domain_fourD_periodic_shell.cpp

/*
    Copyright 2017 Philippe Grandclement
 
    This file is part of Kadath.
 
    Kadath is free software: you can redistribute it and/or modify
    it under the terms of the GNU General Public License as published by
    the Free Software Foundation, either version 3 of the License, or
    (at your option) any later version.
 
    Kadath 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 General Public License for more details.
 
    You should have received a copy of the GNU General Public License
    along with Kadath.  If not, see <http://www.gnu.org/licenses/>.
*/
 
#include "headcpp.hpp"
#include "utilities.hpp"
#include "fourD_periodic.hpp"
#include "point.hpp"
#include "array_math.hpp"
#include "term_eq.hpp"
#include "val_domain.hpp"
#include "term_eq.hpp"
#include "scalar.hpp"
#include "tensor_impl.hpp"
 
namespace Kadath {
void coef_1d (int, Array<double>&) ;
void coef_i_1d (int, Array<double>&) ;
int der_1d (int, Array<double>&) ;
 
// Standard constructor
Domain_fourD_periodic_shell::Domain_fourD_periodic_shell (int num, int ttype, double rin, double rout, double oome, const Dim_array& nbr) :  
        Domain(num, ttype, nbr), alpha((rout-rin)/2.), beta ((rout+rin)/2.), ome(oome), type_time(TO_PI) {
     assert (nbr.get_ndim()==4) ;
     switch (type_time) {
    case TO_PI :
        maxt = M_PI ;
        break ;
    default:
        cerr << "Unknown case for type_time" << endl ;
        abort()  ;
     }
     do_coloc() ;
}
 
// Constructor by copy
Domain_fourD_periodic_shell::Domain_fourD_periodic_shell (const Domain_fourD_periodic_shell& so) : Domain(so), alpha(so.alpha), beta(so.beta), ome(so.ome), 
                type_time(so.type_time), maxt(so.maxt) {
}
 
Domain_fourD_periodic_shell::Domain_fourD_periodic_shell (int num, FILE* fd) : Domain(num, fd) {
    fread_be (&alpha, sizeof(double), 1, fd) ;
    fread_be (&beta, sizeof(double), 1, fd) ;
    fread_be (&ome, sizeof(double), 1, fd) ;
    fread_be (&type_time, sizeof(int), 1, fd) ;   
    switch (type_time) {
      case TO_PI :
        maxt = M_PI ;
        break ;
      default:
        cerr << "Unknown case for type_time" << endl ;
        abort()  ;
    }
    do_coloc() ;
}
 
// Destructor
Domain_fourD_periodic_shell::~Domain_fourD_periodic_shell() {
}
 
void Domain_fourD_periodic_shell::save (FILE* fd) const {
    nbr_points.save(fd) ;
    nbr_coefs.save(fd) ;
    fwrite_be (&ndim, sizeof(int), 1, fd) ;
    fwrite_be (&type_base, sizeof(int), 1, fd) ;
    fwrite_be (&alpha, sizeof(double), 1, fd) ;
    fwrite_be (&beta, sizeof(double), 1, fd) ;
    fwrite_be (&ome, sizeof(double), 1, fd) ;
    fwrite_be (&type_time, sizeof(int), 1, fd) ;
}
 
ostream& Domain_fourD_periodic_shell::print (ostream& o) const {
  o << "fourD_periodic shell" << endl ;
  o << "time goes to " << maxt << endl ;
  o <<  beta-alpha << " < r < " << beta+alpha << endl ;
  o << "Omega   = " << ome << endl ;
  o << "Nbr pts = " << nbr_points << endl ;
  o << endl ;
  return o ;
}
 
// Computes the cartesian coordinates
void Domain_fourD_periodic_shell::do_absol () const {
    for (int i=0 ; i<4 ; i++)
       assert (coloc[i] != 0x0) ;
    for (int i=0 ; i<4 ; i++)
       assert (absol[i] == 0x0) ;
    for (int i=0 ; i<4 ; i++) {
       absol[i] = new Val_domain(this) ;
       absol[i]->allocate_conf() ;
       }
    Index index (nbr_points) ;
    do  {
        
        absol[0]->set(index) = (alpha* ((*coloc[0])(index(0))) +beta)*
         sin((*coloc[1])(index(1)))*cos((*coloc[2])(index(2))) ; //xx
        absol[1]->set(index) = (alpha* ((*coloc[0])(index(0))) +beta) *
         sin((*coloc[1])(index(1)))*sin((*coloc[2])(index(2))) ; //yy
        absol[2]->set(index) = (alpha* ((*coloc[0])(index(0))) + beta) * cos((*coloc[1])(index(1))) ; //zz
        absol[3]->set(index) = (*coloc[3])(index(3)) / ome ; // time
    }
    while (index.inc())  ;
    
}
 
void Domain_fourD_periodic_shell::do_cart () const {
    for (int i=0 ; i<4 ; i++)
       assert (coloc[i] != 0x0) ;
    for (int i=0 ; i<4 ; i++)
       assert (cart[i] == 0x0) ;
    for (int i=0 ; i<4 ; i++) {
       cart[i] = new Val_domain(this) ;
       cart[i]->allocate_conf() ;
       }
    Index index (nbr_points) ;
    do  {
        
        cart[0]->set(index) = (alpha* ((*coloc[0])(index(0))) +beta)*
         sin((*coloc[1])(index(1)))*cos((*coloc[2])(index(2))) ; //xx
        cart[1]->set(index) = (alpha* ((*coloc[0])(index(0))) +beta) *
         sin((*coloc[1])(index(1)))*sin((*coloc[2])(index(2))) ; //yy
        cart[2]->set(index) = (alpha* ((*coloc[0])(index(0))) + beta) * cos((*coloc[1])(index(1))) ; //zz
        cart[3]->set(index) = (*coloc[3])(index(3)) / ome ; // time
    }
    while (index.inc())  ;
 
    // Put base for x and y
    switch (type_base) {
        case CHEB_TYPE:
            set_cheb_base_x_cart(cart[0]->set_base()) ;
            set_cheb_base_y_cart(cart[1]->set_base()) ;
            break ;
        case LEG_TYPE:
            set_legendre_base_x_cart(cart[0]->set_base()) ;
            set_legendre_base_y_cart(cart[1]->set_base()) ;
            break ;
        default :
            cerr << "Unknown type of basis in Domain_fourD_periodic_shell::do_cart" << endl ;
            abort() ;
    }
    
}
 
// Computes the radius
void Domain_fourD_periodic_shell::do_radius ()  const {
 
    for (int i=0 ; i<4 ; i++)
       assert (coloc[i] != 0x0) ;
    assert (radius == 0x0) ;
    radius = new Val_domain(this) ;
    radius->allocate_conf() ;
    Index index (nbr_points) ;
    do
        radius->set(index) = alpha* ((*coloc[0])(index(0))) + beta ;
    while (index.inc())  ;
}
 
 
// Is a point inside this domain ?
bool Domain_fourD_periodic_shell::is_in (const Point& xx, double prec) const {
 
    assert (xx.get_ndim()==4) ;
    
    double x_loc = xx(1) ;
    double y_loc = xx(2) ;
    double z_loc = xx(3) ;
    double air_loc = sqrt (x_loc*x_loc + y_loc*y_loc + z_loc*z_loc) ;
 
    bool res = ((air_loc <= alpha+beta+prec) && (air_loc >= beta-alpha-prec)) ? true : false ;
 
    if ((xx(4)<0-prec) || (xx(4)>maxt/ome + prec))
          res = false ;
 
    return res ;
}
 
// Convert absolute coordinates to numerical ones
const Point Domain_fourD_periodic_shell::absol_to_num(const Point& abs) const {
 
    assert (is_in(abs)) ;
    Point num(4) ;
    
    double x_loc = abs(1) ;
    double y_loc = abs(2) ;
    double z_loc = abs(3) ;
    double air = sqrt(x_loc*x_loc+y_loc*y_loc+z_loc*z_loc) ;
    num.set(1) = (air-beta)/alpha ;
    double rho = sqrt(x_loc*x_loc+y_loc*y_loc) ;
    
    if (rho==0) {
        // On the axis ?
        num.set(2) = (z_loc>=0) ? 0 : M_PI ;
        num.set(3) = 0 ;
    }
    else {
        num.set(2) = atan(rho/z_loc) ;
        num.set(3) = atan2 (y_loc, x_loc) ;
        }   
    
    if (num(2) <0)
        num.set(2) = M_PI + num(2) ;
 
    num.set(4) = abs(4)*ome ;
    
    return num ;
}
 
double coloc_leg(int, int) ;
void Domain_fourD_periodic_shell::do_coloc () {
 
    switch (type_base) {
        case CHEB_TYPE:
            nbr_coefs = nbr_points ;
            nbr_coefs.set(2) += 2 ;
            del_deriv() ;
            for (int i=0 ; i<ndim ; i++)
                coloc[i] = new Array<double> (nbr_points(i)) ;
            for (int i=0 ; i<nbr_points(0) ; i++)
                coloc[0]->set(i) = -cos(M_PI*i/(nbr_points(0)-1)) ;
            for (int j=0 ; j<nbr_points(1) ; j++)
                coloc[1]->set(j) = M_PI/2.*j/(nbr_points(1)-1) ;
            for (int k=0 ; k<nbr_points(2) ; k++)
                coloc[2]->set(k) = M_PI*2.*k/nbr_points(2) ;
            for (int l=0 ; l<nbr_points(3) ; l++)
                coloc[3]->set(l) = maxt*l/(nbr_points(3)-1) ;
            break ;
        case LEG_TYPE:
            nbr_coefs = nbr_points ;
            nbr_coefs.set(2) += 2 ;
            del_deriv() ;
            for (int i=0 ; i<ndim ; i++) 
                coloc[i] = new Array<double> (nbr_points(i)) ;
            for (int i=0 ; i<ndim ; i++) 
                coloc[i] = new Array<double> (nbr_points(i)) ;
            for (int i=0 ; i<nbr_points(0) ; i++)
                coloc[0]->set(i) = coloc_leg(i, nbr_points(0)) ;
            for (int j=0 ; j<nbr_points(1) ; j++)
                coloc[1]->set(j) = M_PI/2.*j/(nbr_points(1)-1) ;
            for (int k=0 ; k<nbr_points(2) ; k++)
                coloc[2]->set(k) = M_PI*2.*k/nbr_points(2) ;
            for (int l=0 ; l<nbr_points(3) ; l++)
                coloc[3]->set(l) = maxt*l/(nbr_points(3)-1) ;
            break ;
        default :
            cerr << "Unknown type of basis in Domain_fourD_periodic_shell::do_coloc" << endl ;
            abort() ;
    }
}
 
 
void Domain_fourD_periodic_shell::set_cheb_base_x_cart(Base_spectral& base) const  {
 
    assert (type_base == CHEB_TYPE) ;
    base.allocate(nbr_coefs) ;
        
    base.def =true ;
    // Time
    base.bases_1d[3]->set(0) = COS ;
    
    for (int l=0 ; l<nbr_coefs(3) ; l++) {
        // Phi
        base.bases_1d[2]->set(l) = COSSIN ;
        for (int k=0 ; k<nbr_coefs(2) ; k++) {
            // Theta
            base.bases_1d[1]->set(k, l) = SIN_ODD ;
            for (int j=0 ; j<nbr_coefs(1) ; j++)
            // r 
            base.bases_1d[0]->set(j, k, l) = CHEB ;
         }
    }   
}
 
 
void Domain_fourD_periodic_shell::set_cheb_base_y_cart(Base_spectral& base) const  {
 
    assert (type_base == CHEB_TYPE) ;
    base.allocate(nbr_coefs) ;
        
    base.def =true ;
    // Time
    base.bases_1d[3]->set(0) = COS ;
    
    for (int l=0 ; l<nbr_coefs(3) ; l++) {
        // Phi
        base.bases_1d[2]->set(l) = COSSIN ;
        for (int k=0 ; k<nbr_coefs(2) ; k++) {
            // Theta
            base.bases_1d[1]->set(k, l) = SIN_ODD ;
            for (int j=0 ; j<nbr_coefs(1) ; j++)
            // r 
            base.bases_1d[0]->set(j, k, l) = CHEB ;
         }
    }   
}
 
void Domain_fourD_periodic_shell::set_legendre_base_x_cart(Base_spectral& base) const  {
 
    assert (type_base == LEG_TYPE) ;
    base.allocate(nbr_coefs) ;
        
    base.def =true ;
    // Time
    base.bases_1d[3]->set(0) = COS ;
    
    for (int l=0 ; l<nbr_coefs(3) ; l++) {
        // Phi
        base.bases_1d[2]->set(l) = COSSIN ;
        for (int k=0 ; k<nbr_coefs(2) ; k++) {
            // Theta
            base.bases_1d[1]->set(k, l) = SIN_ODD ;
            for (int j=0 ; j<nbr_coefs(1) ; j++)
            // r 
            base.bases_1d[0]->set(j, k, l) = LEG ;
         }
    }   
}
 
 
void Domain_fourD_periodic_shell::set_legendre_base_y_cart(Base_spectral& base) const  {
 
    assert (type_base == LEG_TYPE) ;
    base.allocate(nbr_coefs) ;
        
    base.def =true ;
    // Time
    base.bases_1d[3]->set(0) = COS ;
    
    for (int l=0 ; l<nbr_coefs(3) ; l++) {
        // Phi
        base.bases_1d[2]->set(l) = COSSIN ;
        for (int k=0 ; k<nbr_coefs(2) ; k++) {
            // Theta
            base.bases_1d[1]->set(k, l) = SIN_ODD ;
            for (int j=0 ; j<nbr_coefs(1) ; j++)
            // r 
            base.bases_1d[0]->set(j, k, l) = LEG ;
         }
    }   
}
 
 
 
// Computes the derivatives with respect to rho,Z as a function of the numerical ones.
void Domain_fourD_periodic_shell::do_der_abs_from_der_var(const Val_domain *const *const der_var, Val_domain **const der_abs) const {
 
    // d/dx :
    Val_domain sintdr (der_var[0]->mult_sin_theta()/alpha) ;    
    Val_domain dtsr (*der_var[1]/get_radius()) ;
    dtsr.set_base() = der_var[1]->get_base() ;
    Val_domain dpsr (*der_var[2]/get_radius()) ;    
    dpsr.set_base() = der_var[2]->get_base() ;
    Val_domain costdtsr (dtsr.mult_cos_theta()) ;
 
    Val_domain dpsrssint (dpsr.div_sin_theta()) ;
    der_abs[0] = new Val_domain ((sintdr+costdtsr).mult_cos_phi() - dpsrssint.mult_sin_phi()) ;
 
    // d/dy :
    der_abs[1] = new Val_domain ((sintdr+costdtsr).mult_sin_phi() + dpsrssint.mult_cos_phi()) ;
    // d/dz :
    der_abs[2] = new Val_domain (der_var[0]->mult_cos_theta()/alpha - dtsr.mult_sin_theta()) ;
    
    // d/dt :
    der_abs[3] = new Val_domain (*der_var[3]*ome) ;
}
 
// Rules for the multiplication of two basis.
Base_spectral Domain_fourD_periodic_shell::mult (const Base_spectral& a, const Base_spectral& b) const {
 
    assert (a.ndim==4) ;
    assert (b.ndim==4) ;
    
    Base_spectral res(4) ;
    bool res_def = true ;
 
    if (!a.def)
        res_def=false ;
    if (!b.def)
        res_def=false ;
        
    if (res_def) {
 
 
    // Bases in time :
    res.bases_1d[3] = new Array<int> (a.bases_1d[3]->get_dimensions()) ;
    switch ((*a.bases_1d[3])(0)) {
        case COS:
            switch ((*b.bases_1d[3])(0)) {
                case COS:
                    res.bases_1d[3]->set(0) = COS ;
                    break ;
                case SIN:
                    res.bases_1d[3]->set(0) = SIN ;
                    break ;
                default:
                    res_def = false ;
                    break ;
                }
            break ; 
        case SIN:
            switch ((*b.bases_1d[3])(0)) {
                case COS:
                    res.bases_1d[3]->set(0) = SIN ;
                    break ;
                case SIN:
                    res.bases_1d[3]->set(0) = COS ;
                    break ;
                default:
                    res_def = false ;
                    break ;
                }
            break ;
    }
 
    // Base in phi :
    Index index_2 (a.bases_1d[2]->get_dimensions()) ;
    res.bases_1d[2] = new Array<int> (a.bases_1d[2]->get_dimensions()) ;
    do {
    switch ((*a.bases_1d[2])(index_2)) {
        case COSSIN:
            switch ((*b.bases_1d[2])(index_2)) {
                case COSSIN:
                    res.bases_1d[2]->set(index_2) = COSSIN ;
                    break ;
                default:
                    res_def = false ;
                    break ;
                }
            break ;
        default:
            res_def = false ;
            break ;
    }
    } while (index_2.inc()) ;
 
    // Bases in theta :
    Index index_1 (a.bases_1d[1]->get_dimensions()) ;
    res.bases_1d[1] = new Array<int> (a.bases_1d[1]->get_dimensions()) ;
    do {
    switch ((*a.bases_1d[1])(index_1)) {
        case COS_EVEN:
            switch ((*b.bases_1d[1])(index_1)) {
                case COS_EVEN:
                    res.bases_1d[1]->set(index_1) = COS_EVEN  ;
                    break ;
                case COS_ODD:
                    res.bases_1d[1]->set(index_1) =  COS_ODD ;
                    break ;
                case SIN_EVEN:
                    res.bases_1d[1]->set(index_1) =  SIN_EVEN ;
                    break ;
                case SIN_ODD:
                    res.bases_1d[1]->set(index_1) =  SIN_ODD ;
                    break ;
                default:
                    res_def = false ;
                    break ;
                }
            break ;
        case COS_ODD:
            switch ((*b.bases_1d[1])(index_1)) {
                case COS_EVEN:
                    res.bases_1d[1]->set(index_1) = COS_ODD  ;
                    break ;
                case COS_ODD:
                    res.bases_1d[1]->set(index_1) = COS_EVEN  ;
                    break ;
                case SIN_EVEN:
                    res.bases_1d[1]->set(index_1) = SIN_ODD ;
                    break ;
                case SIN_ODD:
                    res.bases_1d[1]->set(index_1) =  SIN_EVEN ;
                    break ;
                default:
                    res_def = false ;
                    break ;
                }
            break ;
        case SIN_EVEN:
            switch ((*b.bases_1d[1])(index_1)) {
                case COS_EVEN:
                    res.bases_1d[1]->set(index_1) = SIN_EVEN ;
                    break ;
                case COS_ODD:
                    res.bases_1d[1]->set(index_1) =  SIN_ODD  ;
                    break ;
                case SIN_EVEN:
                    res.bases_1d[1]->set(index_1) = COS_EVEN  ;
                    break ;
                case SIN_ODD:
                    res.bases_1d[1]->set(index_1) = COS_ODD ;
                    break ;
                default:
                    res_def = false ;
                    break ;
                }
            break ;
        case SIN_ODD:
            switch ((*b.bases_1d[1])(index_1)) {
                case COS_EVEN:
                    res.bases_1d[1]->set(index_1) = SIN_ODD ;
                    break ;
                case COS_ODD:
                    res.bases_1d[1]->set(index_1) = SIN_EVEN ;
                    break ;
                case SIN_EVEN:
                    res.bases_1d[1]->set(index_1) = COS_ODD  ;
                    break ;
                case SIN_ODD:
                    res.bases_1d[1]->set(index_1) =  COS_EVEN ;
                    break ;
                default:
                    res_def = false ;
                    break ;
                }
            break ;
        default:
            res_def = false ;
            break ;
        }
    }
    while (index_1.inc()) ;
 
 
    // Base in r :
    Index index_0 (a.bases_1d[0]->get_dimensions()) ;
    res.bases_1d[0] = new Array<int> (a.bases_1d[0]->get_dimensions()) ;
    do {
    switch ((*a.bases_1d[0])(index_0)) {
        case CHEB:
            switch ((*b.bases_1d[0])(index_0)) {
                case CHEB:
                    res.bases_1d[0]->set(index_0) = CHEB ;
                    break ;
                default:
                    res_def = false ;
                    break ;
                }
            break ;
        case LEG:
            switch ((*b.bases_1d[0])(index_0)) {
                case LEG:
                    res.bases_1d[0]->set(index_0) = LEG ;
                    break ;
                default:
                    res_def = false ;
                    break ;
                }
            break ;
        default:
            res_def = false ;
            break ;
        }
    }
    while (index_0.inc()) ;
    }
        
 
    if (!res_def) 
        for (int dim=0 ; dim<a.ndim ; dim++)
            if (res.bases_1d[dim]!= 0x0) {
                delete res.bases_1d[dim] ;
                res.bases_1d[dim] = 0x0 ;
                }
    res.def = res_def ;
    return res ;
}
 
 
Val_domain Domain_fourD_periodic_shell::translate (const Val_domain& so) const {
 
    Val_domain res(this) ;
 
    // Construction bases 
    Base_spectral base (4) ;
    base.allocate (get_nbr_coefs()) ;
    
    // Time base
    base.bases_1d[3] = new Array<int> (1) ;
    base.bases_1d[3]->set(0) = (*so.get_base().bases_1d[2])(0) ;
 
    // Phi base
    base.bases_1d[2] = new Array<int> (get_nbr_coefs()(3)) ;
    for (int i=0 ; i<get_nbr_coefs()(3) ; i++)
        base.bases_1d[2]->set(i) = COSSIN ;
 
    // Theta base 
    base.bases_1d[1] = new Array<int> (get_nbr_coefs()(2), get_nbr_coefs()(3)) ;
    for (int l=0 ; l<get_nbr_coefs()(3) ; l++)
        for (int k=0 ; k<get_nbr_coefs()(2) ; k++) {
            base.bases_1d[1]->set(k,l) = (*so.get_base().bases_1d[1])(l) ;
    }
 
    // radial base
    base.bases_1d[0] = new Array<int> (get_nbr_coefs()(1), get_nbr_coefs()(2), get_nbr_coefs()(3)) ;
    for (int l=0 ; l<get_nbr_coefs()(3) ; l++)
        for (int k=0 ; k<get_nbr_coefs()(2) ; k++) 
            for (int j=0 ; j<get_nbr_coefs()(1) ; j++) {
            base.bases_1d[0]->set(j, k,l) = (*so.get_base().bases_1d[0])(j, l) ;
    }
    base.def = true ;
    res.set_base() = base ;
 
    // Now affecte the coefficients
    so.coef() ;
    res.annule_hard() ;
    res.coef() ;
    Index pso (so.get_domain()->get_nbr_coefs()) ;
    Index pcf (get_nbr_coefs()) ;
 
    do {
        pcf.set(3) = pso(2) ; // t coef
        pcf.set(2) = 0. ; // phi coef 
        pcf.set(1) = pso(1) ; // Theta coef
        pcf.set(0) = pso(0) ; // r coef
        res.set_coef(pcf) = so.get_coef(pso) ;
    }
    while (pso.inc()) ;
 
    return res ;
 
}
 
 
}