())->get_xyz();
// The number of local degrees of freedom in each variable
const unsigned int n_u_dofs = context.get_dof_indices(this->_flow_vars.u_var()).size();
// The subvectors and submatrices we need to fill:
libMesh::DenseSubMatrix<libMesh::Number> &Kuu = context.get_elem_jacobian(this->_flow_vars.u_var(), this->_flow_vars.u_var()); // R_{u},{u}
libMesh::DenseSubMatrix<libMesh::Number> &Kuv = context.get_elem_jacobian(this->_flow_vars.u_var(), this->_flow_vars.v_var()); // R_{u},{v}
libMesh::DenseSubMatrix<libMesh::Number> &Kvu = context.get_elem_jacobian(this->_flow_vars.v_var(), this->_flow_vars.u_var()); // R_{v},{u}
libMesh::DenseSubMatrix<libMesh::Number> &Kvv = context.get_elem_jacobian(this->_flow_vars.v_var(), this->_flow_vars.v_var()); // R_{v},{v}
libMesh::DenseSubMatrix<libMesh::Number>* Kwu = NULL;
libMesh::DenseSubMatrix<libMesh::Number>* Kwv = NULL;
libMesh::DenseSubMatrix<libMesh::Number>* Kww = NULL;
libMesh::DenseSubMatrix<libMesh::Number>* Kuw = NULL;
libMesh::DenseSubMatrix<libMesh::Number>* Kvw = NULL;
libMesh::DenseSubVector<libMesh::Number> &Fu = context.get_elem_residual(this->_flow_vars.u_var()); // R_{u}
libMesh::DenseSubVector<libMesh::Number> &Fv = context.get_elem_residual(this->_flow_vars.v_var()); // R_{v}
libMesh::DenseSubVector<libMesh::Number>* Fw = NULL;
if( this->_dim == 3 )
{
Kuw = &context.get_elem_jacobian(this->_flow_vars.u_var(), this->_flow_vars.w_var()); // R_{u},{w}
Kvw = &context.get_elem_jacobian(this->_flow_vars.v_var(), this->_flow_vars.w_var()); // R_{v},{w}
Kwu = &context.get_elem_jacobian(this->_flow_vars.w_var(), this->_flow_vars.u_var()); // R_{w},{u}
Kwv = &context.get_elem_jacobian(this->_flow_vars.w_var(), this->_flow_vars.v_var()); // R_{w},{v}
Kww = &context.get_elem_jacobian(this->_flow_vars.w_var(), this->_flow_vars.w_var()); // R_{w},{w}
Fw = &context.get_elem_residual(this->_flow_vars.w_var()); // R_{w}
}
unsigned int n_qpoints = context.get_element_qrule().n_points();
for (unsigned int qp=0; qp != n_qpoints; qp++)
{
// Compute the solution at the old Newton iterate.
libMesh::Number u, v;
u = context.interior_value(this->_flow_vars.u_var(), qp);
v = context.interior_value(this->_flow_vars.v_var(), qp);
libMesh::NumberVectorValue U(u,v);
if (this->_dim == 3)
U(2) = context.interior_value(this->_flow_vars.w_var(), qp); // w
libMesh::NumberVectorValue F;
libMesh::NumberTensorValue dFdU;
libMesh::NumberTensorValue* dFdU_ptr =
compute_jacobian ? &dFdU : NULL;
if (!this->compute_force(u_qpoint[qp], context, U, F, dFdU_ptr))
continue;
const libMesh::Real jac = JxW[qp];
for (unsigned int i=0; i != n_u_dofs; i++)
{
const libMesh::Number jac_i = jac * u_phi[i][qp];
Fu(i) += F(0)*jac_i;
Fv(i) += F(1)*jac_i;
if( this->_dim == 3 )
{
(*Fw)(i) += F(2)*jac_i;
}
if( compute_jacobian )
{
for (unsigned int j=0; j != n_u_dofs; j++)
{
const libMesh::Number jac_ij = context.get_elem_solution_derivative() * jac_i * u_phi[j][qp];
Kuu(i,j) += jac_ij * dFdU(0,0);
Kuv(i,j) += jac_ij * dFdU(0,1);
Kvu(i,j) += jac_ij * dFdU(1,0);
Kvv(i,j) += jac_ij * dFdU(1,1);
if( this->_dim == 3 )
{
(*Kuw)(i,j) += jac_ij * dFdU(0,2);
(*Kvw)(i,j) += jac_ij * dFdU(1,2);
(*Kwu)(i,j) += jac_ij * dFdU(2,0);
(*Kwv)(i,j) += jac_ij * dFdU(2,1);
(*Kww)(i,j) += jac_ij * dFdU(2,2);
}
}
}
}
}
#ifdef GRINS_USE_GRVY_TIMERS
this->_timer->EndTimer("VelocityPenalty::element_time_derivative");
#endif
return;
}
// 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;
}
void BoussinesqBuoyancyAdjointStabilization<Mu>::element_time_derivative( bool compute_jacobian,
AssemblyContext& context,
CachedValues& /*cache*/ )
{
#ifdef GRINS_USE_GRVY_TIMERS
this->_timer->BeginTimer("BoussinesqBuoyancyAdjointStabilization::element_time_derivative");
#endif
// The number of local degrees of freedom in each variable.
const unsigned int n_u_dofs = context.get_dof_indices(_flow_vars.u_var()).size();
const unsigned int n_T_dofs = context.get_dof_indices(_temp_vars.T_var()).size();
// Element Jacobian * quadrature weights for interior integration.
const std::vector<libMesh::Real> &JxW =
context.get_element_fe(_flow_vars.u_var())->get_JxW();
const std::vector<std::vector<libMesh::Real> >& T_phi =
context.get_element_fe(this->_temp_vars.T_var())->get_phi();
const std::vector<std::vector<libMesh::Real> >& u_phi =
context.get_element_fe(this->_flow_vars.u_var())->get_phi();
const std::vector<std::vector<libMesh::RealGradient> >& u_gradphi =
context.get_element_fe(this->_flow_vars.u_var())->get_dphi();
const std::vector<std::vector<libMesh::RealTensor> >& u_hessphi =
context.get_element_fe(this->_flow_vars.u_var())->get_d2phi();
// Get residuals and jacobians
libMesh::DenseSubVector<libMesh::Number> &Fu = context.get_elem_residual(_flow_vars.u_var()); // R_{u}
libMesh::DenseSubVector<libMesh::Number> &Fv = context.get_elem_residual(_flow_vars.v_var()); // R_{v}
libMesh::DenseSubVector<libMesh::Number> *Fw = NULL;
libMesh::DenseSubMatrix<libMesh::Number> &KuT =
context.get_elem_jacobian(_flow_vars.u_var(), _temp_vars.T_var()); // J_{uT}
libMesh::DenseSubMatrix<libMesh::Number> &KvT =
context.get_elem_jacobian(_flow_vars.v_var(), _temp_vars.T_var()); // J_{vT}
libMesh::DenseSubMatrix<libMesh::Number> &Kuu =
context.get_elem_jacobian(_flow_vars.u_var(), _flow_vars.u_var()); // J_{uu}
libMesh::DenseSubMatrix<libMesh::Number> &Kuv =
context.get_elem_jacobian(_flow_vars.u_var(), _flow_vars.v_var()); // J_{uv}
libMesh::DenseSubMatrix<libMesh::Number> &Kvu =
context.get_elem_jacobian(_flow_vars.v_var(), _flow_vars.u_var()); // J_{vu}
libMesh::DenseSubMatrix<libMesh::Number> &Kvv =
context.get_elem_jacobian(_flow_vars.v_var(), _flow_vars.v_var()); // J_{vv}
libMesh::DenseSubMatrix<libMesh::Number> *KwT = NULL;
libMesh::DenseSubMatrix<libMesh::Number> *Kuw = NULL;
libMesh::DenseSubMatrix<libMesh::Number> *Kvw = NULL;
libMesh::DenseSubMatrix<libMesh::Number> *Kwu = NULL;
libMesh::DenseSubMatrix<libMesh::Number> *Kwv = NULL;
libMesh::DenseSubMatrix<libMesh::Number> *Kww = NULL;
if(this->_dim == 3)
{
Fw = &context.get_elem_residual(this->_flow_vars.w_var()); // R_{w}
KwT = &context.get_elem_jacobian
(_flow_vars.w_var(), _temp_vars.T_var()); // J_{wT}
Kuw = &context.get_elem_jacobian
(_flow_vars.u_var(), _flow_vars.w_var()); // J_{uw}
Kvw = &context.get_elem_jacobian
(_flow_vars.v_var(), _flow_vars.w_var()); // J_{vw}
Kwu = &context.get_elem_jacobian
(_flow_vars.w_var(), _flow_vars.u_var()); // J_{wu}
Kwv = &context.get_elem_jacobian
(_flow_vars.w_var(), _flow_vars.v_var()); // J_{wv}
Kww = &context.get_elem_jacobian
(_flow_vars.w_var(), _flow_vars.w_var()); // J_{ww}
}
// Now we will build the element Jacobian and residual.
// Constructing the residual requires the solution and its
// gradient from the previous timestep. This must be
// calculated at each quadrature point by summing the
// solution degree-of-freedom values by the appropriate
// weight functions.
unsigned int n_qpoints = context.get_element_qrule().n_points();
libMesh::FEBase* fe = context.get_element_fe(this->_flow_vars.u_var());
for (unsigned int qp=0; qp != n_qpoints; qp++)
{
libMesh::RealGradient g = this->_stab_helper.compute_g( fe, context, qp );
libMesh::RealTensor G = this->_stab_helper.compute_G( fe, context, qp );
libMesh::RealGradient U( context.interior_value( this->_flow_vars.u_var(), qp ),
context.interior_value( this->_flow_vars.v_var(), qp ) );
if( this->_dim == 3 )
{
U(2) = context.interior_value( this->_flow_vars.w_var(), qp );
}
// Compute the viscosity at this qp
libMesh::Real mu_qp = this->_mu(context, qp);
libMesh::Real tau_M;
libMesh::Real d_tau_M_d_rho;
libMesh::Gradient d_tau_M_dU;
if (compute_jacobian)
this->_stab_helper.compute_tau_momentum_and_derivs
( context, qp, g, G, this->_rho, U, mu_qp,
tau_M, d_tau_M_d_rho, d_tau_M_dU,
this->_is_steady );
else
tau_M = this->_stab_helper.compute_tau_momentum
( context, qp, g, G, this->_rho, U, mu_qp,
this->_is_steady );
// Compute the solution & its gradient at the old Newton iterate.
libMesh::Number T;
T = context.interior_value(_temp_vars.T_var(), qp);
libMesh::RealGradient d_residual_dT = _rho_ref*_beta_T*_g;
// d_residual_dU = 0
libMesh::RealGradient residual = (T-_T_ref)*d_residual_dT;
for (unsigned int i=0; i != n_u_dofs; i++)
{
libMesh::Real test_func = this->_rho*U*u_gradphi[i][qp] +
mu_qp*( u_hessphi[i][qp](0,0) + u_hessphi[i][qp](1,1) + u_hessphi[i][qp](2,2) );
Fu(i) += -tau_M*residual(0)*test_func*JxW[qp];
Fv(i) += -tau_M*residual(1)*test_func*JxW[qp];
if (_dim == 3)
{
(*Fw)(i) += -tau_M*residual(2)*test_func*JxW[qp];
}
if (compute_jacobian)
{
libMesh::Gradient d_test_func_dU = this->_rho*u_gradphi[i][qp];
// d_test_func_dT = 0
for (unsigned int j=0; j != n_u_dofs; ++j)
{
Kuu(i,j) += -tau_M*residual(0)*d_test_func_dU(0)*u_phi[j][qp]*JxW[qp] * context.get_elem_solution_derivative();
Kuu(i,j) += -d_tau_M_dU(0)*u_phi[j][qp]*residual(0)*test_func*JxW[qp] * context.get_elem_solution_derivative();
Kuv(i,j) += -tau_M*residual(0)*d_test_func_dU(1)*u_phi[j][qp]*JxW[qp] * context.get_elem_solution_derivative();
Kuv(i,j) += -d_tau_M_dU(1)*u_phi[j][qp]*residual(0)*test_func*JxW[qp] * context.get_elem_solution_derivative();
Kvu(i,j) += -tau_M*residual(1)*d_test_func_dU(0)*u_phi[j][qp]*JxW[qp] * context.get_elem_solution_derivative();
Kvu(i,j) += -d_tau_M_dU(0)*u_phi[j][qp]*residual(1)*test_func*JxW[qp] * context.get_elem_solution_derivative();
Kvv(i,j) += -tau_M*residual(1)*d_test_func_dU(1)*u_phi[j][qp]*JxW[qp] * context.get_elem_solution_derivative();
Kvv(i,j) += -d_tau_M_dU(1)*u_phi[j][qp]*residual(1)*test_func*JxW[qp] * context.get_elem_solution_derivative();
}
for (unsigned int j=0; j != n_T_dofs; ++j)
{
// KuT(i,j) += -tau_M*residual(0)*dtest_func_dT[j]*JxW[qp] * context.get_elem_solution_derivative();
KuT(i,j) += -tau_M*d_residual_dT(0)*T_phi[j][qp]*test_func*JxW[qp] * context.get_elem_solution_derivative();
// KvT(i,j) += -tau_M*residual(1)*dtest_func_dT[j]*JxW[qp] * context.get_elem_solution_derivative();
KvT(i,j) += -tau_M*d_residual_dT(1)*T_phi[j][qp]*test_func*JxW[qp] * context.get_elem_solution_derivative();
}
if (_dim == 3)
{
for (unsigned int j=0; j != n_T_dofs; ++j)
{
// KwT(i,j) += -tau_M*residual(2)*dtest_func_dT[j]*JxW[qp] * context.get_elem_solution_derivative();
(*KwT)(i,j) += -tau_M*d_residual_dT(2)*T_phi[j][qp]*test_func*JxW[qp] * context.get_elem_solution_derivative();
}
for (unsigned int j=0; j != n_u_dofs; ++j)
{
(*Kuw)(i,j) += -tau_M*residual(0)*d_test_func_dU(2)*u_phi[j][qp]*JxW[qp] * context.get_elem_solution_derivative();
(*Kuw)(i,j) += -d_tau_M_dU(2)*u_phi[j][qp]*residual(0)*test_func*JxW[qp] * context.get_elem_solution_derivative();
(*Kvw)(i,j) += -tau_M*residual(1)*d_test_func_dU(2)*u_phi[j][qp]*JxW[qp] * context.get_elem_solution_derivative();
(*Kvw)(i,j) += -d_tau_M_dU(2)*u_phi[j][qp]*residual(1)*test_func*JxW[qp] * context.get_elem_solution_derivative();
(*Kwu)(i,j) += -tau_M*residual(2)*d_test_func_dU(0)*u_phi[j][qp]*JxW[qp] * context.get_elem_solution_derivative();
(*Kwu)(i,j) += -d_tau_M_dU(0)*u_phi[j][qp]*residual(2)*test_func*JxW[qp] * context.get_elem_solution_derivative();
(*Kwv)(i,j) += -tau_M*residual(2)*d_test_func_dU(1)*u_phi[j][qp]*JxW[qp] * context.get_elem_solution_derivative();
(*Kwv)(i,j) += -d_tau_M_dU(1)*u_phi[j][qp]*residual(2)*test_func*JxW[qp] * context.get_elem_solution_derivative();
(*Kww)(i,j) += -tau_M*residual(2)*d_test_func_dU(2)*u_phi[j][qp]*JxW[qp] * context.get_elem_solution_derivative();
(*Kww)(i,j) += -d_tau_M_dU(2)*u_phi[j][qp]*residual(2)*test_func*JxW[qp] * context.get_elem_solution_derivative();
}
}
} // End compute_jacobian check
} // End i dof loop
} // End quadrature loop
#ifdef GRINS_USE_GRVY_TIMERS
this->_timer->EndTimer("BoussinesqBuoyancyAdjointStabilization::element_time_derivative");
#endif
return;
}
void LowMachNavierStokesSPGSMStabilization<Mu,SH,TC>::assemble_momentum_mass_residual( bool /*compute_jacobian*/,
AssemblyContext& context )
{
// The number of local degrees of freedom in each variable.
const unsigned int n_u_dofs = context.get_dof_indices(this->_flow_vars.u()).size();
// Check number of dofs is same for _flow_vars.u(), v_var and w_var.
libmesh_assert (n_u_dofs == context.get_dof_indices(this->_flow_vars.v()).size());
if (this->mesh_dim(context) == 3)
libmesh_assert (n_u_dofs == context.get_dof_indices(this->_flow_vars.w()).size());
// Element Jacobian * quadrature weights for interior integration.
const std::vector<libMesh::Real> &JxW =
context.get_element_fe(this->_flow_vars.u())->get_JxW();
// The velocity shape function gradients at interior quadrature points.
const std::vector<std::vector<libMesh::RealGradient> >& u_gradphi =
context.get_element_fe(this->_flow_vars.u())->get_dphi();
libMesh::DenseSubVector<libMesh::Number> &Fu = context.get_elem_residual(this->_flow_vars.u()); // R_{u}
libMesh::DenseSubVector<libMesh::Number> &Fv = context.get_elem_residual(this->_flow_vars.v()); // R_{v}
libMesh::DenseSubVector<libMesh::Real>* Fw = NULL;
if( this->mesh_dim(context) == 3 )
{
Fw = &context.get_elem_residual(this->_flow_vars.w()); // R_{w}
}
unsigned int n_qpoints = context.get_element_qrule().n_points();
for (unsigned int qp=0; qp != n_qpoints; qp++)
{
libMesh::Real T = context.fixed_interior_value( this->_temp_vars.T(), qp );
libMesh::Real rho = this->rho( T, this->get_p0_transient( context, qp ) );
libMesh::Real mu = this->_mu(T);
libMesh::RealGradient U( context.fixed_interior_value(this->_flow_vars.u(), qp),
context.fixed_interior_value(this->_flow_vars.v(), qp) );
libMesh::RealGradient grad_u = context.fixed_interior_gradient(this->_flow_vars.u(), qp);
libMesh::RealGradient grad_v = context.fixed_interior_gradient(this->_flow_vars.v(), qp);
libMesh::RealGradient grad_w;
if( this->mesh_dim(context) == 3 )
{
U(2) = context.fixed_interior_value(this->_flow_vars.w(), qp);
grad_w = context.fixed_interior_gradient(this->_flow_vars.w(), qp);
}
libMesh::FEBase* fe = context.get_element_fe(this->_flow_vars.u());
libMesh::RealGradient g = this->_stab_helper.compute_g( fe, context, qp );
libMesh::RealTensor G = this->_stab_helper.compute_G( fe, context, qp );
libMesh::Real tau_M = this->_stab_helper.compute_tau_momentum( context, qp, g, G, rho, U, mu, false );
libMesh::Real tau_C = this->_stab_helper.compute_tau_continuity( tau_M, g );
libMesh::Real RC_t = this->compute_res_continuity_transient( context, qp );
libMesh::RealGradient RM_s = this->compute_res_momentum_steady( context, qp );
libMesh::RealGradient RM_t = this->compute_res_momentum_transient( context, qp );
for (unsigned int i=0; i != n_u_dofs; i++)
{
Fu(i) -= ( tau_C*RC_t*u_gradphi[i][qp](0)
+ tau_M*RM_t(0)*rho*U*u_gradphi[i][qp] )*JxW[qp];
Fv(i) -= ( tau_C*RC_t*u_gradphi[i][qp](1)
+ tau_M*RM_t(1)*rho*U*u_gradphi[i][qp] )*JxW[qp];
if( this->mesh_dim(context) == 3 )
{
(*Fw)(i) -= ( tau_C*RC_t*u_gradphi[i][qp](2)
+ tau_M*RM_t(2)*rho*U*u_gradphi[i][qp] )*JxW[qp];
}
}
}
return;
}
void ElasticCableRayleighDamping<StressStrainLaw>::damping_residual( bool compute_jacobian,
AssemblyContext& context,
CachedValues& /*cache*/)
{
// First, do the "mass" contribution
this->mass_residual_impl(compute_jacobian,
context,
&libMesh::FEMContext::interior_rate,
&libMesh::DiffContext::get_elem_solution_rate_derivative,
_mu_factor);
// Now do the stiffness contribution
const unsigned int n_u_dofs = context.get_dof_indices(this->_disp_vars.u()).size();
const std::vector<libMesh::Real> &JxW =
this->get_fe(context)->get_JxW();
// Residuals that we're populating
libMesh::DenseSubVector<libMesh::Number> &Fu = context.get_elem_residual(this->_disp_vars.u());
libMesh::DenseSubVector<libMesh::Number> &Fv = context.get_elem_residual(this->_disp_vars.v());
libMesh::DenseSubVector<libMesh::Number> &Fw = context.get_elem_residual(this->_disp_vars.w());
//Grab the Jacobian matrix as submatrices
//libMesh::DenseMatrix<libMesh::Number> &K = context.get_elem_jacobian();
libMesh::DenseSubMatrix<libMesh::Number> &Kuu = context.get_elem_jacobian(this->_disp_vars.u(),this->_disp_vars.u());
libMesh::DenseSubMatrix<libMesh::Number> &Kuv = context.get_elem_jacobian(this->_disp_vars.u(),this->_disp_vars.v());
libMesh::DenseSubMatrix<libMesh::Number> &Kuw = context.get_elem_jacobian(this->_disp_vars.u(),this->_disp_vars.w());
libMesh::DenseSubMatrix<libMesh::Number> &Kvu = context.get_elem_jacobian(this->_disp_vars.v(),this->_disp_vars.u());
libMesh::DenseSubMatrix<libMesh::Number> &Kvv = context.get_elem_jacobian(this->_disp_vars.v(),this->_disp_vars.v());
libMesh::DenseSubMatrix<libMesh::Number> &Kvw = context.get_elem_jacobian(this->_disp_vars.v(),this->_disp_vars.w());
libMesh::DenseSubMatrix<libMesh::Number> &Kwu = context.get_elem_jacobian(this->_disp_vars.w(),this->_disp_vars.u());
libMesh::DenseSubMatrix<libMesh::Number> &Kwv = context.get_elem_jacobian(this->_disp_vars.w(),this->_disp_vars.v());
libMesh::DenseSubMatrix<libMesh::Number> &Kww = context.get_elem_jacobian(this->_disp_vars.w(),this->_disp_vars.w());
unsigned int n_qpoints = context.get_element_qrule().n_points();
// All shape function gradients are w.r.t. master element coordinates
const std::vector<std::vector<libMesh::Real> >& dphi_dxi = this->get_fe(context)->get_dphidxi();
const libMesh::DenseSubVector<libMesh::Number>& u_coeffs = context.get_elem_solution( this->_disp_vars.u() );
const libMesh::DenseSubVector<libMesh::Number>& v_coeffs = context.get_elem_solution( this->_disp_vars.v() );
const libMesh::DenseSubVector<libMesh::Number>& w_coeffs = context.get_elem_solution( this->_disp_vars.w() );
const libMesh::DenseSubVector<libMesh::Number>& dudt_coeffs = context.get_elem_solution_rate( this->_disp_vars.u() );
const libMesh::DenseSubVector<libMesh::Number>& dvdt_coeffs = context.get_elem_solution_rate( this->_disp_vars.v() );
const libMesh::DenseSubVector<libMesh::Number>& dwdt_coeffs = context.get_elem_solution_rate( this->_disp_vars.w() );
// Need these to build up the covariant and contravariant metric tensors
const std::vector<libMesh::RealGradient>& dxdxi = this->get_fe(context)->get_dxyzdxi();
const unsigned int dim = 1; // The cable dimension is always 1 for this physics
for (unsigned int qp=0; qp != n_qpoints; qp++)
{
// Gradients are w.r.t. master element coordinates
libMesh::Gradient grad_u, grad_v, grad_w;
libMesh::Gradient dgradu_dt, dgradv_dt, dgradw_dt;
for( unsigned int d = 0; d < n_u_dofs; d++ )
{
libMesh::RealGradient u_gradphi( dphi_dxi[d][qp] );
grad_u += u_coeffs(d)*u_gradphi;
grad_v += v_coeffs(d)*u_gradphi;
grad_w += w_coeffs(d)*u_gradphi;
dgradu_dt += dudt_coeffs(d)*u_gradphi;
dgradv_dt += dvdt_coeffs(d)*u_gradphi;
dgradw_dt += dwdt_coeffs(d)*u_gradphi;
}
libMesh::RealGradient grad_x( dxdxi[qp](0) );
libMesh::RealGradient grad_y( dxdxi[qp](1) );
libMesh::RealGradient grad_z( dxdxi[qp](2) );
libMesh::TensorValue<libMesh::Real> a_cov, a_contra, A_cov, A_contra;
libMesh::Real lambda_sq = 0;
this->compute_metric_tensors( qp, *(this->get_fe(context)), context,
grad_u, grad_v, grad_w,
a_cov, a_contra, A_cov, A_contra,
lambda_sq );
// Compute stress tensor
libMesh::TensorValue<libMesh::Real> tau;
ElasticityTensor C;
this->_stress_strain_law.compute_stress_and_elasticity(dim,a_contra,a_cov,A_contra,A_cov,tau,C);
libMesh::Real jac = JxW[qp];
for (unsigned int i=0; i != n_u_dofs; i++)
{
libMesh::RealGradient u_gradphi( dphi_dxi[i][qp] );
libMesh::Real u_diag_factor = _lambda_factor*this->_A*jac*tau(0,0)*dgradu_dt(0)*u_gradphi(0);
libMesh::Real v_diag_factor = _lambda_factor*this->_A*jac*tau(0,0)*dgradv_dt(0)*u_gradphi(0);
libMesh::Real w_diag_factor = _lambda_factor*this->_A*jac*tau(0,0)*dgradw_dt(0)*u_gradphi(0);
const libMesh::Real C1 = _lambda_factor*this->_A*jac*C(0,0,0,0)*u_gradphi(0);
const libMesh::Real gamma_u = (grad_x(0)+grad_u(0));
const libMesh::Real gamma_v = (grad_y(0)+grad_v(0));
const libMesh::Real gamma_w = (grad_z(0)+grad_w(0));
const libMesh::Real x_term = C1*gamma_u;
const libMesh::Real y_term = C1*gamma_v;
const libMesh::Real z_term = C1*gamma_w;
const libMesh::Real dt_term = dgradu_dt(0)*gamma_u + dgradv_dt(0)*gamma_v + dgradw_dt(0)*gamma_w;
Fu(i) += u_diag_factor + x_term*dt_term;
Fv(i) += v_diag_factor + y_term*dt_term;
Fw(i) += w_diag_factor + z_term*dt_term;
}
if( compute_jacobian )
{
for(unsigned int i=0; i != n_u_dofs; i++)
{
libMesh::RealGradient u_gradphi_I( dphi_dxi[i][qp] );
for(unsigned int j=0; j != n_u_dofs; j++)
{
libMesh::RealGradient u_gradphi_J( dphi_dxi[j][qp] );
libMesh::Real common_factor = _lambda_factor*this->_A*jac*u_gradphi_I(0);
const libMesh::Real diag_term_1 = common_factor*tau(0,0)*u_gradphi_J(0)*context.get_elem_solution_rate_derivative();
const libMesh::Real dgamma_du = ( u_gradphi_J(0)*(grad_x(0)+grad_u(0)) );
const libMesh::Real dgamma_dv = ( u_gradphi_J(0)*(grad_y(0)+grad_v(0)) );
const libMesh::Real dgamma_dw = ( u_gradphi_J(0)*(grad_z(0)+grad_w(0)) );
const libMesh::Real diag_term_2_factor = common_factor*C(0,0,0,0)*context.get_elem_solution_derivative();
Kuu(i,j) += diag_term_1 + dgradu_dt(0)*diag_term_2_factor*dgamma_du;
Kuv(i,j) += dgradu_dt(0)*diag_term_2_factor*dgamma_dv;
Kuw(i,j) += dgradu_dt(0)*diag_term_2_factor*dgamma_dw;
Kvu(i,j) += dgradv_dt(0)*diag_term_2_factor*dgamma_du;
Kvv(i,j) += diag_term_1 + dgradv_dt(0)*diag_term_2_factor*dgamma_dv;
Kvw(i,j) += dgradv_dt(0)*diag_term_2_factor*dgamma_dw;
Kwu(i,j) += dgradw_dt(0)*diag_term_2_factor*dgamma_du;
Kwv(i,j) += dgradw_dt(0)*diag_term_2_factor*dgamma_dv;
Kww(i,j) += diag_term_1 + dgradw_dt(0)*diag_term_2_factor*dgamma_dw;
const libMesh::Real C1 = common_factor*C(0,0,0,0);
const libMesh::Real gamma_u = (grad_x(0)+grad_u(0));
const libMesh::Real gamma_v = (grad_y(0)+grad_v(0));
const libMesh::Real gamma_w = (grad_z(0)+grad_w(0));
const libMesh::Real x_term = C1*gamma_u;
const libMesh::Real y_term = C1*gamma_v;
const libMesh::Real z_term = C1*gamma_w;
const libMesh::Real ddtterm_du = u_gradphi_J(0)*(gamma_u*context.get_elem_solution_rate_derivative()
+ dgradu_dt(0)*context.get_elem_solution_derivative());
const libMesh::Real ddtterm_dv = u_gradphi_J(0)*(gamma_v*context.get_elem_solution_rate_derivative()
+ dgradv_dt(0)*context.get_elem_solution_derivative());
const libMesh::Real ddtterm_dw = u_gradphi_J(0)*(gamma_w*context.get_elem_solution_rate_derivative()
+ dgradw_dt(0)*context.get_elem_solution_derivative());
Kuu(i,j) += x_term*ddtterm_du;
Kuv(i,j) += x_term*ddtterm_dv;
Kuw(i,j) += x_term*ddtterm_dw;
Kvu(i,j) += y_term*ddtterm_du;
Kvv(i,j) += y_term*ddtterm_dv;
Kvw(i,j) += y_term*ddtterm_dw;
Kwu(i,j) += z_term*ddtterm_du;
Kwv(i,j) += z_term*ddtterm_dv;
Kww(i,j) += z_term*ddtterm_dw;
const libMesh::Real dt_term = dgradu_dt(0)*gamma_u + dgradv_dt(0)*gamma_v + dgradw_dt(0)*gamma_w;
// Here, we're missing derivatives of C(0,0,0,0) w.r.t. strain
// Nonzero for hyperelasticity models
const libMesh::Real dxterm_du = C1*u_gradphi_J(0)*context.get_elem_solution_derivative();
const libMesh::Real dyterm_dv = dxterm_du;
const libMesh::Real dzterm_dw = dxterm_du;
Kuu(i,j) += dxterm_du*dt_term;
Kvv(i,j) += dyterm_dv*dt_term;
Kww(i,j) += dzterm_dw*dt_term;
} // end j-loop
} // end i-loop
} // end if(compute_jacobian)
} // end qp loop
}
void BoussinesqBuoyancy::element_time_derivative
( bool compute_jacobian,
AssemblyContext & context )
{
// The number of local degrees of freedom in each variable.
const unsigned int n_u_dofs = context.get_dof_indices(_flow_vars.u()).size();
const unsigned int n_T_dofs = context.get_dof_indices(_temp_vars.T()).size();
// Element Jacobian * quadrature weights for interior integration.
const std::vector<libMesh::Real> &JxW =
context.get_element_fe(_flow_vars.u())->get_JxW();
// The velocity shape functions at interior quadrature points.
const std::vector<std::vector<libMesh::Real> >& vel_phi =
context.get_element_fe(_flow_vars.u())->get_phi();
// The temperature shape functions at interior quadrature points.
const std::vector<std::vector<libMesh::Real> >& T_phi =
context.get_element_fe(_temp_vars.T())->get_phi();
// Get residuals
libMesh::DenseSubVector<libMesh::Number> &Fu = context.get_elem_residual(_flow_vars.u()); // R_{u}
libMesh::DenseSubVector<libMesh::Number> &Fv = context.get_elem_residual(_flow_vars.v()); // R_{v}
libMesh::DenseSubVector<libMesh::Number>* Fw = NULL;
// Get Jacobians
libMesh::DenseSubMatrix<libMesh::Number> &KuT = context.get_elem_jacobian(_flow_vars.u(), _temp_vars.T()); // R_{u},{T}
libMesh::DenseSubMatrix<libMesh::Number> &KvT = context.get_elem_jacobian(_flow_vars.v(), _temp_vars.T()); // R_{v},{T}
libMesh::DenseSubMatrix<libMesh::Number>* KwT = NULL;
if( this->_flow_vars.dim() == 3 )
{
Fw = &context.get_elem_residual(_flow_vars.w()); // R_{w}
KwT = &context.get_elem_jacobian(_flow_vars.w(), _temp_vars.T()); // R_{w},{T}
}
// Now we will build the element Jacobian and residual.
// Constructing the residual requires the solution and its
// gradient from the previous timestep. This must be
// calculated at each quadrature point by summing the
// solution degree-of-freedom values by the appropriate
// weight functions.
unsigned int n_qpoints = context.get_element_qrule().n_points();
for (unsigned int qp=0; qp != n_qpoints; qp++)
{
// Compute the solution & its gradient at the old Newton iterate.
libMesh::Number T;
T = context.interior_value(_temp_vars.T(), qp);
// First, an i-loop over the velocity degrees of freedom.
// We know that n_u_dofs == n_v_dofs so we can compute contributions
// for both at the same time.
for (unsigned int i=0; i != n_u_dofs; i++)
{
Fu(i) += -_rho*_beta_T*(T - _T_ref)*_g(0)*vel_phi[i][qp]*JxW[qp];
Fv(i) += -_rho*_beta_T*(T - _T_ref)*_g(1)*vel_phi[i][qp]*JxW[qp];
if (this->_flow_vars.dim() == 3)
(*Fw)(i) += -_rho*_beta_T*(T - _T_ref)*_g(2)*vel_phi[i][qp]*JxW[qp];
if (compute_jacobian)
{
for (unsigned int j=0; j != n_T_dofs; j++)
{
KuT(i,j) += context.get_elem_solution_derivative() *
-_rho*_beta_T*_g(0)*vel_phi[i][qp]*T_phi[j][qp]*JxW[qp];
KvT(i,j) += context.get_elem_solution_derivative() *
-_rho*_beta_T*_g(1)*vel_phi[i][qp]*T_phi[j][qp]*JxW[qp];
if (this->_flow_vars.dim() == 3)
(*KwT)(i,j) += context.get_elem_solution_derivative() *
-_rho*_beta_T*_g(2)*vel_phi[i][qp]*T_phi[j][qp]*JxW[qp];
} // End j dof loop
} // End compute_jacobian check
} // End i dof loop
} // End quadrature loop
}
void ElasticMembraneConstantPressure::element_time_derivative( bool compute_jacobian,
AssemblyContext& context,
CachedValues& /*cache*/ )
{
const unsigned int n_u_dofs = context.get_dof_indices(_disp_vars.u()).size();
const std::vector<libMesh::Real> &JxW =
this->get_fe(context)->get_JxW();
const std::vector<std::vector<libMesh::Real> >& u_phi =
this->get_fe(context)->get_phi();
libMesh::DenseSubVector<libMesh::Number> &Fu = context.get_elem_residual(_disp_vars.u());
libMesh::DenseSubVector<libMesh::Number> &Fv = context.get_elem_residual(_disp_vars.v());
libMesh::DenseSubVector<libMesh::Number> &Fw = context.get_elem_residual(_disp_vars.w());
libMesh::DenseSubMatrix<libMesh::Number>& Kuv = context.get_elem_jacobian(_disp_vars.u(),_disp_vars.v());
libMesh::DenseSubMatrix<libMesh::Number>& Kuw = context.get_elem_jacobian(_disp_vars.u(),_disp_vars.w());
libMesh::DenseSubMatrix<libMesh::Number>& Kvu = context.get_elem_jacobian(_disp_vars.v(),_disp_vars.u());
libMesh::DenseSubMatrix<libMesh::Number>& Kvw = context.get_elem_jacobian(_disp_vars.v(),_disp_vars.w());
libMesh::DenseSubMatrix<libMesh::Number>& Kwu = context.get_elem_jacobian(_disp_vars.w(),_disp_vars.u());
libMesh::DenseSubMatrix<libMesh::Number>& Kwv = context.get_elem_jacobian(_disp_vars.w(),_disp_vars.v());
unsigned int n_qpoints = context.get_element_qrule().n_points();
// All shape function gradients are w.r.t. master element coordinates
const std::vector<std::vector<libMesh::Real> >& dphi_dxi =
this->get_fe(context)->get_dphidxi();
const std::vector<std::vector<libMesh::Real> >& dphi_deta =
this->get_fe(context)->get_dphideta();
const libMesh::DenseSubVector<libMesh::Number>& u_coeffs = context.get_elem_solution( _disp_vars.u() );
const libMesh::DenseSubVector<libMesh::Number>& v_coeffs = context.get_elem_solution( _disp_vars.v() );
const libMesh::DenseSubVector<libMesh::Number>& w_coeffs = context.get_elem_solution( _disp_vars.w() );
const std::vector<libMesh::RealGradient>& dxdxi = this->get_fe(context)->get_dxyzdxi();
const std::vector<libMesh::RealGradient>& dxdeta = this->get_fe(context)->get_dxyzdeta();
for (unsigned int qp=0; qp != n_qpoints; qp++)
{
// sqrt(det(a_cov)), a_cov being the covariant metric tensor of undeformed body
libMesh::Real sqrt_a = sqrt( dxdxi[qp]*dxdxi[qp]*dxdeta[qp]*dxdeta[qp]
- dxdxi[qp]*dxdeta[qp]*dxdeta[qp]*dxdxi[qp] );
// Gradients are w.r.t. master element coordinates
libMesh::Gradient grad_u, grad_v, grad_w;
for( unsigned int d = 0; d < n_u_dofs; d++ )
{
libMesh::RealGradient u_gradphi( dphi_dxi[d][qp], dphi_deta[d][qp] );
grad_u += u_coeffs(d)*u_gradphi;
grad_v += v_coeffs(d)*u_gradphi;
grad_w += w_coeffs(d)*u_gradphi;
}
libMesh::RealGradient dudxi( grad_u(0), grad_v(0), grad_w(0) );
libMesh::RealGradient dudeta( grad_u(1), grad_v(1), grad_w(1) );
libMesh::RealGradient A_1 = dxdxi[qp] + dudxi;
libMesh::RealGradient A_2 = dxdeta[qp] + dudeta;
libMesh::RealGradient A_3 = A_1.cross(A_2);
/* The formula here is actually
P*\sqrt{\frac{A}{a}}*A_3, where A_3 is a unit vector
But, |A_3| = \sqrt{A} so the normalizing part kills
the \sqrt{A} in the numerator, so we can leave it out
and *not* normalize A_3.
*/
libMesh::RealGradient traction = _pressure/sqrt_a*A_3;
libMesh::Real jac = JxW[qp];
for (unsigned int i=0; i != n_u_dofs; i++)
{
Fu(i) -= traction(0)*u_phi[i][qp]*jac;
Fv(i) -= traction(1)*u_phi[i][qp]*jac;
Fw(i) -= traction(2)*u_phi[i][qp]*jac;
if( compute_jacobian )
{
for (unsigned int j=0; j != n_u_dofs; j++)
{
libMesh::RealGradient u_gradphi( dphi_dxi[j][qp], dphi_deta[j][qp] );
const libMesh::Real dt0_dv = _pressure/sqrt_a*(u_gradphi(0)*A_2(2) - A_1(2)*u_gradphi(1));
const libMesh::Real dt0_dw = _pressure/sqrt_a*(A_1(1)*u_gradphi(1) - u_gradphi(0)*A_2(1));
const libMesh::Real dt1_du = _pressure/sqrt_a*(A_1(2)*u_gradphi(1) - u_gradphi(0)*A_2(2));
const libMesh::Real dt1_dw = _pressure/sqrt_a*(u_gradphi(0)*A_2(0) - A_1(0)*u_gradphi(1));
const libMesh::Real dt2_du = _pressure/sqrt_a*(u_gradphi(0)*A_2(1) - A_1(1)*u_gradphi(1));
const libMesh::Real dt2_dv = _pressure/sqrt_a*(A_1(0)*u_gradphi(1) - u_gradphi(0)*A_2(0));
Kuv(i,j) -= dt0_dv*u_phi[i][qp]*jac;
Kuw(i,j) -= dt0_dw*u_phi[i][qp]*jac;
Kvu(i,j) -= dt1_du*u_phi[i][qp]*jac;
Kvw(i,j) -= dt1_dw*u_phi[i][qp]*jac;
Kwu(i,j) -= dt2_du*u_phi[i][qp]*jac;
Kwv(i,j) -= dt2_dv*u_phi[i][qp]*jac;
}
}
}
}
return;
}