void
KernelGrad::computeJacobian()
{
DenseMatrix<Number> & ke = _assembly.jacobianBlock(_var.number(), _var.number());
_local_ke.resize(ke.m(), ke.n());
_local_ke.zero();
const unsigned int n_test = _test.size();
for (_qp = 0; _qp < _qrule->n_points(); _qp++)
for (_j = 0; _j < _phi.size(); _j++)
{
RealGradient value = precomputeQpJacobian() * _JxW[_qp] * _coord[_qp];
for (_i = 0; _i < n_test; _i++) // target for auto vectorization
_local_ke(_i, _j) += value * _grad_test[_i][_qp];
}
ke += _local_ke;
if (_has_diag_save_in)
{
const unsigned int rows = ke.m();
DenseVector<Number> diag(rows);
for (unsigned int i = 0; i < rows; i++) // target for auto vectorization
diag(i) = _local_ke(i,i);
Threads::spin_mutex::scoped_lock lock(Threads::spin_mtx);
for (unsigned int i = 0; i < _diag_save_in.size(); i++)
_diag_save_in[i]->sys().solution().add_vector(diag, _diag_save_in[i]->dofIndices());
}
}
void
KernelValue::computeJacobian()
{
DenseMatrix<Number> & ke = _assembly.jacobianBlock(_var.number(), _var.number());
_local_ke.resize(ke.m(), ke.n());
_local_ke.zero();
for (_qp = 0; _qp < _qrule->n_points(); _qp++)
{
for (_j = 0; _j < _phi.size(); _j++)
{
// NOTE: is it possible to move this out of the for-loop and multiply the _value by _phi[_j][_qp]
_value = precomputeQpJacobian();
for (_i = 0; _i < _test.size(); _i++)
_local_ke(_i, _j) += _JxW[_qp]*_coord[_qp]*_value*_test[_i][_qp];
}
}
ke += _local_ke;
if (_has_diag_save_in)
{
unsigned int rows = ke.m();
DenseVector<Number> diag(rows);
for(unsigned int i=0; i<rows; i++)
diag(i) = _local_ke(i,i);
Threads::spin_mutex::scoped_lock lock(Threads::spin_mtx);
for(unsigned int i=0; i<_diag_save_in.size(); i++)
_diag_save_in[i]->sys().solution().add_vector(diag, _diag_save_in[i]->dofIndices());
}
}
void
EigenKernel::computeJacobian()
{
if (!_is_implicit) return;
DenseMatrix<Number> & ke = _assembly.jacobianBlock(_var.number(), _var.number());
_local_ke.resize(ke.m(), ke.n());
_local_ke.zero();
mooseAssert(*_eigenvalue != 0.0, "Can't divide by zero eigenvalue in EigenKernel!");
Real one_over_eigen = 1.0 / *_eigenvalue;
for (_i = 0; _i < _test.size(); _i++)
for (_j = 0; _j < _phi.size(); _j++)
for (_qp = 0; _qp < _qrule->n_points(); _qp++)
_local_ke(_i, _j) += _JxW[_qp] * _coord[_qp] * one_over_eigen * computeQpJacobian();
ke += _local_ke;
if (_has_diag_save_in)
{
unsigned int rows = ke.m();
DenseVector<Number> diag(rows);
for (unsigned int i=0; i<rows; i++)
diag(i) = _local_ke(i,i);
Threads::spin_mutex::scoped_lock lock(Threads::spin_mtx);
for (unsigned int i=0; i<_diag_save_in.size(); i++)
_diag_save_in[i]->sys().solution().add_vector(diag, _diag_save_in[i]->dofIndices());
}
}
void
ADIntegratedBCTempl<T, compute_stage>::computeJacobian()
{
DenseMatrix<Number> & ke = _assembly.jacobianBlock(_var.number(), _var.number());
_local_ke.resize(ke.m(), ke.n());
_local_ke.zero();
size_t ad_offset = _var.number() * _sys.getMaxVarNDofsPerElem();
for (_qp = 0; _qp < _qrule->n_points(); _qp++)
for (_i = 0; _i < _test.size(); _i++)
{
DualReal residual = computeQpResidual();
for (_j = 0; _j < _var.phiSize(); ++_j)
_local_ke(_i, _j) += (_ad_JxW[_qp] * _coord[_qp] * residual).derivatives()[ad_offset + _j];
}
ke += _local_ke;
if (_has_diag_save_in)
{
unsigned int rows = ke.m();
DenseVector<Number> diag(rows);
for (unsigned int i = 0; i < rows; i++)
diag(i) = _local_ke(i, i);
Threads::spin_mutex::scoped_lock lock(Threads::spin_mtx);
for (unsigned int i = 0; i < _diag_save_in.size(); i++)
_diag_save_in[i]->sys().solution().add_vector(diag, _diag_save_in[i]->dofIndices());
}
}
void
Kernel::computeJacobian()
{
DenseMatrix<Number> & ke = _assembly.jacobianBlock(_var.index(), _var.index());
_local_ke.resize(ke.m(), ke.n());
_local_ke.zero();
for (_i = 0; _i < _test.size(); _i++)
for (_j = 0; _j < _phi.size(); _j++)
for (_qp = 0; _qp < _qrule->n_points(); _qp++)
_local_ke(_i, _j) += _JxW[_qp] * _coord[_qp] * computeQpJacobian();
ke += _local_ke;
if (_has_diag_save_in)
{
unsigned int rows = ke.m();
DenseVector<Number> diag(rows);
for(unsigned int i=0; i<rows; i++)
diag(i) = _local_ke(i,i);
Threads::spin_mutex::scoped_lock lock(Threads::spin_mtx);
for(unsigned int i=0; i<_diag_save_in.size(); i++)
_diag_save_in[i]->sys().solution().add_vector(diag, _diag_save_in[i]->dofIndices());
}
}
void
StressDivergenceTruss::computeJacobian()
{
DenseMatrix<Number> & ke = _assembly.jacobianBlock(_var.number(), _var.number());
_local_ke.resize(ke.m(), ke.n());
_local_ke.zero();
ColumnMajorMatrix stiff_global(3,3);
computeStiffness( stiff_global );
for (_i = 0; _i < _test.size(); _i++)
{
for (_j = 0; _j < _phi.size(); _j++)
{
int sign( _i == _j ? 1 : -1 );
_local_ke(_i, _j) += sign * stiff_global(_component, _component);
}
}
ke += _local_ke;
if(_has_diag_save_in)
{
unsigned int rows = ke.m();
DenseVector<Number> diag(rows);
for(unsigned int i=0; i<rows; i++)
diag(i) = _local_ke(i,i);
Threads::spin_mutex::scoped_lock lock(Threads::spin_mtx);
for(unsigned int i=0; i<_diag_save_in.size(); i++)
_diag_save_in[i]->sys().solution().add_vector(diag, _diag_save_in[i]->dofIndices());
}
}
void
InertialForceBeam::computeJacobian()
{
DenseMatrix<Number> & ke = _assembly.jacobianBlock(_var.number(), _var.number());
_local_ke.resize(ke.m(), ke.n());
_local_ke.zero();
mooseAssert(_beta > 0.0, "InertialForceBeam: Beta parameter should be positive.");
Real factor = 0.0;
if (isParamValid("beta"))
factor = 1.0 / (_beta * _dt * _dt) + _eta[0] * (1.0 + _alpha) * _gamma / _beta / _dt;
else
factor = (*_du_dotdot_du)[0] + _eta[0] * (1.0 + _alpha) * (*_du_dot_du)[0];
for (unsigned int i = 0; i < _test.size(); ++i)
{
for (unsigned int j = 0; j < _phi.size(); ++j)
{
if (_component < 3)
_local_ke(i, j) = (i == j ? 1.0 / 3.0 : 1.0 / 6.0) * _density[0] * _area[0] *
_original_length[0] * factor;
else if (_component > 2)
{
RankTwoTensor I;
if (isParamValid("Ix"))
I(0, 0) = _Ix[0];
else
I(0, 0) = _Iy[0] + _Iz[0];
I(1, 1) = _Iz[0];
I(2, 2) = _Iy[0];
// conversion from local config to global coordinate system
RankTwoTensor Ig = _original_local_config[0].transpose() * I * _original_local_config[0];
_local_ke(i, j) = (i == j ? 1.0 / 3.0 : 1.0 / 6.0) * _density[0] *
Ig(_component - 3, _component - 3) * _original_length[0] * factor;
}
}
}
ke += _local_ke;
if (_has_diag_save_in)
{
unsigned int rows = ke.m();
DenseVector<Number> diag(rows);
for (unsigned int i = 0; i < rows; ++i)
diag(i) = _local_ke(i, i);
Threads::spin_mutex::scoped_lock lock(Threads::spin_mtx);
for (unsigned int i = 0; i < _diag_save_in.size(); ++i)
_diag_save_in[i]->sys().solution().add_vector(diag, _diag_save_in[i]->dofIndices());
}
}
void
StressDivergence::computeJacobian()
{
DenseMatrix<Number> & ke = _assembly.jacobianBlock(_var.number(), _var.number());
_local_ke.resize(ke.m(), ke.n());
_local_ke.zero();
if (_volumetric_locking_correction)
{
// calculate volume averaged value of shape function derivative
_avg_grad_test.resize(_test.size());
for (_i = 0; _i < _test.size(); _i++)
{
_avg_grad_test[_i].resize(3);
_avg_grad_test[_i][_component] = 0.0;
for (_qp = 0; _qp < _qrule->n_points(); _qp++)
_avg_grad_test[_i][_component] += _grad_test[_i][_qp](_component) * _JxW[_qp] * _coord[_qp];
_avg_grad_test[_i][_component] /= _current_elem_volume;
}
_avg_grad_phi.resize(_phi.size());
for (_i = 0; _i < _phi.size(); _i++)
{
_avg_grad_phi[_i].resize(3);
for (unsigned int component = 0; component < _mesh.dimension(); component++)
{
_avg_grad_phi[_i][component] = 0.0;
for (_qp = 0; _qp < _qrule->n_points(); _qp++)
_avg_grad_phi[_i][component] += _grad_phi[_i][_qp](component) * _JxW[_qp] * _coord[_qp];
_avg_grad_phi[_i][component] /= _current_elem_volume;
}
}
}
for (_i = 0; _i < _test.size(); _i++)
for (_j = 0; _j < _phi.size(); _j++)
for (_qp = 0; _qp < _qrule->n_points(); _qp++)
_local_ke(_i, _j) += _JxW[_qp] * _coord[_qp] * computeQpJacobian();
ke += _local_ke;
if (_has_diag_save_in)
{
unsigned int rows = ke.m();
DenseVector<Number> diag(rows);
for (unsigned int i = 0; i < rows; i++)
diag(i) = _local_ke(i, i);
Threads::spin_mutex::scoped_lock lock(Threads::spin_mtx);
for (const auto & var : _diag_save_in)
var->sys().solution().add_vector(diag, var->dofIndices());
}
}
void
FDKernel::computeOffDiagJacobian(unsigned int jvar_index)
{
DenseMatrix<Number> & ke = _assembly.jacobianBlock(_var.number(), jvar_index);
DenseMatrix<Number> local_ke;
local_ke.resize(ke.m(), ke.n());
local_ke.zero();
// FIXME: pull out the already computed element residual instead of recomputing it
Real h;
DenseVector<Number> re = perturbedResidual(_var.number(),0,0.0,h);
for (_j = 0; _j < _phi.size(); _j++) {
DenseVector<Number> p_re = perturbedResidual(jvar_index,_j,_scale,h);
for (_i = 0; _i < _test.size(); _i++) {
local_ke(_i,_j) = (p_re(_i) - re(_i))/h;
}
}
ke += local_ke;
if (jvar_index == _var.number()) {
_local_ke = local_ke;
if (_has_diag_save_in) {
unsigned int rows = ke.m();
DenseVector<Number> diag(rows);
for (unsigned int i=0; i<rows; i++)
diag(i) = _local_ke(i,i);
Threads::spin_mutex::scoped_lock lock(Threads::spin_mtx);
for (unsigned int i=0; i<_diag_save_in.size(); i++)
_diag_save_in[i]->sys().solution().add_vector(diag, _diag_save_in[i]->dofIndices());
}
}
}
void
IntegratedBC::computeJacobianBlock(MooseVariableFEBase & jvar)
{
size_t jvar_num = jvar.number();
prepareMatrixTag(_assembly, _var.number(), jvar_num);
for (_qp = 0; _qp < _qrule->n_points(); _qp++)
for (_i = 0; _i < _test.size(); _i++)
for (_j = 0; _j < jvar.phiFaceSize(); _j++)
{
if (_var.number() == jvar_num)
_local_ke(_i, _j) += _JxW[_qp] * _coord[_qp] * computeQpJacobian();
else
_local_ke(_i, _j) += _JxW[_qp] * _coord[_qp] * computeQpOffDiagJacobian(jvar_num);
}
accumulateTaggedLocalMatrix();
}
void
IntegratedBC::computeJacobianBlock(unsigned int jvar)
{
mooseDeprecated("The computeJacobianBlock method signature has changed. Developers, please "
"pass in a MooseVariableFEBase reference instead of the variable number");
prepareMatrixTag(_assembly, _var.number(), jvar);
for (_qp = 0; _qp < _qrule->n_points(); _qp++)
for (_i = 0; _i < _test.size(); _i++)
for (_j = 0; _j < _phi.size(); _j++)
{
if (_var.number() == jvar)
_local_ke(_i, _j) += _JxW[_qp] * _coord[_qp] * computeQpJacobian();
else
_local_ke(_i, _j) += _JxW[_qp] * _coord[_qp] * computeQpOffDiagJacobian(jvar);
}
accumulateTaggedLocalMatrix();
}
void
AuxKernel::compute()
{
precalculateValue();
if (isNodal()) /* nodal variables */
{
if (_var.isNodalDefined())
{
_qp = 0;
Real value = computeValue();
// update variable data, which is referenced by other kernels, so the value is up-to-date
_var.setNodalValue(value);
}
}
else /* elemental variables */
{
_n_local_dofs = _var.numberOfDofs();
if (_n_local_dofs == 1) /* p0 */
{
Real value = 0;
for (_qp = 0; _qp < _qrule->n_points(); _qp++)
value += _JxW[_qp] * _coord[_qp] * computeValue();
value /= (_bnd ? _current_side_volume : _current_elem_volume);
// update the variable data refernced by other kernels.
// Note that this will update the values at the quadrature points too
// (because this is an Elemental variable)
_var.setNodalValue(value);
}
else /* high-order */
{
_local_re.resize(_n_local_dofs);
_local_re.zero();
_local_ke.resize(_n_local_dofs, _n_local_dofs);
_local_ke.zero();
// assemble the local mass matrix and the load
for (unsigned int i = 0; i < _test.size(); i++)
for (_qp = 0; _qp < _qrule->n_points(); _qp++)
{
Real t = _JxW[_qp] * _coord[_qp] * _test[i][_qp];
_local_re(i) += t * computeValue();
for (unsigned int j = 0; j < _test.size(); j++)
_local_ke(i, j) += t * _test[j][_qp];
}
// mass matrix is always SPD
_local_sol.resize(_n_local_dofs);
_local_ke.cholesky_solve(_local_re, _local_sol);
_var.setNodalValue(_local_sol);
}
}
}
void
NodalEqualValueConstraint::computeJacobian()
{
prepareMatrixTag(_assembly, _var.number(), _var.number());
// put zeroes on the diagonal (we have to do it, otherwise PETSc will complain!)
for (unsigned int i = 0; i < _local_ke.m(); i++)
for (unsigned int j = 0; j < _local_ke.n(); j++)
_local_ke(i, j) = 0.;
assignTaggedLocalMatrix();
for (unsigned int k = 0; k < _value.size(); k++)
{
prepareMatrixTag(_assembly, _var.number(), _val_number[k]);
_local_ke(k, 0) = 1.;
_local_ke(k, 1) = -1.;
assignTaggedLocalMatrix();
}
}
void
IntegratedBC::computeJacobianBlockScalar(unsigned int jvar)
{
prepareMatrixTag(_assembly, _var.number(), jvar);
MooseVariableScalar & jv = _sys.getScalarVariable(_tid, jvar);
for (_qp = 0; _qp < _qrule->n_points(); _qp++)
for (_i = 0; _i < _test.size(); _i++)
for (_j = 0; _j < jv.order(); _j++)
_local_ke(_i, _j) += _JxW[_qp] * _coord[_qp] * computeQpOffDiagJacobian(jvar);
accumulateTaggedLocalMatrix();
}
void
IntegratedBC::computeJacobian()
{
prepareMatrixTag(_assembly, _var.number(), _var.number());
for (_qp = 0; _qp < _qrule->n_points(); _qp++)
for (_i = 0; _i < _test.size(); _i++)
for (_j = 0; _j < _phi.size(); _j++)
_local_ke(_i, _j) += _JxW[_qp] * _coord[_qp] * computeQpJacobian();
accumulateTaggedLocalMatrix();
if (_has_diag_save_in)
{
unsigned int rows = _local_ke.m();
DenseVector<Number> diag(rows);
for (unsigned int i = 0; i < rows; i++)
diag(i) = _local_ke(i, i);
Threads::spin_mutex::scoped_lock lock(Threads::spin_mtx);
for (unsigned int i = 0; i < _diag_save_in.size(); i++)
_diag_save_in[i]->sys().solution().add_vector(diag, _diag_save_in[i]->dofIndices());
}
}
void
ODEKernel::computeJacobian()
{
prepareMatrixTag(_assembly, _var.number(), _var.number());
for (_i = 0; _i < _var.order(); _i++)
for (_j = 0; _j < _var.order(); _j++)
_local_ke(_i, _j) += computeQpJacobian();
accumulateTaggedLocalMatrix();
// compute off-diagonal jacobians wrt scalar variables
const std::vector<MooseVariableScalar *> & scalar_vars = _sys.getScalarVariables(_tid);
for (const auto & var : scalar_vars)
computeOffDiagJacobian(var->number());
}
void
ODEKernel::computeOffDiagJacobian(unsigned int jvar)
{
if (_sys.isScalarVariable(jvar))
{
prepareMatrixTag(_assembly, _var.number(), jvar);
MooseVariableScalar & var_j = _sys.getScalarVariable(_tid, jvar);
for (_i = 0; _i < _var.order(); _i++)
for (_j = 0; _j < var_j.order(); _j++)
{
if (jvar != _var.number())
_local_ke(_i, _j) += computeQpOffDiagJacobian(jvar);
}
accumulateTaggedLocalMatrix();
}
}
void
PorousFlowDarcyBase::upwind(JacRes res_or_jac, unsigned int jvar)
{
if ((res_or_jac == JacRes::CALCULATE_JACOBIAN) &&
_porousflow_dictator.notPorousFlowVariable(jvar))
return;
/// The PorousFlow variable index corresponding to the variable number jvar
const unsigned int pvar =
((res_or_jac == JacRes::CALCULATE_JACOBIAN) ? _porousflow_dictator.porousFlowVariableNum(jvar)
: 0);
/// The number of nodes in the element
const unsigned int num_nodes = _test.size();
/// Compute the residual and jacobian without the mobility terms. Even if we are computing the Jacobian
/// we still need this in order to see which nodes are upwind and which are downwind.
std::vector<std::vector<Real>> component_re(num_nodes);
for (_i = 0; _i < num_nodes; ++_i)
{
component_re[_i].assign(_num_phases, 0.0);
for (_qp = 0; _qp < _qrule->n_points(); _qp++)
for (unsigned ph = 0; ph < _num_phases; ++ph)
component_re[_i][ph] += _JxW[_qp] * _coord[_qp] * darcyQp(ph);
}
DenseMatrix<Number> & ke = _assembly.jacobianBlock(_var.number(), jvar);
if ((ke.n() == 0) &&
(res_or_jac == JacRes::CALCULATE_JACOBIAN)) // this removes a problem encountered in
// the initial timestep when
// use_displaced_mesh=true
return;
std::vector<std::vector<std::vector<Real>>> component_ke;
if (res_or_jac == JacRes::CALCULATE_JACOBIAN)
{
component_ke.resize(ke.m());
for (_i = 0; _i < _test.size(); _i++)
{
component_ke[_i].resize(ke.n());
for (_j = 0; _j < _phi.size(); _j++)
{
component_ke[_i][_j].resize(_num_phases);
for (_qp = 0; _qp < _qrule->n_points(); _qp++)
for (unsigned ph = 0; ph < _num_phases; ++ph)
component_ke[_i][_j][ph] += _JxW[_qp] * _coord[_qp] * darcyQpJacobian(jvar, ph);
}
}
}
/**
* Now perform the upwinding by multiplying the residuals at the upstream nodes by their
*mobilities.
* Mobility is different for each phase, and in each situation:
* mobility = density / viscosity for single-component Darcy flow
* mobility = mass_fraction * density * relative_perm / viscosity for multi-component,
*multiphase flow
* mobility = enthalpy * density * relative_perm / viscosity for heat convection
*
* The residual for the kernel is the sum over Darcy fluxes for each phase.
* The Darcy flux for a particular phase is
* R_i = int{mobility*flux_no_mob} = int{mobility*grad(pot)*permeability*grad(test_i)}
* for node i. where int is the integral over the element.
* However, in fully-upwind, the first step is to take the mobility outside the integral,
* which was done in the _component_re calculation above.
*
* NOTE: Physically _component_re[i][ph] is a measure of fluid of phase ph flowing out of node i.
* If we had left in mobility, it would be exactly the component mass flux flowing out of node i.
*
* This leads to the definition of upwinding:
*
* If _component_re(i)[ph] is positive then we use mobility_i. That is we use the upwind value of
*mobility.
*
* The final subtle thing is we must also conserve fluid mass: the total component mass flowing
*out of node i
* must be the sum of the masses flowing into the other nodes.
**/
// Following are used below in steady-state calculations
Real knorm = 0.0;
for (unsigned int qp = 0; qp < _qrule->n_points(); ++qp)
knorm += _permeability[qp].tr();
const Real lsq = _grad_test[0][0] * _grad_test[0][0];
const unsigned int dim = _mesh.dimension();
const Real l2md = std::pow(lsq, 0.5 * (2.0 - dim));
const Real l1md = std::pow(lsq, 0.5 * (1.0 - dim));
/// Loop over all the phases
for (unsigned int ph = 0; ph < _num_phases; ++ph)
{
// FIRST:
// this is a dirty way of getting around precision loss problems
// and problems at steadystate where upwinding oscillates from
// node-to-node causing nonconvergence.
// The residual = int_{ele}*grad_test*k*(gradP - rho*g) = L^(d-1)*k*(gradP - rho*g), where d is
// dimension
// I assume that if one nodal P changes by P*1E-8 then this is
// a "negligible" change. The residual will change by L^(d-2)*k*P*1E-8
// Similarly if rho*g changes by rho*g*1E-8 then this is a "negligible change"
// Hence the formulae below, with grad_test = 1/L
Real pnorm = 0.0;
Real gravnorm = 0.0;
for (unsigned int n = 0; n < num_nodes; ++n)
{
pnorm += _pp[n][ph] * _pp[n][ph];
gravnorm += _fluid_density_node[n][ph] * _fluid_density_node[n][ph];
}
gravnorm *= _gravity * _gravity;
const Real cutoff = 1.0E-8 * knorm * (std::sqrt(pnorm) * l2md + std::sqrt(gravnorm) * l1md);
bool reached_steady = true;
for (unsigned int nodenum = 0; nodenum < num_nodes; ++nodenum)
{
if (component_re[nodenum][ph] >= cutoff)
{
reached_steady = false;
break;
}
}
Real mob;
Real dmob;
/// Define variables used to ensure mass conservation
Real total_mass_out = 0.0;
Real total_in = 0.0;
/// The following holds derivatives of these
std::vector<Real> dtotal_mass_out;
std::vector<Real> dtotal_in;
if (res_or_jac == JacRes::CALCULATE_JACOBIAN)
{
dtotal_mass_out.resize(num_nodes);
dtotal_in.resize(num_nodes);
for (unsigned int n = 0; n < num_nodes; ++n)
{
dtotal_mass_out[n] = 0.0;
dtotal_in[n] = 0.0;
}
}
/// Perform the upwinding using the mobility
std::vector<bool> upwind_node(num_nodes);
for (unsigned int n = 0; n < num_nodes; ++n)
{
if (component_re[n][ph] >= cutoff || reached_steady) // upstream node
{
upwind_node[n] = true;
/// The mobility at the upstream node
mob = mobility(n, ph);
if (res_or_jac == JacRes::CALCULATE_JACOBIAN)
{
/// The derivative of the mobility wrt the PorousFlow variable
dmob = dmobility(n, ph, pvar);
for (_j = 0; _j < _phi.size(); _j++)
component_ke[n][_j][ph] *= mob;
if (_test.size() == _phi.size())
/* mobility at node=n depends only on the variables at node=n, by construction. For
* linear-lagrange variables, this means that Jacobian entries involving the derivative
* of mobility will only be nonzero for derivatives wrt variables at node=n. Hence the
* [n][n] in the line below. However, for other variable types (eg constant monomials)
* I cannot tell what variable number contributes to the derivative. However, in all
* cases I can possibly imagine, the derivative is zero anyway, since in the full
* upwinding scheme, mobility shouldn't depend on these other sorts of variables.
*/
component_ke[n][n][ph] += dmob * component_re[n][ph];
for (_j = 0; _j < _phi.size(); _j++)
dtotal_mass_out[_j] += component_ke[n][_j][ph];
}
component_re[n][ph] *= mob;
total_mass_out += component_re[n][ph];
}
else
{
upwind_node[n] = false;
total_in -= component_re[n][ph]; /// note the -= means the result is positive
if (res_or_jac == JacRes::CALCULATE_JACOBIAN)
for (_j = 0; _j < _phi.size(); _j++)
dtotal_in[_j] -= component_ke[n][_j][ph];
}
}
/// Conserve mass over all phases by proportioning the total_mass_out mass to the inflow nodes, weighted by their component_re values
if (!reached_steady)
{
for (unsigned int n = 0; n < num_nodes; ++n)
{
if (!upwind_node[n]) // downstream node
{
if (res_or_jac == JacRes::CALCULATE_JACOBIAN)
for (_j = 0; _j < _phi.size(); _j++)
{
component_ke[n][_j][ph] *= total_mass_out / total_in;
component_ke[n][_j][ph] +=
component_re[n][ph] * (dtotal_mass_out[_j] / total_in -
dtotal_in[_j] * total_mass_out / total_in / total_in);
}
component_re[n][ph] *= total_mass_out / total_in;
}
}
}
}
/// Add results to the Residual or Jacobian
if (res_or_jac == JacRes::CALCULATE_RESIDUAL)
{
DenseVector<Number> & re = _assembly.residualBlock(_var.number());
_local_re.resize(re.size());
_local_re.zero();
for (_i = 0; _i < _test.size(); _i++)
for (unsigned int ph = 0; ph < _num_phases; ++ph)
_local_re(_i) += component_re[_i][ph];
re += _local_re;
if (_has_save_in)
{
Threads::spin_mutex::scoped_lock lock(Threads::spin_mtx);
for (unsigned int i = 0; i < _save_in.size(); i++)
_save_in[i]->sys().solution().add_vector(_local_re, _save_in[i]->dofIndices());
}
}
if (res_or_jac == JacRes::CALCULATE_JACOBIAN)
{
_local_ke.resize(ke.m(), ke.n());
_local_ke.zero();
for (_i = 0; _i < _test.size(); _i++)
for (_j = 0; _j < _phi.size(); _j++)
for (unsigned int ph = 0; ph < _num_phases; ++ph)
_local_ke(_i, _j) += component_ke[_i][_j][ph];
ke += _local_ke;
if (_has_diag_save_in && jvar == _var.number())
{
unsigned int rows = ke.m();
DenseVector<Number> diag(rows);
for (unsigned int i = 0; i < rows; i++)
diag(i) = _local_ke(i, i);
Threads::spin_mutex::scoped_lock lock(Threads::spin_mtx);
for (unsigned int i = 0; i < _diag_save_in.size(); i++)
_diag_save_in[i]->sys().solution().add_vector(diag, _diag_save_in[i]->dofIndices());
}
}
}
void
Q2PPorepressureFlux::upwind(bool compute_res, bool compute_jac, unsigned int jvar)
{
if (compute_jac && !(jvar == _var.number() || jvar == _sat_var))
return;
// calculate the mobility values and their derivatives
prepareNodalValues();
// compute the residual without the mobility terms
// Even if we are computing the jacobian we still need this
// in order to see which nodes are upwind and which are downwind
DenseVector<Number> & re = _assembly.residualBlock(_var.number());
_local_re.resize(re.size());
_local_re.zero();
for (_i = 0; _i < _test.size(); _i++)
for (_qp = 0; _qp < _qrule->n_points(); _qp++)
_local_re(_i) += _JxW[_qp] * _coord[_qp] * computeQpResidual();
DenseMatrix<Number> & ke = _assembly.jacobianBlock(_var.number(), jvar);
if (compute_jac)
{
_local_ke.resize(ke.m(), ke.n());
_local_ke.zero();
for (_i = 0; _i < _test.size(); _i++)
for (_j = 0; _j < _phi.size(); _j++)
for (_qp = 0; _qp < _qrule->n_points(); _qp++)
_local_ke(_i, _j) += _JxW[_qp] * _coord[_qp] * computeQpJac(jvar);
}
// Now perform the upwinding by multiplying the residuals at the
// upstream nodes by their mobilities
//
// The residual for the kernel is the darcy flux.
// This is
// R_i = int{mobility*flux_no_mob} = int{mobility*grad(pot)*permeability*grad(test_i)}
// for node i. where int is the integral over the element.
// However, in fully-upwind, the first step is to take the mobility outside the
// integral, which was done in the _local_re calculation above.
//
// NOTE: Physically _local_re(_i) is a measure of fluid flowing out of node i
// If we had left in mobility, it would be exactly the mass flux flowing out of node i.
//
// This leads to the definition of upwinding:
// ***
// If _local_re(i) is positive then we use mobility_i. That is
// we use the upwind value of mobility.
// ***
//
// The final subtle thing is we must also conserve fluid mass: the total mass
// flowing out of node i must be the sum of the masses flowing
// into the other nodes.
// FIRST:
// this is a dirty way of getting around precision loss problems
// and problems at steadystate where upwinding oscillates from
// node-to-node causing nonconvergence.
// I'm not sure if i actually need to do this in moose. Certainly
// in cosflow it is necessary.
// I will code a better algorithm if necessary
bool reached_steady = true;
for (unsigned int nodenum = 0; nodenum < _num_nodes; ++nodenum)
{
if (_local_re(nodenum) >= 1E-20)
{
reached_steady = false;
break;
}
}
reached_steady = false;
// DEFINE VARIABLES USED TO ENSURE MASS CONSERVATION
// total mass out - used for mass conservation
Real total_mass_out = 0;
// total flux in
Real total_in = 0;
// the following holds derivatives of these
std::vector<Real> dtotal_mass_out;
std::vector<Real> dtotal_in;
if (compute_jac)
{
dtotal_mass_out.assign(_num_nodes, 0);
dtotal_in.assign(_num_nodes, 0);
}
// PERFORM THE UPWINDING!
for (unsigned int nodenum = 0; nodenum < _num_nodes; ++nodenum)
{
if (_local_re(nodenum) >= 0 || reached_steady) // upstream node
{
if (compute_jac)
{
for (_j = 0; _j < _phi.size(); _j++)
_local_ke(nodenum, _j) *= _mobility[nodenum];
if (jvar == _var.number())
// deriv wrt P
_local_ke(nodenum, nodenum) += _dmobility_dp[nodenum] * _local_re(nodenum);
else
// deriv wrt S
_local_ke(nodenum, nodenum) += _dmobility_ds[nodenum] * _local_re(nodenum);
for (_j = 0; _j < _phi.size(); _j++)
dtotal_mass_out[_j] += _local_ke(nodenum, _j);
}
_local_re(nodenum) *= _mobility[nodenum];
total_mass_out += _local_re(nodenum);
}
else
{
total_in -= _local_re(nodenum); // note the -= means the result is positive
if (compute_jac)
for (_j = 0; _j < _phi.size(); _j++)
dtotal_in[_j] -= _local_ke(nodenum, _j);
}
}
// CONSERVE MASS
// proportion the total_mass_out mass to the inflow nodes, weighting by their _local_re values
if (!reached_steady)
for (unsigned int nodenum = 0; nodenum < _num_nodes; ++nodenum)
if (_local_re(nodenum) < 0)
{
if (compute_jac)
for (_j = 0; _j < _phi.size(); _j++)
{
_local_ke(nodenum, _j) *= total_mass_out / total_in;
_local_ke(nodenum, _j) +=
_local_re(nodenum) * (dtotal_mass_out[_j] / total_in -
dtotal_in[_j] * total_mass_out / total_in / total_in);
}
_local_re(nodenum) *= total_mass_out / total_in;
}
// ADD RESULTS TO RESIDUAL OR JACOBIAN
if (compute_res)
{
re += _local_re;
if (_has_save_in)
{
Threads::spin_mutex::scoped_lock lock(Threads::spin_mtx);
for (unsigned int i = 0; i < _save_in.size(); i++)
_save_in[i]->sys().solution().add_vector(_local_re, _save_in[i]->dofIndices());
}
}
if (compute_jac)
{
ke += _local_ke;
if (_has_diag_save_in && jvar == _var.number())
{
const unsigned int rows = ke.m();
DenseVector<Number> diag(rows);
for (unsigned int i = 0; i < rows; i++)
diag(i) = _local_ke(i, i);
Threads::spin_mutex::scoped_lock lock(Threads::spin_mtx);
for (unsigned int i = 0; i < _diag_save_in.size(); i++)
_diag_save_in[i]->sys().solution().add_vector(diag, _diag_save_in[i]->dofIndices());
}
}
}
void
PorousFlowDarcyBase::computeResidualAndJacobian(JacRes res_or_jac, unsigned int jvar)
{
if ((res_or_jac == JacRes::CALCULATE_JACOBIAN) && _dictator.notPorousFlowVariable(jvar))
return;
// The PorousFlow variable index corresponding to the variable number jvar
const unsigned int pvar =
((res_or_jac == JacRes::CALCULATE_JACOBIAN) ? _dictator.porousFlowVariableNum(jvar) : 0);
DenseMatrix<Number> & ke = _assembly.jacobianBlock(_var.number(), jvar);
if ((ke.n() == 0) && (res_or_jac == JacRes::CALCULATE_JACOBIAN)) // this removes a problem
// encountered in the initial
// timestep when
// use_displaced_mesh=true
return;
// The number of nodes in the element
const unsigned int num_nodes = _test.size();
// Compute the residual and jacobian without the mobility terms. Even if we are computing the
// Jacobian we still need this in order to see which nodes are upwind and which are downwind.
for (unsigned ph = 0; ph < _num_phases; ++ph)
{
_proto_flux[ph].assign(num_nodes, 0);
for (_qp = 0; _qp < _qrule->n_points(); _qp++)
{
for (_i = 0; _i < num_nodes; ++_i)
_proto_flux[ph][_i] += _JxW[_qp] * _coord[_qp] * darcyQp(ph);
}
}
// for this element, record whether each node is "upwind" or "downwind" (or neither)
const unsigned elem = _current_elem->id();
if (_num_upwinds.find(elem) == _num_upwinds.end())
{
_num_upwinds[elem] = std::vector<std::vector<unsigned>>(_num_phases);
_num_downwinds[elem] = std::vector<std::vector<unsigned>>(_num_phases);
for (unsigned ph = 0; ph < _num_phases; ++ph)
{
_num_upwinds[elem][ph].assign(num_nodes, 0);
_num_downwinds[elem][ph].assign(num_nodes, 0);
}
}
// record the information once per nonlinear iteration
if (res_or_jac == JacRes::CALCULATE_JACOBIAN && jvar == _var.number())
{
for (unsigned ph = 0; ph < _num_phases; ++ph)
{
for (unsigned nod = 0; nod < num_nodes; ++nod)
{
if (_proto_flux[ph][nod] > 0)
_num_upwinds[elem][ph][nod]++;
else if (_proto_flux[ph][nod] < 0)
_num_downwinds[elem][ph][nod]++;
}
}
}
// based on _num_upwinds and _num_downwinds, calculate the maximum number
// of upwind-downwind swaps that have been encountered in this timestep
// for this element
std::vector<unsigned> max_swaps(_num_phases, 0);
for (unsigned ph = 0; ph < _num_phases; ++ph)
{
for (unsigned nod = 0; nod < num_nodes; ++nod)
max_swaps[ph] = std::max(
max_swaps[ph], std::min(_num_upwinds[elem][ph][nod], _num_downwinds[elem][ph][nod]));
}
// size the _jacobian correctly and calculate it for the case residual = _proto_flux
if (res_or_jac == JacRes::CALCULATE_JACOBIAN)
{
for (unsigned ph = 0; ph < _num_phases; ++ph)
{
_jacobian[ph].resize(ke.m());
for (_i = 0; _i < _test.size(); _i++)
{
_jacobian[ph][_i].assign(ke.n(), 0.0);
for (_j = 0; _j < _phi.size(); _j++)
for (_qp = 0; _qp < _qrule->n_points(); _qp++)
_jacobian[ph][_i][_j] += _JxW[_qp] * _coord[_qp] * darcyQpJacobian(jvar, ph);
}
}
}
// Loop over all the phases, computing the mass flux, which
// gets placed into _proto_flux, and the derivative of this
// which gets placed into _jacobian
for (unsigned int ph = 0; ph < _num_phases; ++ph)
{
if (max_swaps[ph] < _full_upwind_threshold)
fullyUpwind(res_or_jac, ph, pvar);
else
{
switch (_fallback_scheme)
{
case FallbackEnum::QUICK:
quickUpwind(res_or_jac, ph, pvar);
break;
case FallbackEnum::HARMONIC:
harmonicMean(res_or_jac, ph, pvar);
break;
}
}
}
// Add results to the Residual or Jacobian
if (res_or_jac == JacRes::CALCULATE_RESIDUAL)
{
DenseVector<Number> & re = _assembly.residualBlock(_var.number());
_local_re.resize(re.size());
_local_re.zero();
for (_i = 0; _i < _test.size(); _i++)
for (unsigned int ph = 0; ph < _num_phases; ++ph)
_local_re(_i) += _proto_flux[ph][_i];
re += _local_re;
if (_has_save_in)
{
Threads::spin_mutex::scoped_lock lock(Threads::spin_mtx);
for (unsigned int i = 0; i < _save_in.size(); i++)
_save_in[i]->sys().solution().add_vector(_local_re, _save_in[i]->dofIndices());
}
}
if (res_or_jac == JacRes::CALCULATE_JACOBIAN)
{
_local_ke.resize(ke.m(), ke.n());
_local_ke.zero();
for (_i = 0; _i < _test.size(); _i++)
for (_j = 0; _j < _phi.size(); _j++)
for (unsigned int ph = 0; ph < _num_phases; ++ph)
_local_ke(_i, _j) += _jacobian[ph][_i][_j];
ke += _local_ke;
if (_has_diag_save_in && jvar == _var.number())
{
unsigned int rows = ke.m();
DenseVector<Number> diag(rows);
for (unsigned int i = 0; i < rows; i++)
diag(i) = _local_ke(i, i);
Threads::spin_mutex::scoped_lock lock(Threads::spin_mtx);
for (unsigned int i = 0; i < _diag_save_in.size(); i++)
_diag_save_in[i]->sys().solution().add_vector(diag, _diag_save_in[i]->dofIndices());
}
}
}