main.cpp

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#include <cmath>
#include <complex>
#include <fstream>
#include <omp.h>
#include <string>
#include <vector>
 
#include "PenningTrap.hpp"
#include "constants.hpp"
#include "utils.hpp"
 
#define PARTICLES 100
#define N 40000
 
// Particles used for testing
Particle p1(vec3{20., 0., 20.}, vec3{0., 25., 0.}); 
Particle p2(vec3{25., 25., 0.}, vec3{0., 40., 5.}); 
 
vec3 analytical_solution_particle_1(double t)
{
    double w_0 = T / CA_MASS;
    double w_z2 = (50. * V / 1000.) / (CA_MASS * 500. * 500.);
    double w_p = (w_0 + std::sqrt(w_0 * w_0 - 2. * w_z2)) / 2.;
    double w_n = (w_0 - std::sqrt(w_0 * w_0 - 2. * w_z2)) / 2.;
    double A_p = (25. + w_n * 20.) / (w_n - w_p);
    double A_n = -(25. + w_p * 20.) / (w_n - w_p);
    std::complex<double> f =
        A_p * std::exp(std::complex<double>(0., -w_p * t))
        + A_n * std::exp(std::complex<double>(0., -w_n * t));
    vec3 res{std::real(f), std::imag(f), 20. * std::cos(std::sqrt(w_z2) * t)};
    return res;
}
 
void simulate_single_particle()
{
    // Initialize trap with particle 1
    PenningTrap trap(std::vector<Particle>{p1});
 
    double time = 50.; // microseconds
 
    // Simulate and write results to file
    trap.write_simulation_to_dir("output/simulate_single_particle", time, N,
                                 "rk4", false);
}
 
void simulate_two_particles()
{
    // Initialize traps with particles
    PenningTrap trap_no_interaction(std::vector<Particle>{p1, p2});
    PenningTrap trap_with_interaction(std::vector<Particle>{p1, p2});
 
    double time = 50.; // microseconds
 
    // Simulate and write results to files
    trap_no_interaction.write_simulation_to_dir(
        "output/simulate_2_particles/no_interaction", time, N, "rk4", false);
    trap_with_interaction.write_simulation_to_dir(
        "output/simulate_2_particles/with_interaction", time, N);
}
 
void simulate_single_particle_with_different_steps()
{
    double time = 50.; // microseconds
 
    std::ofstream ofile;
 
    // Calculate relative error for RK4
    std::string path = "output/relative_error/RK4/";
    mkpath(path);
#pragma omp parallel for
    for (int i = 0; i < 4; i++) {
        int steps = 4000 * std::pow(2, i);
        double dt = time / (double)steps;
        ofile.open(path + std::to_string(steps) + "_steps.txt");
        PenningTrap trap(std::vector<Particle>{p1});
        simulation_t res = trap.simulate(time, steps, "rk4", false);
        for (int i = 0; i < steps; i++) {
            ofile << arma::norm(res.r_vecs[0][i]
                                - analytical_solution_particle_1(dt * i))
                  << '\n';
        }
        ofile.close();
    }
 
    // Calculate relative error for forward Euler
    path = "output/relative_error/euler/";
    mkpath(path);
#pragma omp parallel for
    for (int i = 0; i < 4; i++) {
        int steps = 4000 * std::pow(2, i);
        double dt = time / (double)steps;
        ofile.open(path + std::to_string(steps) + "_steps.txt");
        PenningTrap trap(std::vector<Particle>{p1});
        simulation_t res = trap.simulate(time, steps, "euler", false);
        for (int i = 0; i < steps; i++) {
            ofile << arma::norm(res.r_vecs[0][i]
                                - analytical_solution_particle_1(dt * i))
                  << '\n';
        }
        ofile.close();
    }
}
 
void simulate_100_particles()
{
    PenningTrap trap((unsigned)100);
 
    double time = 50.; // microseconds
 
    trap.write_simulation_to_dir("output/simulate_100_particles", time, N,
                                 "rk4", false);
}
 
void potential_resonance_wide_sweep()
{
    double time = 500.;
 
    double amplitudes[]{.1, .4, .7};
 
    double freq_start = .2;
    double freq_end = 2.5;
    double freq_increment = .02;
    size_t freq_iterations =
        (size_t)((freq_end - freq_start) / freq_increment) + 1;
 
    double res[4][freq_iterations];
 
    std::string path = "output/time_dependent_potential/";
    mkpath(path);
 
    std::ofstream ofile;
 
#pragma omp parallel for
    // Insert frequencies
    for (size_t i = 0; i < freq_iterations; i++) {
        res[0][i] = freq_start + freq_increment * i;
    }
 
#pragma omp parallel
    {
        // Each thread creates a PenningTrap instance and reuses it throughout
        // the sweep.
        PenningTrap trap((uint)100);
#pragma omp for collapse(2)
        for (size_t i = 0; i < 3; i++) {
            for (size_t j = 0; j < freq_iterations; j++) {
                // Reset particles and give new time dependent potential.
                trap.reinitialize(amplitudes[i], res[0][j]);
                res[i + 1][j] =
                    trap.fraction_of_particles_left(time, N, "rk4", false);
            }
        }
    }
 
    // Write results to file
    ofile.open(path + "wide_sweep.txt");
    for (size_t i = 0; i < freq_iterations; i++) {
        ofile << res[0][i] << ',' << res[1][i] << ',' << res[2][i] << ','
              << res[3][i] << '\n';
    }
    ofile.close();
}
 
void potential_resonance_narrow_sweep()
{
    double time = 500.;
 
    double amplitudes[]{.1, .4, .7};
 
    double freq_start = 1.;
    double freq_end = 1.7;
    double freq_increment = .002;
    size_t freq_iterations = (size_t)((freq_end - freq_start) / freq_increment);
 
    double res[4][freq_iterations];
 
    std::string path = "output/time_dependent_potential/";
    mkpath(path);
 
    std::ofstream ofile;
 
#pragma omp parallel for
    // Insert frequencies
    for (size_t i = 0; i < freq_iterations; i++) {
        res[0][i] = freq_start + freq_increment * i;
    }
 
#pragma omp parallel
    {
        // Each thread creates a PenningTrap instance and reuses it throughout
        // the sweep.
        PenningTrap trap((uint)100);
#pragma omp for collapse(2)
        for (size_t i = 0; i < 3; i++) {
            for (size_t j = 0; j < freq_iterations; j++) {
                // Reset particles and give new time dependent potential.
                trap.reinitialize(amplitudes[i], res[0][j]);
                res[i + 1][j] =
                    trap.fraction_of_particles_left(time, N, "rk4", false);
            }
        }
    }
 
    // Write results to file
    ofile.open(path + "narrow_sweep.txt");
    for (size_t i = 0; i < freq_iterations; i++) {
        ofile << res[0][i] << ',' << res[1][i] << ',' << res[2][i] << ','
              << res[3][i] << '\n';
    }
    ofile.close();
}
 
void potential_resonance_narrow_sweep_interaction()
{
    double time = 500.;
 
    double amplitudes[]{.1, .4, .7};
 
    double freq_start = 1.;
    double freq_end = 1.7;
    double freq_increment = .002;
    size_t freq_iterations = (size_t)((freq_end - freq_start) / freq_increment);
 
    double res[4][freq_iterations];
 
    std::string path = "output/time_dependent_potential/";
    mkpath(path);
 
    std::ofstream ofile;
 
#pragma omp parallel for
    for (size_t i = 0; i < freq_iterations; i++) {
        res[0][i] = freq_start + freq_increment * i;
    }
 
#pragma omp parallel
    {
        // Each thread creates a PenningTrap instance and reuses it throughout
        // the sweep.
        PenningTrap trap((uint)100);
#pragma omp for collapse(2)
        for (size_t i = 0; i < 3; i++) {
            for (size_t j = 0; j < freq_iterations; j++) {
                // Reset particles and give new time dependent potential.
                trap.reinitialize(amplitudes[i], res[0][j]);
                res[i + 1][j] = trap.fraction_of_particles_left(time, N);
            }
        }
    }
 
    // Write results to file
    ofile.open(path + "narrow_sweep_interactions.txt");
    for (size_t i = 0; i < freq_iterations; i++) {
        ofile << res[0][i] << ',' << res[1][i] << ',' << res[2][i] << ','
              << res[3][i] << '\n';
    }
    ofile.close();
}
 
int main()
{
    double start, end, t1, t2;
    start = omp_get_wtime();
 
    simulate_single_particle();
 
    simulate_two_particles();
 
    simulate_single_particle_with_different_steps();
 
    t2 = omp_get_wtime();
 
    std::cout << "Time single and double            : " << (t2 - start)
              << " seconds" << std::endl;
 
    t1 = omp_get_wtime();
 
    simulate_100_particles();
 
    t2 = omp_get_wtime();
 
    std::cout << "Time 100 particles                : " << (t2 - t1)
              << " seconds" << std::endl;
 
    t1 = omp_get_wtime();
 
    potential_resonance_wide_sweep();
 
    t2 = omp_get_wtime();
 
    std::cout << "Time wide sweep                   : " << (t2 - t1)
              << " seconds" << std::endl;
 
    t1 = omp_get_wtime();
 
    potential_resonance_narrow_sweep();
 
    t2 = omp_get_wtime();
 
    std::cout << "Time narrow sweep no interaction  : " << (t2 - t1)
              << " seconds" << std::endl;
 
    t1 = omp_get_wtime();
 
    potential_resonance_narrow_sweep_interaction();
 
    t2 = omp_get_wtime();
 
    std::cout << "Time narrow sweep with interaction: " << (t2 - t1)
              << " seconds" << std::endl;
 
    end = omp_get_wtime();
 
    std::cout << "Time                              : " << (end - start)
              << " seconds" << std::endl;
 
    return 0;
}