domain_spheric_periodic_compact.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 "spheric_periodic.hpp"
#include "array_math.hpp"
#include "val_domain.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_spheric_periodic_compact::Domain_spheric_periodic_compact (int num, int ttype, int typet, double rint, double oome, const Dim_array& nbr) :  
        Domain(num, ttype, nbr), alpha(-0.5/rint), ome(oome), type_time (typet) {
     assert (nbr.get_ndim()==2) ; 
    switch (type_time) {
    case TO_PI :
        maxt = M_PI ;
        break ;
    case TO_PI_OVER_2 :
        maxt = M_PI / 2. ;
        break ;
    default:
        cerr << "Unknown case for type_time" << endl ;
        abort()  ;
     }
     do_coloc() ;
}
 
// Constructor by copy
Domain_spheric_periodic_compact::Domain_spheric_periodic_compact (const Domain_spheric_periodic_compact& so) : Domain(so), alpha(so.alpha), ome(so.ome),
                      type_time(so.type_time), maxt (so.maxt) {
}
 
Domain_spheric_periodic_compact::Domain_spheric_periodic_compact (int num, FILE* fd) : Domain(num, fd) {
    fread_be (&alpha, 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 ;
      case TO_PI_OVER_2 :
        maxt = M_PI / 2. ;
        break ;
      default:
        cerr << "Unknown case for type_time" << endl ;
        abort()  ;
    }
    do_coloc() ;
}
 
// Destructor
Domain_spheric_periodic_compact::~Domain_spheric_periodic_compact() {}
 
void Domain_spheric_periodic_compact::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 (&ome, sizeof(double), 1, fd) ;
    fwrite_be (&type_time, sizeof(int), 1, fd) ;
}
 
ostream& Domain_spheric_periodic_compact::print (ostream& o) const {
  o << "Spheric-periodic compact" << endl ;
  o << "Rint    = " << -0.5/alpha << endl ;  
  o << "time goes to " << maxt << endl ;
  o << "Omega   = " << ome << endl ;
  o << "Nbr pts = " << nbr_points << endl ;
  o << endl ;
  return o ;
}
 
 
Val_domain Domain_spheric_periodic_compact::der_normal (const Val_domain& so, int bound) const {
 
    Val_domain res (so.der_var(1)) ;
    switch (bound) {
        case OUTER_BC :
            res = res.mult_xm1() ;
            res = res.mult_xm1() ;
            res *= -alpha ;
            break ;
        case INNER_BC :
            res = res.mult_xm1() ;
            res = res.mult_xm1() ;
            res *= -alpha ;
            break ;
        default:
            cerr << "Unknown boundary case in Domain_spheric_periodic_compact::der_normal" << endl ;
            abort() ;
        }
return res ;
}
 
// Computes the cartesian coordinates
void Domain_spheric_periodic_compact::do_absol () const {
    for (int i=0 ; i<2 ; i++)
       assert (coloc[i] != 0x0) ;
    for (int i=0 ; i<2 ; i++)
       assert (absol[i] == 0x0) ;
    for (int i=0 ; i<2 ; i++) {
       absol[i] = new Val_domain(this) ;
       absol[i]->allocate_conf() ;
       }
    Index index (nbr_points) ;
    do  {
        absol[0]->set(index) = 1./alpha / ((*coloc[0])(index(0))-1) ;
        absol[1]->set(index) = (*coloc[1])(index(1)) / ome ;
    }
    while (index.inc())  ;
    
}
 
// Computes the radius
void Domain_spheric_periodic_compact::do_radius ()  const {
 
    for (int i=0 ; i<2 ; i++)
       assert (coloc[i] != 0x0) ;
    assert (radius == 0x0) ;
    radius = new Val_domain(this) ;
    radius->allocate_conf() ;
    Index index (nbr_points) ;
    do
        radius->set(index) = 1./alpha/ ((*coloc[0])(index(0))-1) ;
    while (index.inc())  ;
}
 
// Is a point inside this domain ?
bool Domain_spheric_periodic_compact::is_in (const Point& xx, double prec) const {
 
    assert (xx.get_ndim()==2) ;
    
    
    bool res = (xx(1) >= -0.5/alpha+prec) ? true : false ;
    if ((xx(2)<0-prec) || (xx(2)>maxt/ome + prec))
          res = false ;
    return res ;
}
 
// Convert absolute coordinates to numerical ones
const Point Domain_spheric_periodic_compact::absol_to_num(const Point& abs) const {
 
    assert (is_in(abs)) ;
    Point num(2) ;
    
    num.set(1) = 1 + 1./abs(1)/alpha ;
    num.set(2) = abs(2)*ome ;
    
    return num ;
}
 
double coloc_leg(int, int) ;
void Domain_spheric_periodic_compact::do_coloc () {
 
    switch (type_base) {
        case CHEB_TYPE:
            nbr_coefs = nbr_points ;
            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) = maxt*j/(nbr_points(1)-1) ;
            break ;
        case LEG_TYPE:
            nbr_coefs = nbr_points ;
            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) = coloc_leg(i, nbr_points(0)) ;
            for (int j=0 ; j<nbr_points(1) ; j++)
                coloc[1]->set(j) = maxt*j/(nbr_points(1)-1) ;
            break ;
        default :
            cerr << "Unknown type of basis in Domain_spheric_periodic_compact::do_coloc" << endl ;
            abort() ;
    }
}
 
// Base for a function symetric in z, using Chebyshev
void Domain_spheric_periodic_compact::set_cheb_base(Base_spectral& base) const {
 
    assert (type_base == CHEB_TYPE) ;
    base.allocate(nbr_coefs) ;
    
    Index index(base.bases_1d[0]->get_dimensions()) ;
    
    base.def=true ;
    switch (type_time) {
      case TO_PI :
        base.bases_1d[1]->set(0) = COS ;
        break ;
      case TO_PI_OVER_2 :
        base.bases_1d[1]->set(0) = COS_EVEN ;
        break ;
      default:
        cerr << "Unknown case for type_time" << endl ;
        abort()  ;
    }
    for (int j=0 ; j<nbr_coefs(1) ; j++)
        base.bases_1d[0]->set(j) = CHEB ;
}
void Domain_spheric_periodic_compact::set_cheb_base_odd(Base_spectral& base) const {
 
    assert (type_base == CHEB_TYPE) ;
    base.allocate(nbr_coefs) ;
    
    Index index(base.bases_1d[0]->get_dimensions()) ;
    
    base.def=true ;
    switch (type_time) {
      case TO_PI_OVER_2 :
        base.bases_1d[1]->set(0) = COS_ODD ;
        break ;
      default:
        cerr << "Unknown case for type_time" << endl ;
        abort()  ;
    }
    for (int j=0 ; j<nbr_coefs(1) ; j++)
        base.bases_1d[0]->set(j) = CHEB ;
}
void Domain_spheric_periodic_compact::set_anti_cheb_base(Base_spectral& base) const {
 
    assert (type_base == CHEB_TYPE) ;
    base.allocate(nbr_coefs) ;
    
    Index index(base.bases_1d[0]->get_dimensions()) ;
    
    base.def=true ;
    switch (type_time) {
      case TO_PI :
        base.bases_1d[1]->set(0) = COS ;
        break ;
      case TO_PI_OVER_2 :
        base.bases_1d[1]->set(0) = COS_EVEN ;
        break ;
      default:
        cerr << "Unknown case for type_time" << endl ;
        abort()  ;
    }
    for (int j=0 ; j<nbr_coefs(1) ; j++)
        base.bases_1d[0]->set(j) = CHEB ;
}
 
// Base for a function symetric in z, using Legendre
void Domain_spheric_periodic_compact::set_legendre_base_odd(Base_spectral& base) const  {
 
    assert (type_base == LEG_TYPE) ;
    base.allocate(nbr_coefs) ;
    
    Index index(base.bases_1d[0]->get_dimensions()) ;
    base.def=true ;
    switch (type_time) {
      case TO_PI_OVER_2 :
        base.bases_1d[1]->set(0) = COS_ODD ;
        break ;
      default:
        cerr << "Unknown case for type_time" << endl ;
        abort()  ;
    }
    for (int j=0 ; j<nbr_coefs(1) ; j++)
        base.bases_1d[0]->set(j) = LEG ;
 }
// Base for a function symetric in z, using Legendre
void Domain_spheric_periodic_compact::set_legendre_base(Base_spectral& base) const  {
 
    assert (type_base == LEG_TYPE) ;
    base.allocate(nbr_coefs) ;
    
    Index index(base.bases_1d[0]->get_dimensions()) ;
    base.def=true ;
    switch (type_time) {
      case TO_PI :
        base.bases_1d[1]->set(0) = COS ;
        break ;
      case TO_PI_OVER_2 :
        base.bases_1d[1]->set(0) = COS_EVEN ;
        break ;
      default:
        cerr << "Unknown case for type_time" << endl ;
        abort()  ;
    }
    for (int j=0 ; j<nbr_coefs(1) ; j++)
        base.bases_1d[0]->set(j) = LEG ;
 }
void Domain_spheric_periodic_compact::set_anti_legendre_base(Base_spectral& base) const  {
 
    assert (type_base == LEG_TYPE) ;
    base.allocate(nbr_coefs) ;
    
    Index index(base.bases_1d[0]->get_dimensions()) ;
    base.def=true ;
    switch (type_time) {
      case TO_PI :
        base.bases_1d[1]->set(0) = COS ;
        break ;
      case TO_PI_OVER_2 :
        base.bases_1d[1]->set(0) = COS_EVEN ;
        break ;
      default:
        cerr << "Unknown case for type_time" << endl ;
        abort()  ;
    }
    for (int j=0 ; j<nbr_coefs(1) ; j++)
        base.bases_1d[0]->set(j) = LEG ;
 }
// Computes the derivatives with respect to rho,Z as a function of the numerical ones.
void Domain_spheric_periodic_compact::do_der_abs_from_der_var(const Val_domain *const *const der_var, Val_domain **const der_abs) const {
    // d/dr
    der_abs[0] = new Val_domain (-der_var[0]->mult_xm1()) ;
    // d/dt :
    der_abs[1] = new Val_domain (*der_var[1]*ome) ;
}
 
 
// sets the value at infinity
void Domain_spheric_periodic_compact::set_val_inf (Val_domain& so, double x) const {
 
    assert (so.get_domain() == this) ;
 
    so.coef_i() ;
    so.set_in_conf() ;
    Index inf (nbr_points) ;
    inf.set(0) = nbr_points(0)-1 ;
    do 
        so.set(inf) = x ;
    while (inf.inc1(1)) ;
}
 
 
// Rules for the multiplication of two basis.
Base_spectral Domain_spheric_periodic_compact::mult (const Base_spectral& a, const Base_spectral& b) const {
 
 
    assert (a.ndim==2) ;
    assert (b.ndim==2) ;
    
    Base_spectral res(2) ;
    bool res_def = true ;
 
    if (!a.def)
        res_def=false ;
    if (!b.def)
        res_def=false ;
        
    if (res_def) {
 
 
    // Bases in theta :
    res.bases_1d[1] = new Array<int> (a.bases_1d[1]->get_dimensions()) ;
    switch ((*a.bases_1d[1])(0)) {
        case COS:
            switch ((*b.bases_1d[1])(0)) {
                case COS:
                    res.bases_1d[1]->set(0) = COS ;
                    break ;
                case SIN:
                    res.bases_1d[1]->set(0) = SIN ;
                    break ;
                default:
                    res_def = false ;
                    break ;
                }
            break ;
 
        case SIN:
            switch ((*b.bases_1d[1])(0)) {
                case COS:
                    res.bases_1d[1]->set(0) = SIN ;
                    break ;
                case SIN:
                    res.bases_1d[1]->set(0) = COS ;
                    break ;
                default:
                    res_def = false ;
                    break ;
                }
            break ;
        case COS_EVEN:
            switch ((*b.bases_1d[1])(0)) {
                case COS_EVEN:
                    res.bases_1d[1]->set(0) = COS_EVEN ;
                    break ;
                case COS_ODD:
                    res.bases_1d[1]->set(0) = COS_ODD ;
                    break ;
                case SIN_EVEN:
                    res.bases_1d[1]->set(0) = SIN_EVEN ;
                    break ;
                case SIN_ODD:
                    res.bases_1d[1]->set(0) = SIN_ODD ;
                    break ;
                default:
                    res_def = false ;
                    break ;
                }
            break ;
        case COS_ODD:
            switch ((*b.bases_1d[1])(0)) {
                case COS_EVEN:
                    res.bases_1d[1]->set(0) = COS_ODD ;
                    break ;
                case COS_ODD:
                    res.bases_1d[1]->set(0) = COS_EVEN ;
                    break ;
                case SIN_EVEN:
                    res.bases_1d[1]->set(0) = SIN_ODD ;
                    break ;
                case SIN_ODD:
                    res.bases_1d[1]->set(0) = SIN_EVEN ;
                    break ;
                default:
                    res_def = false ;
                    break ;
                }
            break ;
        case SIN_EVEN:
            switch ((*b.bases_1d[1])(0)) {
                case COS_EVEN:
                    res.bases_1d[1]->set(0) = SIN_EVEN ;
                    break ;
                case COS_ODD:
                    res.bases_1d[1]->set(0) = SIN_ODD ;
                    break ;
                case SIN_EVEN:
                    res.bases_1d[1]->set(0) = COS_EVEN ;
                    break ;
                case SIN_ODD:
                    res.bases_1d[1]->set(0) = COS_ODD ;
                    break ;
                default:
                    res_def = false ;
                    break ;
                }
            break ;
        case SIN_ODD:
            switch ((*b.bases_1d[1])(0)) {
                case COS_EVEN:
                    res.bases_1d[1]->set(0) = SIN_ODD ;
                    break ;
                case COS_ODD:
                    res.bases_1d[1]->set(0) = SIN_EVEN ;
                    break ;
                case SIN_EVEN:
                    res.bases_1d[1]->set(0) = COS_ODD ;
                    break ;
                case SIN_ODD:
                    res.bases_1d[1]->set(0) = COS_EVEN ;
                    break ;
                default:
                    res_def = false ;
                    break ;
                }
            break ;
        default:
            res_def = false ;
            break ;
    }
 
    // 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 ;
}
}