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Add distance weighted average interpolator
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‎doc/modules/changes/20240609_gassmoeller

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Added: A new particle interpolator plugin 'distance weighted average' that
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computes the interpolated properties as an average of particle properties
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weighted by a distance function. This plugin is similarly accurate
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as the 'cell average' interpolator, but provides smoother results and is
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less susceptible to jumps in interpolated properties if particles move
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small distances.
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<br>
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(Rene Gassmoeller, 2024/06/09)

‎include/aspect/particle/interpolator/distance_weighted_average.h

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/*
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Copyright (C) 2024 by the authors of the ASPECT code.
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This file is part of ASPECT.
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ASPECT is free software; you can redistribute it and/or modify
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation; either version 2, or (at your option)
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any later version.
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ASPECT is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with ASPECT; see the file LICENSE. If not see
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<http://www.gnu.org/licenses/>.
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*/
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#ifndef _aspect_particle_interpolator_distance_weighted_average_h
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#define _aspect_particle_interpolator_distance_weighted_average_h
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#include <aspect/particle/interpolator/interface.h>
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#include <aspect/simulator_access.h>
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#include <deal.II/grid/grid_tools_cache.h>
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namespace aspect
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{
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namespace Particle
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{
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namespace Interpolator
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{
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/**
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* Return the interpolated properties of all particles of the given cell using bilinear least squares method.
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* Currently, only the two dimensional model is supported.
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*
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* @ingroup ParticleInterpolators
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*/
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template <int dim>
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class DistanceWeightedAverage : public Interface<dim>, public aspect::SimulatorAccess<dim>
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{
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public:
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/**
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* Update function. Called once at the beginning of each time step.
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*/
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void update() override;
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/**
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* Return the cell-wise evaluated particle properties at the given @p positions.
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*/
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std::vector<std::vector<double>>
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properties_at_points(const ParticleHandler<dim> &particle_handler,
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const std::vector<Point<dim>> &positions,
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const ComponentMask &selected_properties,
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const typename parallel::distributed::Triangulation<dim>::active_cell_iterator &cell) const override;
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// avoid -Woverloaded-virtual:
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using Interface<dim>::properties_at_points;
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private:
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/**
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* Cached information.
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*/
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std::vector<std::set<typename Triangulation<dim>::active_cell_iterator>> vertex_to_cell_map;
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};
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}
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}
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}
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#endif

‎source/particle/interpolator/distance_weighted_average.cc

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/*
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Copyright (C) 2024 by the authors of the ASPECT code.
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This file is part of ASPECT.
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ASPECT is free software; you can redistribute it and/or modify
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation; either version 2, or (at your option)
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any later version.
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ASPECT is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with ASPECT; see the file LICENSE. If not see
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<http://www.gnu.org/licenses/>.
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*/
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#include <aspect/particle/interpolator/distance_weighted_average.h>
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#include <deal.II/base/signaling_nan.h>
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#include <deal.II/grid/grid_tools.h>
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namespace aspect
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{
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namespace Particle
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{
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namespace Interpolator
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{
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namespace internal
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{
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double weight (const double distance, const double cell_width)
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{
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// linear weight function (hat function)
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return std::max(1.0 - (distance/cell_width),0.0);
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}
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}
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template <int dim>
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void
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DistanceWeightedAverage<dim>::update()
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{
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vertex_to_cell_map = GridTools::vertex_to_cell_map(this->get_triangulation());
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}
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template <int dim>
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std::vector<std::vector<double>>
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DistanceWeightedAverage<dim>::properties_at_points(const ParticleHandler<dim> &particle_handler,
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const std::vector<Point<dim>> &positions,
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const ComponentMask &selected_properties,
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const typename parallel::distributed::Triangulation<dim>::active_cell_iterator &cell) const
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{
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const unsigned int n_interpolate_positions = positions.size();
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const unsigned int n_particle_properties = particle_handler.n_properties_per_particle();
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// Create with signaling NaNs
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std::vector<std::vector<double>> cell_properties(n_interpolate_positions,
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std::vector<double>(n_particle_properties,
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numbers::signaling_nan<double>()));
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// Set requested properties to 0.0
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for (unsigned int index_positions = 0; index_positions < n_interpolate_positions; ++index_positions)
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for (unsigned int index_properties = 0; index_properties < n_particle_properties; ++index_properties)
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if (selected_properties[index_properties])
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cell_properties[index_positions][index_properties] = 0.0;
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std::set<typename Triangulation<dim>::active_cell_iterator> cell_and_neighbors;
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for (const auto v : cell->vertex_indices())
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{
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const unsigned int vertex_index = cell->vertex_index(v);
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cell_and_neighbors.insert(vertex_to_cell_map[vertex_index].begin(),
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vertex_to_cell_map[vertex_index].end());
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}
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const double interpolation_support = 0.5 * cell->diameter();
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std::vector<double> integrated_weight(n_interpolate_positions,0.0);
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for (const auto &current_cell: cell_and_neighbors)
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{
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const typename ParticleHandler<dim>::particle_iterator_range particle_range =
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particle_handler.particles_in_cell(current_cell);
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for (const auto &particle: particle_range)
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{
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const ArrayView<const double> particle_properties = particle.get_properties();
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unsigned int index_positions = 0;
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for (const auto &interpolation_point: positions)
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{
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const double distance = particle.get_location().distance(interpolation_point);
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const double weight = internal::weight(distance,interpolation_support);
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for (unsigned int index_properties = 0; index_properties < particle_properties.size(); ++index_properties)
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if (selected_properties[index_properties])
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cell_properties[index_positions][index_properties] += weight * particle_properties[index_properties];
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integrated_weight[index_positions] += weight;
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++index_positions;
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}
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}
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}
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for (unsigned int index_positions = 0; index_positions < n_interpolate_positions; ++index_positions)
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{
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AssertThrow(integrated_weight[index_positions] > 0.0, ExcInternalError());
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for (unsigned int index_properties = 0; index_properties < n_particle_properties; ++index_properties)
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if (selected_properties[index_properties])
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cell_properties[index_positions][index_properties] /= integrated_weight[index_positions];
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}
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return cell_properties;
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}
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}
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}
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}
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// explicit instantiations
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namespace aspect
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{
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namespace Particle
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{
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namespace Interpolator
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{
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ASPECT_REGISTER_PARTICLE_INTERPOLATOR(DistanceWeightedAverage,
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"distance weighted average",
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"Interpolates particle properties onto a vector of points using a "
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"distance weighed averaging method.")
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}
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}
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}

‎tests/particle_interpolator_distance_weighted_average.prm

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# A test that performs interpolation from particle properties to
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# compositional fields that are flagged as 'particle' advected
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# fields.
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# MPI: 2
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set Dimension = 2
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set End time = 70
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set Use years in output instead of seconds = false
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subsection Geometry model
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set Model name = box
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subsection Box
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set X extent = 0.9142
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set Y extent = 1.0000
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end
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end
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subsection Boundary velocity model
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set Tangential velocity boundary indicators = left, right
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set Zero velocity boundary indicators = bottom, top
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end
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subsection Material model
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set Model name = simple
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subsection Simple model
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set Reference density = 1010
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set Viscosity = 1e2
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set Thermal expansion coefficient = 0
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set Density differential for compositional field 1 = -10
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end
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end
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subsection Gravity model
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set Model name = vertical
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subsection Vertical
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set Magnitude = 10
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end
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end
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############### Parameters describing the temperature field
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# Note: The temperature plays no role in this model
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subsection Initial temperature model
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set Model name = function
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subsection Function
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set Function expression = 0
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end
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end
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############### Parameters describing the compositional field
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# Note: The compositional field is what drives the flow
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# in this example
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subsection Compositional fields
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set Number of fields = 3
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set Names of fields = advection_field, advection_particle, advection_particle2
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set Compositional field methods = field, particles, particles
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set Mapped particle properties = advection_particle2:velocity [1], advection_particle:function
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end
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subsection Initial composition model
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set Model name = function
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subsection Function
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set Variable names = x,z
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set Function constants = pi=3.1415926
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set Function expression = 0.5*(1+tanh((0.2+0.02*cos(pi*x/0.9142)-z)/0.02));0.0;0.0
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end
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end
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subsection Discretization
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set Use discontinuous composition discretization = true
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end
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############### Parameters describing the discretization
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subsection Mesh refinement
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set Initial adaptive refinement = 0
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set Strategy = composition
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set Initial global refinement = 4
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set Time steps between mesh refinement = 0
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set Coarsening fraction = 0.05
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set Refinement fraction = 0.3
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end
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############### Parameters describing what to do with the solution
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subsection Postprocess
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set List of postprocessors = velocity statistics, composition statistics,particles
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subsection Visualization
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set Interpolate output = false
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set Time between graphical output = 70
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end
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subsection Particles
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set Number of particles = 100000
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set Time between data output = 70
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set Data output format = none
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set List of particle properties = velocity, function, initial composition
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set Interpolation scheme = distance weighted average
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set Update ghost particles = true
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set Particle generator name = random uniform
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subsection Function
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set Variable names = x,z
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set Function expression = 0.5*(1+tanh((0.2+0.02*cos(pi*x/0.9142)-z)/0.02))
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end
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subsection Generator
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subsection Probability density function
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set Variable names = x,z
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set Function expression = x*x*z
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end
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end
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end
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end

‎tests/particle_interpolator_distance_weighted_average/screen-output

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Number of active cells: 256 (on 5 levels)
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Number of degrees of freedom: 10,468 (2,178+289+1,089+2,304+2,304+2,304)
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*** Timestep 0: t=0 seconds, dt=0 seconds
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Skipping temperature solve because RHS is zero.
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Advecting particles... done.
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Solving advection_field system ... 0 iterations.
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Rebuilding Stokes preconditioner...
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Solving Stokes system... 34+0 iterations.
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Postprocessing:
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RMS, max velocity: 0.000181 m/s, 0.000404 m/s
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Compositions min/max/mass: 0/1/0.1825 // 0/1/0.1828 // 0/0/0
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Number of advected particles: 100000
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*** Timestep 1: t=70 seconds, dt=70 seconds
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Skipping temperature solve because RHS is zero.
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Advecting particles... done.
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Solving advection_field system ... 5 iterations.
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Solving Stokes system... 34+0 iterations.
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Postprocessing:
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RMS, max velocity: 0.000328 m/s, 0.000732 m/s
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Compositions min/max/mass: -0.007595/1.023/0.1825 // 0/1/0.1829 // -0.0002466/0.0003166/-1.013e-08
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Number of advected particles: 100000
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Termination requested by criterion: end time
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