LMWeightedGapUserObject.C

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//* This file is part of the MOOSE framework
//* https://mooseframework.inl.gov
//*
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//* https://github.com/idaholab/moose/blob/master/COPYRIGHT
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//* Licensed under LGPL 2.1, please see LICENSE for details
//* https://www.gnu.org/licenses/lgpl-2.1.html
 
#include "LMWeightedGapUserObject.h"
#include "MooseVariableFE.h"
#include "SystemBase.h"
#include "MortarContactUtils.h"
#include "AutomaticMortarGeneration.h"
 
#include "libmesh/fe.h"
 
registerMooseObject("ContactApp", LMWeightedGapUserObject);
 
InputParameters
LMWeightedGapUserObject::newParams()
{
  auto params = emptyInputParameters();
  params.addRequiredCoupledVar(
      "lm_variable", "The Lagrange multiplier variable representing the contact pressure.");
  params.addParam<bool>(
      "use_petrov_galerkin", false, "Whether to use the Petrov-Galerkin approach.");
  params.addCoupledVar("aux_lm",
                       "Auxiliary Lagrange multiplier variable that is utilized together with the "
                       "Petrov-Galerkin approach.");
  params.addParam<bool>(
      "use_nodal_scaling",
      false,
      "Whether to apply the node-based Lagrange-multiplier scaling of Popp et al. (2013) to "
      "improve the conditioning of the linear system when secondary elements are only partially "
      "covered (edge dropping). See the documentation for the current limitations.");
  return params;
}
 
InputParameters
LMWeightedGapUserObject::validParams()
{
  InputParameters params = WeightedGapUserObject::validParams();
  params.addClassDescription(
      "Provides the mortar normal Lagrange multiplier for constraint enforcement.");
  params += LMWeightedGapUserObject::newParams();
  return params;
}
 
LMWeightedGapUserObject::LMWeightedGapUserObject(const InputParameters & parameters)
  : WeightedGapUserObject(parameters),
    _lm_var(getVar("lm_variable", 0)),
    _use_petrov_galerkin(getParam<bool>("use_petrov_galerkin")),
    _aux_lm_var(isCoupled("aux_lm") ? getVar("aux_lm", 0) : nullptr),
    _use_nodal_scaling(getParam<bool>("use_nodal_scaling"))
{
  checkInput(_lm_var, "lm_variable");
  verifyLagrange(*_lm_var, "lm_variable");
 
  if (_use_petrov_galerkin && ((!isParamValid("aux_lm")) || _aux_lm_var == nullptr))
    paramError("use_petrov_galerkin",
               "We need to specify an auxiliary variable `aux_lm` while using the Petrov-Galerkin "
               "approach");
 
  if (_use_petrov_galerkin && _aux_lm_var->useDual())
    paramError("aux_lm",
               "Auxiliary LM variable needs to use standard shape function, i.e., set `use_dual = "
               "false`.");
 
  if (_use_nodal_scaling)
  {
    // kappa_j's denominator int_e N_j is zero at TRI6 and TET10 vertices and negative at QUAD8 and
    // HEX20 corners, and its numerator has to be integrated with the same basis, so every variable
    // entering kappa_j has to be first order.
    if (_lm_var->feType().order != FIRST || _disp_x_var->feType().order != FIRST ||
        (_use_petrov_galerkin && _aux_lm_var->feType().order != FIRST))
      paramError("use_nodal_scaling",
                 "Node-based scaling is only implemented for first-order Lagrange multiplier and "
                 "displacement variables.");
 
    // Scaling rescales the partially covered multiplier DOFs that the default treatment zeroes.
    if (!getParam<bool>("correct_edge_dropping"))
      paramError("use_nodal_scaling",
                 "Node-based scaling requires 'correct_edge_dropping = true'.");
 
    // Built once here rather than per element in fullNodalIntegrals().
    const FEType fe_type(FIRST, LAGRANGE);
    const auto lower_dim = _subproblem.mesh().dimension() - 1;
    _nodal_scaling_fe = FEBase::build(lower_dim, fe_type);
    _nodal_scaling_qrule = std::make_unique<QGauss>(lower_dim, fe_type.default_quadrature_order());
    _nodal_scaling_fe->attach_quadrature_rule(_nodal_scaling_qrule.get());
  }
}
 
void
LMWeightedGapUserObject::checkInput(const MooseVariable * const var,
                                    const std::string & var_param_name) const
{
  if (isCoupledConstant(var_param_name))
    paramError(var_param_name,
               "The Lagrange multiplier variable must be an actual variable and not a constant.");
  else if (!var)
    paramError(var_param_name,
               "The Lagrange multiplier variables must be provided and be actual variables.");
}
 
void
LMWeightedGapUserObject::verifyLagrange(const MooseVariable & var,
                                        const std::string & var_param_name) const
{
  if (var.feType().family != LAGRANGE)
    paramError(var_param_name, "The Lagrange multiplier variables must be of Lagrange type");
}
 
const VariableTestValue &
LMWeightedGapUserObject::test() const
{
  return _use_petrov_galerkin ? _aux_lm_var->phiLower() : _lm_var->phiLower();
}
 
const ADVariableValue &
LMWeightedGapUserObject::contactPressure() const
{
  return _use_nodal_scaling ? _scaled_contact_pressure : _lm_var->adSlnLower();
}
 
void
LMWeightedGapUserObject::initialize()
{
  WeightedGapUserObject::initialize();
  initializeNodalScaling();
}
 
void
LMWeightedGapUserObject::finalize()
{
  WeightedGapUserObject::finalize();
  finalizeNodalScaling();
}
 
void
LMWeightedGapUserObject::computeQpIProperties()
{
  WeightedGapUserObject::computeQpIProperties();
  computeQpINodalScaling();
}
 
void
LMWeightedGapUserObject::initializeNodalScaling()
{
  if (!_use_nodal_scaling)
    return;
 
  _dof_to_covered_fraction_sum.clear();
  _dof_to_nodal_scale.clear();
  _elem_to_full_nodal_integral.clear();
  _dof_to_full_normalization.clear();
  _full_normalization_elems.clear();
}
 
void
LMWeightedGapUserObject::computeQpINodalScaling()
{
  if (!_use_nodal_scaling)
    return;
 
  const auto * const dof = static_cast<const DofObject *>(_lower_secondary_elem->node_ptr(_i));
 
  // Numerator of kappa_j (Popp 2013 eq. 36): covered fraction (int_{e_int} N_j)/(int_e N_j) summed
  // over adjacent elements. Both use the standard N_j (fePhiLower), not the dual test, so kappa_j
  // is 1 at full coverage in every coordinate system.
  const auto & std_phi = _assembly.fePhiLower<Real>(_disp_x_var->feType());
  const auto & full_integrals = fullNodalIntegrals(_lower_secondary_elem);
  _dof_to_covered_fraction_sum[dof] += std_phi[_i][_qp] * _qp_factor / full_integrals[_i];
 
  // Coverage-independent divisor for `normalize_c` (see normalizeCDivisor()): sum the full-element
  // integral int_e N_j once per distinct adjacent element, not once per quadrature point, since it
  // does not depend on qp and multiple mortar segments may cover the same element.
  if (_full_normalization_elems[dof].insert(_lower_secondary_elem->id()).second)
    _dof_to_full_normalization[dof] += full_integrals[_i];
}
 
void
LMWeightedGapUserObject::finalizeNodalScaling()
{
  if (!_use_nodal_scaling)
    return;
 
  // Reduce the processor-local numerators (the thread sums only rank-owned elements).
  // send_data_back = true: non-owner ranks also need kappa_j for the primary-side coupling.
  Moose::Mortar::Contact::communicateRealObject(_dof_to_covered_fraction_sum,
                                                _subproblem.mesh(),
                                                _nodal,
                                                _communicator,
                                                /*send_data_back=*/true);
 
  // Same reduction for the normalize_c divisor sum; also needed on non-owner ranks.
  Moose::Mortar::Contact::communicateRealObject(_dof_to_full_normalization,
                                                _subproblem.mesh(),
                                                _nodal,
                                                _communicator,
                                                /*send_data_back=*/true);
 
  // Divide by n_j^e (adjacent-element count, including fully dropped neighbors) for the eq. 36
  // mean; the fully ghosted mortar interface makes that count global on every process.
  const auto & nodes_to_secondary_elem = amg().nodesToSecondaryElem();
  for (const auto & [dof, fraction_sum] : _dof_to_covered_fraction_sum)
    _dof_to_nodal_scale[dof] =
        fraction_sum / libmesh_map_find(nodes_to_secondary_elem, dof->id()).size();
}
 
const std::vector<Real> &
LMWeightedGapUserObject::fullNodalIntegrals(const Elem * const elem)
{
  const auto it = _elem_to_full_nodal_integral.find(elem->id());
  if (it != _elem_to_full_nodal_integral.end())
    return it->second;
 
  // A separate finite element avoids reinit of the shared mortar-segment state.
  const std::vector<Real> & JxW = _nodal_scaling_fe->get_JxW();
  const std::vector<Point> & q_points = _nodal_scaling_fe->get_xyz();
  const std::vector<std::vector<Real>> & phi = _nodal_scaling_fe->get_phi();
  _nodal_scaling_fe->reinit(elem);
 
  std::vector<Real> integrals(phi.size(), 0);
  for (const auto qp : make_range(_nodal_scaling_qrule->n_points()))
  {
    Real coord;
    coordTransformFactor(_subproblem, elem->subdomain_id(), q_points[qp], coord);
    for (const auto j : index_range(integrals))
      integrals[j] += phi[j][qp] * JxW[qp] * coord;
  }
 
  return _elem_to_full_nodal_integral.emplace(elem->id(), std::move(integrals)).first->second;
}
 
void
LMWeightedGapUserObject::reinit()
{
  if (!_use_nodal_scaling)
    return;
 
  // The stored multiplier is scaled (zhat_j = kappa_j lambda_j); interpolate the physical pressure
  // sum_j Phi_j (zhat_j/kappa_j) for the coupling (Popp 2013 eq. 39), cached once per segment.
  // Phi_j is Real, so the multiplier derivatives are seeded exactly.
  const auto & phi = _lm_var->phiLower();
  const Elem * const lower_elem = _assembly.lowerDElem();
  const auto sys_num = _lm_var->sys().number();
  const auto var_num = _lm_var->number();
  const auto & current_solution = *_lm_var->sys().currentSolution();
 
  mooseAssert(phi.size(), "The Lagrange multiplier should have lower-dimensional shape functions");
  const std::size_t n_qp = phi[0].size();
  _scaled_contact_pressure.resize(n_qp);
  for (const auto qp : make_range(n_qp))
    _scaled_contact_pressure[qp] = 0;
 
  // Loop over the multiplier's shape functions, which on a second-order mesh are fewer than the
  // element's nodes
  for (const auto j : index_range(phi))
  {
    const Node * const node = lower_elem->node_ptr(j);
    const auto dof_index = node->dof_number(sys_num, var_num, /*component=*/0);
    ADReal lm_value = current_solution(dof_index);
    Moose::derivInsert(lm_value.derivatives(), dof_index, 1.);
    const ADReal physical_pressure = lm_value / nodalScale(node);
    for (const auto qp : make_range(n_qp))
      _scaled_contact_pressure[qp] += phi[j][qp] * physical_pressure;
  }
}
 
Real
LMWeightedGapUserObject::getNormalContactPressure(const Node * const node) const
{
  const auto sys_num = _lm_var->sys().number();
  const auto var_num = _lm_var->number();
  if (!node->n_dofs(sys_num, var_num))
    mooseError("No degrees of freedom for the Lagrange multiplier at the node. If this is being "
               "called from an aux kernel make sure that your aux variable has the same order as "
               "your Lagrange multiplier");
 
  const auto dof_number = node->dof_number(sys_num, var_num, /*component=*/0);
  // Recover the physical pressure lambda_j = zhat_j / kappa_j (Popp 2013 eq. 39). nodalScale() is
  // keyed by the displaced-mesh node pointer, and callers may pass a different pointer of the same
  // id, so map through the mesh to match -- exactly as getNormalGap() does above.
  return (*_lm_var->sys().currentSolution())(dof_number) /
         nodalScale(_subproblem.mesh().nodePtr(node->id()));
}