quadratic_least_squares.h

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/*
 Copyright (C) 2019 - 2022-2020 by the authors of the ASPECT code.

 This file is part of ASPECT.

 ASPECT is free software; you can redistribute it and/or modify
 it under the terms of the GNU General Public License as published by
 the Free Software Foundation; either version 2, or (at your option)
 any later version.

 ASPECT is distributed in the hope that it will be useful,
 but WITHOUT ANY WARRANTY; without even the implied warranty of
 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 GNU General Public License for more details.

 You should have received a copy of the GNU General Public License
 along with ASPECT; see the file LICENSE.  If not see
 <http://www.gnu.org/licenses/>.
 */

#ifndef _aspect_particle_interpolator_quadratic_least_squares_h
#define _aspect_particle_interpolator_quadratic_least_squares_h

#include <aspect/particle/interpolator/interface.h>
#include <aspect/particle/interpolator/cell_average.h>
#include <aspect/simulator_access.h>
#include <deal.II/lac/lapack_full_matrix.h>

namespace aspect
{
  namespace Particle
  {
    namespace Interpolator
    {
      template <int dim>
      class QuadraticLeastSquares : public Interface<dim>, public aspect::SimulatorAccess<dim>
      {
        public:
          std::vector<std::vector<double>>
          properties_at_points(const ParticleHandler<dim> &particle_handler,
                               const std::vector<Point<dim>> &positions,
                               const ComponentMask &selected_properties,
                               const typename parallel::distributed::Triangulation<dim>::active_cell_iterator &cell) const override;

          // avoid -Woverloaded-virtual:
          using Interface<dim>::properties_at_points;

          static
          void
          declare_parameters (ParameterHandler &prm);

          void
          parse_parameters (ParameterHandler &prm) override;

        private:
          Interpolator::CellAverage<dim> fallback_interpolator;

          ComponentMask use_quadratic_least_squares_limiter;

          ComponentMask use_boundary_extrapolation;

          double evaluate_interpolation_function(const Vector<double> &coefficients, const Point<dim> &position) const;

          std::pair<double, double> get_interpolation_bounds(const ::Vector<double> &coefficients) const;

          /*
           * Find all points that may contain the minimum or maximum values of the interpolation in the cell.
           */
          std::vector<::Point<dim>> get_critical_points(const ::Vector<double> &coefficients) const;

      };
    }
  }
}

#endif