lorentz_force.cpp

Calculate Lorentz fore from magnetic field.It is not attemt to have accurate or realistic model of moving particles in magnetic field. This example was create to show how field evaluator works with precalculated magnetic field.

Todo:

use physical quantities

take in account higher order geometry

code panellisation, works serial only

Exaltation

\[ v_i = (p_{i+1} - p_{i-1}) / (2 \delta t) \\ (p_{i-1} - 2 p_i + p_{i+1}) / \delta t^2 = \frac{q}{m} v_i \times B_i \\ (p_{i-1} - 2 p_i + p_{i+1}) / \delta t^2 = \frac{q}{m} (p_{i+1} - p_{i-1}) / (2 \delta t) \times B_i \\ (p_{i-1} - 2 p_i + p_{i+1}) / \delta t = \frac{q}{m} (p_{i+1} - p_{i-1}) \times B_i / 2 \\ p_{i+1} / \delta t - p_{i+1} \times B_i / 2= (2 p_i - p_{i-1}) / \delta t - p_{i-1} \times B_i / 2 \\ p_{i+1} (\mathbf{1} / \delta t - \frac{q}{m} \mathbf{1} \times B_i / 2 )= (2 p_i - p_{i-1}) / \delta t - \frac{q}{m} p_{i-1} \times B_i / 2 \]

/**
 * \file lorentz_force.cpp
 * \example lorentz_force.cpp
 * \brief Calculate Lorentz fore from magnetic field.
 *
 * It is not attemt to have accurate or realistic model of moving particles in
 * magnetic field. This example was create to show how field evaluator works
 * with precalculated magnetic field.
 *
 * \todo use physical quantities
 * \todo take in account higher order geometry
 * \todo code panellisation, works serial only
 *
 * Exaltation
 * \f[
 *  v_i = (p_{i+1} - p_{i-1}) / (2 \delta t) \\
 *  (p_{i-1} - 2 p_i + p_{i+1}) / \delta t^2 = \frac{q}{m} v_i \times B_i \\
 *  (p_{i-1} - 2 p_i + p_{i+1}) / \delta t^2 = \frac{q}{m} (p_{i+1} - p_{i-1}) /
 * (2 \delta t)  \times B_i \\
 *  (p_{i-1} - 2 p_i + p_{i+1}) / \delta t = \frac{q}{m} (p_{i+1} - p_{i-1})
 * \times B_i / 2  \\
 *  p_{i+1} / \delta t - p_{i+1} \times B_i / 2= (2 p_i - p_{i-1}) / \delta t -
 * p_{i-1} \times B_i / 2 \\ p_{i+1} (\mathbf{1} / \delta t - \frac{q}{m}
 * \mathbf{1} \times B_i / 2 )= (2 p_i - p_{i-1}) / \delta t - \frac{q}{m}
 * p_{i-1} \times B_i / 2 \f]
 *
 * \ingroup maxwell_element
 */
 
/* This file is part of MoFEM.
 * MoFEM is free software: you can redistribute it and/or modify it under
 * the terms of the GNU Lesser General Public License as published by the
 * Free Software Foundation, either version 3 of the License, or (at your
 * option) any later version.
 *
 * MoFEM 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 Lesser General Public
 * License for more details.
 *
 * You should have received a copy of the GNU Lesser General Public
 * License along with MoFEM. If not, see <http://www.gnu.org/licenses/>. */
 
#include <BasicFiniteElements.hpp>
using namespace MoFEM;
 
static char help[] = "...\n\n";
 
int main(int argc, char *argv[]) {
 
  MoFEM::Core::Initialize(&argc, &argv, (char *)0, help);
 
  try {
 
    moab::Core mb_instance;
    moab::Interface &moab = mb_instance;
 
    ParallelComm *pcomm = ParallelComm::get_pcomm(&moab, MYPCOMM_INDEX);
    if (pcomm == NULL)
      pcomm = new ParallelComm(&moab, PETSC_COMM_WORLD);
 
    // Read parameters from line command
    PetscBool flg_file;
    char mesh_file_name[255];
    CHKERR PetscOptionsBegin(PETSC_COMM_WORLD, "", "Lorenz force configure",
                             "none");
    CHKERR PetscOptionsString("-my_file", "mesh file name", "", "solution.h5m",
                              mesh_file_name, 255, &flg_file);
    ierr = PetscOptionsEnd();
    CHKERRG(ierr);
 
    const char *option;
    option = "";
    CHKERR moab.load_file(mesh_file_name, 0, option);
 
    // Create mofem interface
    MoFEM::Core core(moab);
    MoFEM::Interface &m_field = core;
 
    CHKERR m_field.build_fields();
    CHKERR m_field.build_finite_elements();
    CHKERR m_field.build_adjacencies(BitRefLevel().set(0));
 
    // set up DM
    DM dm;
    CHKERR DMRegister_MoFEM("DMMOFEM");
    CHKERR DMCreate(PETSC_COMM_WORLD, &dm);
    CHKERR DMSetType(dm, "DMMOFEM");
    CHKERR DMMoFEMCreateMoFEM(dm, &m_field, "MAGNETIC_PROBLEM",
                              BitRefLevel().set(0));
    CHKERR DMSetFromOptions(dm);
    // add elements to blockData.dM
    CHKERR DMMoFEMAddElement(dm, "MAGNETIC");
    CHKERR DMSetUp(dm);
 
    using VolEle = VolumeElementForcesAndSourcesCore;
    using VolOp = VolumeElementForcesAndSourcesCore::UserDataOperator;
    // using SetPtsData = FieldEvaluatorInterface::SetPtsData;
    // using SetPts = FieldEvaluatorInterface::SetPts;
 
    /**
     * @brief Only for debuging
     */
    struct MyOpDebug : public VolOp {
 
      boost::shared_ptr<MatrixDouble> B;
      MyOpDebug(decltype(B) b) : VolOp("MAGNETIC_POTENTIAL", OPROW), B(b) {}
 
      MoFEMErrorCode doWork(int side, EntityType type,
                            DataForcesAndSourcesCore::EntData &data) {
        MoFEMFunctionBegin;
        if (type == MBEDGE && side == 0) {
          std::cout << "found " << (*B) << endl;
          std::cout << "data " << data.getFieldData() << endl;
        }
 
        MoFEMFunctionReturn(0);
      }
    };
 
    const double dist = 1e-12;             // Distance for tree search
    const int nb_random_points = 100;      // number of points
    const int nb_steps = 10000;            // number of time steps
    const int mod_step = 10;               // save every step
    const double dt = 1e-5;                // Time step size
    const double velocity_scale = 0.1;     // scale velocity vector
    const double magnetic_field_scale = 1; // scale magnetic field vector
    const double scale_box = 0.5; // scale box where partices are placed
 
    FieldEvaluatorInterface *field_eval_ptr;
    CHKERR m_field.getInterface(field_eval_ptr);
 
    // Get access to data
    auto data_at_pts = field_eval_ptr->getData<VolEle>();
    auto vol_ele = data_at_pts->feMethodPtr.lock();
    if (!vol_ele)
      SETERRQ(PETSC_COMM_SELF, MOFEM_DATA_INCONSISTENCY,
              "Pointer to element does not exists");
    auto get_rule = [&](int order_row, int order_col, int order_data) {
      return -1;
    };
    vol_ele->getRuleHook = get_rule;
 
    boost::shared_ptr<MatrixDouble> B(new MatrixDouble());
    vol_ele->getOpPtrVector().push_back(
        new OpCalculateHcurlVectorCurl<3>("MAGNETIC_POTENTIAL", B));
    // vol_ele->getOpPtrVector().push_back(new MyOpDebug(B));
 
    const MoFEM::Problem *prb_ptr;
    CHKERR DMMoFEMGetProblemPtr(dm, &prb_ptr);
 
    CHKERR field_eval_ptr->buildTree3D(data_at_pts, "MAGNETIC");
    BoundBox box;
    CHKERR data_at_pts->treePtr->get_bounding_box(box);
 
    const double bMin = box.bMin[0];
    const double bMax = box.bMax[0];
 
    auto create_vertices = [nb_random_points, bMin, bMax,
                            scale_box](moab::Interface &moab, auto &verts,
                                       auto &arrays_coord) {
      MoFEMFunctionBegin;
      ReadUtilIface *iface;
      EntityHandle startv;
      CHKERR moab.query_interface(iface);
      CHKERR iface->get_node_coords(3, nb_random_points, 0, startv,
                                    arrays_coord);
      FTensor::Tensor1<FTensor::PackPtr<double *, 1>, 3> t_coords = {
          arrays_coord[0], arrays_coord[1], arrays_coord[2]};
      FTensor::Index<'i', 3> i;
      verts = Range(startv, startv + nb_random_points - 1);
      for (int n = 0; n != nb_random_points; ++n) {
        t_coords(0) = 0;
        for (auto ii : {1, 2}) {
          t_coords(ii) = scale_box * (bMax - bMin) *
                             (std::rand() / static_cast<double>(RAND_MAX)) -
                         bMax * scale_box;
        }
        ++t_coords;
      }
      MoFEMFunctionReturn(0);
    };
 
    auto set_positions = [nb_random_points, dt, velocity_scale](
                             moab::Interface &moab, auto &arrays_coord) {
      MatrixDouble init_pos(3, nb_random_points);
      FTensor::Tensor1<FTensor::PackPtr<double *, 1>, 3> t_coords = {
          arrays_coord[0], arrays_coord[1], arrays_coord[2]};
      FTensor::Tensor1<FTensor::PackPtr<double *, 1>, 3> t_init_coords = {
          &init_pos(0, 0), &init_pos(1, 0), &init_pos(2, 0)};
      FTensor::Index<'i', 3> i;
      for (int n = 0; n != nb_random_points; ++n) {
 
        FTensor::Tensor1<double, 3> t_velocity;
        for (auto ii : {0, 1, 2})
          t_velocity(ii) = (rand() / static_cast<double>(RAND_MAX) - 0.5);
        t_velocity(i) /= sqrt(t_velocity(i) * t_velocity(i));
        t_init_coords(i) = t_coords(i) + dt * velocity_scale * t_velocity(i);
 
        ++t_coords;
        ++t_init_coords;
      }
      return init_pos;
    };
 
    moab::Core mb_charged_partices;
    moab::Interface &moab_charged_partices = mb_charged_partices;
    vector<double *> arrays_coord;
    Range verts;
    CHKERR create_vertices(moab_charged_partices, verts, arrays_coord);
    auto init_positions = set_positions(moab, arrays_coord);
 
    auto get_t_coords = [&]() {
      return FTensor::Tensor1<FTensor::PackPtr<double *, 1>, 3>(
          arrays_coord[0], arrays_coord[1], arrays_coord[2]);
    };
 
    auto get_t_init_coords = [&]() {
      return FTensor::Tensor1<FTensor::PackPtr<double *, 1>, 3>(
          &init_positions(0, 0), &init_positions(1, 0), &init_positions(2, 0));
    };
 
    auto calc_rhs = [&](auto &t_p, auto &t_init_p, auto &t_B) {
      FTensor::Tensor1<double, 3> t_rhs;
      FTensor::Index<'i', 3> i;
      FTensor::Index<'j', 3> j;
      FTensor::Index<'k', 3> k;
      t_rhs(k) = (2 * t_p(k) - t_init_p(k)) / dt -
                 levi_civita(j, i, k) * t_init_p(i) * t_B(j);
      return t_rhs;
    };
 
    auto calc_lhs = [&](auto &t_B) {
      FTensor::Tensor2<double, 3, 3> t_lhs;
      FTensor::Index<'i', 3> i;
      FTensor::Index<'j', 3> j;
      FTensor::Index<'k', 3> k;
      t_lhs(i, k) = levi_civita(j, i, k) * (-t_B(j));
      for (auto ii : {0, 1, 2})
        t_lhs(ii, ii) += 1 / dt;
      return t_lhs;
    };
 
    // auto set_periodicity = [&](auto &t_p, auto &t_init_p) {
    //   for (int i : {0, 1, 2})
    //     if (t_p(i) > bMax) {
    //       t_p(i) -= 2 * bMax;
    //       t_init_p(i) -= 2 * bMax;
    //     } else if (t_p(i) < bMin) {
    //       t_p(i) -= 2 * bMin;
    //       t_init_p(i) -= 2 * bMin;
    //     }
    // };
 
    auto is_out = [&](auto &t_p) {
      for (int i : {0, 1, 2})
        if (t_p(i) > bMax) {
          return true;
        } else if (t_p(i) < bMin) {
          return true;
        }
      return false;
    };
 
    auto calc_position = [&]() {
      auto t_p = get_t_coords();
      auto t_init_p = get_t_init_coords();
      FTensor::Index<'i', 3> i;
      FTensor::Index<'j', 3> j;
 
      for (int n = 0; n != nb_random_points; ++n) {
 
        if (is_out(t_p)) {
          ++t_p;
          ++t_init_p;
          continue;
        }
 
        std::array<double, 3> point = {t_p(0), t_p(1), t_p(2)};
        data_at_pts->setEvalPoints(point.data(), 1);
 
        CHKERR field_eval_ptr->evalFEAtThePoint3D(
            point.data(), dist, prb_ptr->getName(), "MAGNETIC", data_at_pts,
            m_field.get_comm_rank(), m_field.get_comm_rank(), MF_EXIST, QUIET);
 
        FTensor::Tensor1<double, 3> t_B;
 
        if (B->size2())
          for (int ii : {0, 1, 2})
            t_B(ii) = (*B)(ii, 0);
        else
          t_B(i) = 0;
 
        t_B(i) *= magnetic_field_scale * 0.5;
 
        auto t_rhs = calc_rhs(t_p, t_init_p, t_B);
        auto t_lhs = calc_lhs(t_B);
 
        double det;
        CHKERR determinantTensor3by3(t_lhs, det);
        FTensor::Tensor2<double, 3, 3> t_inv_lhs;
        CHKERR invertTensor3by3(t_lhs, det, t_inv_lhs);
 
        t_init_p(i) = t_p(i);
        t_p(i) = t_inv_lhs(i, j) * t_rhs(j);
 
        // set_periodicity(t_p, t_init_p);
 
        ++t_p;
        ++t_init_p;
      }
    };
 
    for (int t = 0; t != nb_steps; ++t) {
 
      std::string print_step =
          "Step : " + boost::lexical_cast<std::string>(t) + "\r";
      std::cout << print_step << std::flush;
 
      calc_position();
 
      if ((t % mod_step) == 0) {
        // write points
        CHKERR moab_charged_partices.write_file(
            ("step_" + boost::lexical_cast<std::string>(t / mod_step) + ".vtk")
                .c_str(),
            "VTK", "");
      }
    }
 
    std::cout << endl;
 
    CHKERR DMDestroy(&dm);
  }
  CATCH_ERRORS;
 
  MoFEM::Core::Finalize();
 
  return 0;
}