main2.cpp

//
// Created by Abhinav Singh @absingh on 26/04/2021
//
 
// Include Vector Expression,Vector Expressions for Subset,DCPSE,Odeint header files
#include "Operators/Vector/vector_dist_operators.hpp"
#include "Vector/vector_dist_subset.hpp"
#include "DCPSE/DCPSE_op/DCPSE_op.hpp"
#include "OdeIntegrators/OdeIntegrators.hpp"
 
 
 
constexpr int x = 0;
constexpr int y = 1;
 
double dt=1e-2,tf=1.0,vf=1.0;
 
void *PointerDistGlobal, *PointerDistSubset,*PointerDistSubset2;
 
typedef aggregate<VectorS<2, double>, VectorS<2, double>, VectorS<2, double>> Property_type;
typedef vector_dist_ws<2, double, Property_type> dist_vector_type;
typedef vector_dist_subset<2, double, Property_type> dist_vector_subset_type;
 
template<typename DXX,typename DYY>
struct RHSFunctor
{
    //Intializing the operators
    DXX &Dxx;
    DYY &Dyy;
    //Constructor
    RHSFunctor(DXX &Dxx,DYY &Dyy):Dxx(Dxx),Dyy(Dyy)
    {}
 
    void operator()( const state_type_2d_ofp &X , state_type_2d_ofp &dxdt , const double t ) const
    {
        //Casting the pointers to OpenFPM vector distributions
        dist_vector_type &Particles= *(dist_vector_type *) PointerDistGlobal;
        dist_vector_subset_type &Particles_bulk= *(dist_vector_subset_type *) PointerDistSubset;
 
        //Aliasing the properties.
        auto C = getV<0>(Particles);
        auto C_bulk = getV<0>(Particles_bulk);
        auto dC = getV<2>(Particles);
        auto dC_bulk = getV<2>(Particles_bulk);
 
        //Since the state vector does not have enough information to compute derivates, we copy them back to the Particle Distribution.
        //In this way we can compute all the things that are required to be computed in each stage of the ode integrator.
        // Note that we are going to use bulk expressions as needed. Whenever we don't want to update the boundaries (Due to the boundary conditions).
 
        //These expressions only update the bulk values of C.
        C_bulk[x]=X.data.get<0>();
        C_bulk[y]=X.data.get<1>();
        Particles.ghost_get<0>();
 
        // We do the RHS computations for the Laplacian (Updating bulk only).
        dC_bulk[x] = 0.1*(Dxx(C[x])+Dyy(C[x]));
        dC_bulk[y] = 0.1*(Dxx(C[y])+Dyy(C[y]));
 
        //We copy back to the dxdt state_type for Odeint
        dxdt.data.get<0>()=dC[x];
        dxdt.data.get<1>()=dC[y];
    }
};
 
 
template<typename DXX, typename DYY, typename VerletList_type>
struct ObserverFunctor {
 
    DXX &Dxx;
    DYY &Dyy;
    VerletList_type &verletList;
    int ctr;
    double t_old;
    double rCut;
 
    //Constructor
    ObserverFunctor(DXX &Dxx, DYY &Dyy, VerletList_type& verletList, double rCut) : Dxx(Dxx), Dyy(Dyy), verletList(verletList), rCut(rCut) {
        //a counter for counting the np. of steps
        ctr = 0;
        //Starting with t=0, we compute the step size take by t-t_old. So for the first observed step size is what we provide. Which will be 0-(-dt)=dt.
        t_old = -dt;
    }
 
    void operator()(state_type_2d_ofp &X, double t) {
        //Casting the pointers to OpenFPM vector distributions
        dist_vector_type &Particles = *(dist_vector_type *) PointerDistGlobal;
        dist_vector_subset_type &Particles_bulk = *(dist_vector_subset_type *) PointerDistSubset;
        dist_vector_subset_type &Particles_boundary = *(dist_vector_subset_type *) PointerDistSubset2;
 
        //Aliasing the position and properties.
        auto Pos = getV<POS_PROP>(Particles);
        auto Concentration = getV<0>(Particles);
        auto Velocity = getV<1>(Particles);
        auto Concentration_bulk = getV<0>(Particles_bulk);
        auto Velocity_bulk = getV<1>(Particles_bulk);
 
        //We would like to move the particles after t=0. (Remember, odeint calls the observer before taking the step.)
        if (t != 0) {
            //copy back the state after the time step into data structure. This is required as we are going to move the particles and the distributed state can be resized correctly (by copying back after map). Also this expression preserves the boundary condition on concentration.
            Concentration_bulk[x] = X.data.get<0>();
            Concentration_bulk[y] = X.data.get<1>();
            //computing the velocity and move the particles
            Velocity_bulk[x] = -vf*Pos[y] * exp(-10.0 * (Pos[x] * Pos[x] + Pos[y] * Pos[y]));
            Velocity_bulk[y] = vf*Pos[x] * exp(-10.0 * (Pos[x] * Pos[x] + Pos[y] * Pos[y]));
            Pos = Pos + dt * Velocity;
            //Map and ghost_get is required after moving particles.
            Particles.map();
            Particles.ghost_get<0>();
            //Updating the subset and operators based on new positions
            Particles_bulk.update();
            Particles_boundary.update();
            Particles.updateVerlet(verletList,rCut);
            Dxx.update(Particles);
            Dyy.update(Particles);
 
            //Since we did Map, we assign the Odeint state again.
            X.data.get<0>() = Concentration[x];
            X.data.get<1>() = Concentration[y];
            //counting the step number
 
        }
        ctr++;
        std::cout<<"Taking a step at t="<<t<<" with dt="<<t-t_old<<std::endl;
        t_old=t;
        //Writing the data after every step
        Particles.deleteGhost();
        Particles.write_frame("PDE_sol", ctr);
        Particles.ghost_get<0>();
 
    }
};
 
int main(int argc, char *argv[])
{
    //  initialize library
    openfpm_init(&argc, &argv);
 
    dt=std::atof(argv[1]);
    tf=std::atof(argv[2]);
    vf=std::atof(argv[3]);
 
    const size_t sz[2] = {41, 41};
    Box<2, double> box({-1, -1}, {1.0, 1.0});
    size_t bc[2] = {NON_PERIODIC, NON_PERIODIC};
    double spacing[2];
    spacing[0] = 2.0 / (sz[0] - 1);
    spacing[1] = 2.0 / (sz[1] - 1);
    double rCut = 3.1 * spacing[0];
    Ghost<2, double> ghost(rCut);
 
    dist_vector_type Particles(0, box, bc, ghost);
    Particles.setPropNames({"Concentration", "Velocity", "TempConcentration"});
 
    auto it = Particles.getGridIterator(sz);
    while (it.isNext()) {
        Particles.add();
        auto key = it.get();
        double x = -1.0 + key.get(0) * spacing[0];
        Particles.getLastPos()[0] = x;
        double y = -1.0 + key.get(1) * spacing[1];
        Particles.getLastPos()[1] = y;
        //We detect Boundaries. By labelling the subset to be 0 for bulk and 1 for the boundary. Subsets will be constructed later based on the label.
        if (x != -1.0 && x != 1.0 && y != -1.0 && y != 1) {
            Particles.getLastSubset(0);
        } else {
            Particles.getLastSubset(1);
        }
        // Here fill the Initial value of the concentration.
        if (x == 0.0 && y > -0.5 && y < 0) {
            Particles.template getLastProp<0>()[0] = 1.0;
            Particles.template getLastProp<0>()[1] = 0.0;
        } else if (x == 0.0 && y > 0 && y < 0.5) {
            Particles.template getLastProp<0>()[0] = 0.0;
            Particles.template getLastProp<0>()[1] = 1.0;
        } else {
            Particles.template getLastProp<0>()[0] = 0.0;
            Particles.template getLastProp<0>()[1] = 0.0;
        }
        ++it;
    }
    Particles.map();
    Particles.ghost_get<0>();
 
    //We write the particles to check if the initialization is correct.
    Particles.write("Init");
 
    // Now we initialize the grid with a filled circle. Outside the circle, the value of Phi_0 will be -1, inside +1.
    //Now we construct the subsets based on the subset number.
    dist_vector_subset_type Particles_bulk(Particles, 0);
    dist_vector_subset_type Particles_boundary(Particles, 1);
 
    //We cast the global pointers to Particles and Particles_bulk as expected by the RHS functor.
    PointerDistGlobal = (void *) &Particles;
    PointerDistSubset = (void *) &Particles_bulk;
    PointerDistSubset2 = (void *) &Particles_boundary;
 
    //We create the DCPSE Based operators for discretization of the operators.
    auto verletList = Particles.template getVerlet<VL_NON_SYMMETRIC|VL_SKIP_REF_PART>(rCut);
 
    Derivative_xx<decltype(verletList)> Dxx(Particles, verletList, 2, rCut);
    Derivative_yy<decltype(verletList)> Dyy(Particles, verletList, 2, rCut);
    //We create aliases for referring to property and and positions.
    auto Pos = getV<POS_PROP>(Particles);
    auto C = getV<0>(Particles);
    auto V = getV<1>(Particles);
    auto dC = getV<2>(Particles);
 
    //We create aliases for referring to the subset properties.
    auto C_bulk = getV<0>(Particles_bulk);
    auto dC_bulk = getV<2>(Particles_bulk);
 
    //Now we create a odeint stepper object (RK4). Since we are in 2d, we are going to use "state_type_2d_ofp". Which is a structure or state_type compatible with odeint. We further pass all the parameters including "boost::numeric::odeint::vector_space_algebra_ofp",which tell odeint to use openfpm algebra.
    // The template parameters are: state_type_2d_ofp (state type of X), double (type of the value inside the state), state_type_2d_ofp (state type of DxDt), double (type of the time), boost::numeric::odeint::vector_space_algebra_ofp (our algebra)
    boost::numeric::odeint::runge_kutta4<state_type_2d_ofp, double, state_type_2d_ofp, double, boost::numeric::odeint::vector_space_algebra_ofp> Odeint_rk4;
 
    //The method Odeint_rk4 from Odeint, requires system (a function which computes RHS of the PDE), an instance of the Compute RHS functor. We create the System with the correct types and parameteres for the operators as declared before.
    RHSFunctor<Derivative_xx<decltype(verletList)>, Derivative_yy<decltype(verletList)>> System(Dxx, Dyy);
 
    //Since we are using Odeint to control the time steps, we also create a observer instance. Which also updates the position via an euler step for moving thr particles.
    ObserverFunctor<Derivative_xx<decltype(verletList)>, Derivative_yy<decltype(verletList)>, decltype(verletList)> ObserveAndUpdate(Dxx, Dyy, verletList, rCut);
 
 
    //Furhter, odeint needs data in a state type "state_type_2d_ofp", we create one and fill in the initial condition.
    state_type_2d_ofp X;
    //Since we created a 2d state_type we initialize the two fields in the object data using the method get.
    X.data.get<x>() = C[0];
    X.data.get<y>() = C[1];
 
    std::vector<double> inter_times; // vector to store intermediate time steps taken by odeint.
 
    size_t steps = boost::numeric::odeint::integrate_const(Odeint_rk4, System, X, 0.0, tf, dt, ObserveAndUpdate);
    /* From Odeint: (Please refer to Odeint on more details about these steppers.)
    runge_kutta_dopri5 is maybe the best default stepper. It has step size control as well as dense-output functionality. Simple create a dense-output stepper by make_dense_output( 1.0e-6 , 1.0e-5 , runge_kutta_dopri5< state_type >() ).
    runge_kutta4 is a good stepper for constant step sizes. It is widely used and very well known. If you need to create artificial time series this stepper should be the first choice.
    'runge_kutta_fehlberg78' is similar to the 'runge_kutta4' with the advantage that it has higher precision. It can also be used with step size control.
    adams_bashforth_moulton is very well suited for ODEs where the r.h.s. is expensive (in terms of computation time). It will calculate the system function only once during each step.*/
    /*Below are listed examples of using different steppers and their usage.*/
    //size_t steps = integrate_adaptive(controlled_stepper_type() , System , X , t , tf , dt, ObserveAndUpdate);
    //size_t steps = boost::numeric::odeint::integrate_adaptive( boost::numeric::odeint::make_controlled( 1.0e-7 , 1.0e-7 ,boost::numeric::odeint::runge_kutta_cash_karp54< state_type_2d_ofp,double,state_type_2d_ofp,double,boost::numeric::odeint::vector_space_algebra_ofp>() ) , System , X , t , tf , dt, ObserveAndUpdate );
    //size_t steps = boost::numeric::odeint::integrate_const( boost::numeric::odeint::make_dense_output(1.0e-7, 1.0e-7,  boost::numeric::odeint::runge_kutta_dopri5< state_type_2d_ofp,double,state_type_2d_ofp,double,boost::numeric::odeint::vector_space_algebra_ofp >() ) , System , X , t , tf , dt, ObserveAndUpdate );
    //size_t steps = boost::numeric::odeint::integrate_adaptive( boost::numeric::odeint::make_dense_output( 1.0e-8 , 1.0e-8 ,  boost::numeric::odeint::runge_kutta_dopri5< state_type_2d_ofp,double,state_type_2d_ofp,double,boost::numeric::odeint::vector_space_algebra_ofp >() ) , System , X , t , tf , dt, ObserveAndUpdate );
    //size_t steps = boost::numeric::odeint::integrate_adaptive( boost::numeric::odeint::make_controlled( 1.0e-7 , 1.0e-7 ,  boost::numeric::odeint::runge_kutta_dopri5< state_type_2d_ofp,double,state_type_2d_ofp,double,boost::numeric::odeint::vector_space_algebra_ofp >() ) , System , X , t , tf , dt, ObserveAndUpdate );
 
 
    std::cout << "No. of Time steps taken: " << steps << std::endl;
    //Copying back the final solution and outputting the number of steps taken by Odeint.
    C_bulk[x] = X.data.get<0>();
    C_bulk[y] = X.data.get<1>();
    //Deallocating the operators
    Dxx.deallocate(Particles);
    Dyy.deallocate(Particles);
    openfpm_finalize(); // Finalize openFPM library
    return 0;
} //main end