v0.13.1
lorentz_force.cpp

Calculate Lorentz fore from magnetic field.

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
*/
#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);
auto moab_comm_wrap =
boost::make_shared<WrapMPIComm>(PETSC_COMM_WORLD, false);
if (pcomm == NULL)
pcomm =
new ParallelComm(&moab, moab_comm_wrap->get_comm());
// 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();
const char *option;
option = "";
// Create mofem interface
MoFEM::Core core(moab);
MoFEM::Interface &m_field = core;
CHKERR m_field.build_fields();
// set up DM
DM dm;
CHKERR DMCreate(PETSC_COMM_WORLD, &dm);
CHKERR DMSetType(dm, "DMMOFEM");
CHKERR DMMoFEMCreateMoFEM(dm, &m_field, "MAGNETIC_PROBLEM",
BitRefLevel().set(0));
CHKERR DMSetFromOptions(dm);
CHKERR DMSetUp(dm);
// 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) {}
if (type == MBEDGE && side == 0) {
std::cout << "found " << (*B) << endl;
std::cout << "data " << data.getFieldData() << endl;
}
}
};
const double dist = 1e-12; // Distance for tree search
const int nb_random_points = 5000; // 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);
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 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) {
EntityHandle startv;
CHKERR moab.query_interface(iface);
CHKERR iface->get_node_coords(3, nb_random_points, 0, startv,
arrays_coord);
arrays_coord[0], arrays_coord[1], arrays_coord[2]};
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;
}
};
auto set_positions = [nb_random_points, dt, velocity_scale](
moab::Interface &moab, auto &arrays_coord) {
MatrixDouble init_pos(3, nb_random_points);
arrays_coord[0], arrays_coord[1], arrays_coord[2]};
&init_pos(0, 0), &init_pos(1, 0), &init_pos(2, 0)};
for (int n = 0; n != nb_random_points; ++n) {
for (auto ii : {0, 1, 2})
t_velocity(ii) = (rand() / static_cast<double>(RAND_MAX) - 0.5);
t_velocity(i) /= std::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 = [&]() {
arrays_coord[0], arrays_coord[1], arrays_coord[2]);
};
auto get_t_init_coords = [&]() {
&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) {
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) {
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 cache_ptr = boost::make_shared<CacheTuple>();
CHKERR m_field.cache_problem_entities(prb_ptr->getName(), cache_ptr);
auto calc_position = [&]() {
auto t_p = get_t_coords();
auto t_init_p = get_t_init_coords();
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(), cache_ptr,
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 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);
}
return 0;
}
ForcesAndSourcesCore::UserDataOperator UserDataOperator
@ QUIET
Definition: definitions.h:208
#define CATCH_ERRORS
Catch errors.
Definition: definitions.h:372
@ MF_EXIST
Definition: definitions.h:100
#define MYPCOMM_INDEX
default communicator number PCOMM
Definition: definitions.h:215
#define MoFEMFunctionBegin
First executable line of each MoFEM function, used for error handling. Final line of MoFEM functions ...
Definition: definitions.h:346
#define CHKERRG(n)
Check error code of MoFEM/MOAB/PETSc function.
Definition: definitions.h:483
@ MOFEM_DATA_INCONSISTENCY
Definition: definitions.h:31
#define MoFEMFunctionReturn(a)
Last executable line of each PETSc function used for error handling. Replaces return()
Definition: definitions.h:416
#define CHKERR
Inline error check.
Definition: definitions.h:535
auto get_rule
FTensor::Index< 'n', SPACE_DIM > n
PetscErrorCode DMMoFEMCreateMoFEM(DM dm, MoFEM::Interface *m_field_ptr, const char problem_name[], const MoFEM::BitRefLevel bit_level, const MoFEM::BitRefLevel bit_mask=MoFEM::BitRefLevel().set())
Must be called by user to set MoFEM data structures.
Definition: DMMMoFEM.cpp:118
PetscErrorCode DMMoFEMAddElement(DM dm, const char fe_name[])
Definition: DMMMoFEM.cpp:450
PetscErrorCode DMMoFEMGetProblemPtr(DM dm, const MoFEM::Problem **problem_ptr)
Get pointer to problem data structure.
Definition: DMMMoFEM.cpp:373
PetscErrorCode DMRegister_MoFEM(const char sname[])
Register MoFEM problem.
Definition: DMMMoFEM.cpp:47
virtual MoFEMErrorCode build_finite_elements(int verb=DEFAULT_VERBOSITY)=0
Build finite elements.
virtual MoFEMErrorCode build_fields(int verb=DEFAULT_VERBOSITY)=0
FTensor::Index< 'i', SPACE_DIM > i
double dt
Definition: heat_method.cpp:26
int main(int argc, char *argv[])
static char help[]
FTensor::Index< 'j', 3 > j
FTensor::Index< 'k', 3 > k
char mesh_file_name[255]
constexpr std::enable_if<(Dim0<=2 &&Dim1<=2), Tensor2_Expr< Levi_Civita< T >, T, Dim0, Dim1, i, j > >::type levi_civita(const Index< i, Dim0 > &, const Index< j, Dim1 > &)
levi_civita functions to make for easy adhoc use
static MoFEMErrorCodeGeneric< PetscErrorCode > ierr
Definition: Exceptions.hpp:76
PetscErrorCode MoFEMErrorCode
MoFEM/PETSc error code.
Definition: Exceptions.hpp:56
UBlasMatrix< double > MatrixDouble
Definition: Types.hpp:77
std::bitset< BITREFLEVEL_SIZE > BitRefLevel
Bit structure attached to each entity identifying to what mesh entity is attached.
Definition: Types.hpp:40
implementation of Data Operators for Forces and Sources
Definition: MoFEM.hpp:24
MoFEMErrorCode invertTensor3by3(ublas::matrix< T, L, A > &jac_data, ublas::vector< T, A > &det_data, ublas::matrix< T, L, A > &inv_jac_data)
Calculate inverse of tensor rank 2 at integration points.
Definition: Templates.hpp:1204
CoreTmp< 0 > Core
Definition: Core.hpp:1086
DeprecatedCoreInterface Interface
Definition: Interface.hpp:1955
static auto determinantTensor3by3(T &t)
Calculate the determinant of a 3x3 matrix or a tensor of rank 2.
Definition: Templates.hpp:1193
constexpr double t
plate stiffness
Definition: plate.cpp:59
virtual MoFEMErrorCode cache_problem_entities(const std::string prb_name, CacheTupleWeakPtr cache_ptr)=0
Cache variables.
virtual MoFEMErrorCode build_adjacencies(const Range &ents, int verb=DEFAULT_VERBOSITY)=0
virtual int get_comm_rank() const =0
Core (interface) class.
Definition: Core.hpp:82
static MoFEMErrorCode Initialize(int *argc, char ***args, const char file[], const char help[])
Initializes the MoFEM database PETSc, MOAB and MPI.
Definition: Core.cpp:72
static MoFEMErrorCode Finalize()
Checks for options to be called at the conclusion of the program.
Definition: Core.cpp:112
virtual MoFEMErrorCode doWork(int row_side, int col_side, EntityType row_type, EntityType col_type, EntitiesFieldData::EntData &row_data, EntitiesFieldData::EntData &col_data)
Operator for bi-linear form, usually to calculate values on left hand side.
Deprecated interface functions.
Data on single entity (This is passed as argument to DataOperator::doWork)
const VectorDouble & getFieldData() const
get dofs values
Field evaluator interface.
MoFEMErrorCode buildTree3D(boost::shared_ptr< SetPtsData > spd_ptr, const std::string finite_element)
Build spatial tree.
boost::shared_ptr< SPD > getData(const double *ptr=nullptr, const int nb_eval_points=0, const double eps=1e-12, VERBOSITY_LEVELS verb=QUIET)
Get the Data object.
MoFEMErrorCode evalFEAtThePoint3D(const double *const point, const double distance, const std::string problem, const std::string finite_element, boost::shared_ptr< SetPtsData > data_ptr, int lower_rank, int upper_rank, boost::shared_ptr< CacheTuple > cache_ptr, MoFEMTypes bh=MF_EXIST, VERBOSITY_LEVELS verb=QUIET)
Evaluate field at artbitray position.
boost::ptr_vector< UserDataOperator > & getOpPtrVector()
Use to push back operator for row operator.
RuleHookFun getRuleHook
Hook to get rule.
Calculate curl of vector field.