domain_polar_compact_ope.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 "polar.hpp"
#include "val_domain.hpp"
#include "array_math.hpp"
namespace Kadath {
int mult_cos_1d (int, Array<double>&) ;
int mult_sin_1d (int, Array<double>&) ;
int div_sin_1d (int, Array<double>&) ;
int div_xm1_1d (int, Array<double>&) ;
int mult_xm1_1d (int, Array<double>&) ;
int div_xp1_1d (int, Array<double>&) ;
 
Val_domain Domain_polar_compact::mult_cos_theta (const Val_domain& so) const {
    so.coef() ;
    Val_domain res(this) ;
 
    res.base = so.base ;    
    
    res.cf = new Array<double> (so.base.ope_1d(mult_cos_1d, 1, *so.cf, res.base)) ;
    res.in_coef = true ;
    return res ;
}
 
Val_domain Domain_polar_compact::mult_sin_theta (const Val_domain& so) const {
    so.coef() ;
    Val_domain res(this) ;
 
    res.base= so.base ;
    
    res.cf = new Array<double> (so.base.ope_1d(mult_sin_1d, 1, *so.cf, res.base)) ;
    res.in_coef = true ;
    return res ;
}
 
Val_domain Domain_polar_compact::div_sin_theta (const Val_domain& so) const {
    so.coef() ;
    Val_domain res(this) ;
 
    res.base = so.base ;    
    
    res.cf = new Array<double> (so.base.ope_1d(div_sin_1d, 1, *so.cf, res.base)) ;
    res.in_coef = true ;
    return res ;
}
 
 
Val_domain Domain_polar_compact::mult_xm1 (const Val_domain& so) const {
    so.coef() ;
    Val_domain res(this) ;
 
    res.base= so.base ;
    
    res.cf = new Array<double> (so.base.ope_1d(mult_xm1_1d, 0, *so.cf, res.base)) ;
    res.in_coef = true ;
    return res ;
}
 
Val_domain Domain_polar_compact::div_xm1 (const Val_domain& so) const {
    so.coef() ;
    Val_domain res(this) ;
 
    res.base = so.base ;    
    
    res.cf = new Array<double> (so.base.ope_1d(div_xm1_1d, 0, *so.cf, res.base)) ;
    res.in_coef = true ;
    return res ;
}
 
Val_domain Domain_polar_compact::mult_r (const Val_domain& so) const {
    so.coef() ;
    Val_domain res(div_xm1(so)) ;
    res /= alpha ;
    return res ;
}
 
Val_domain Domain_polar_compact::div_r (const Val_domain& so) const {
    so.coef() ;
    Val_domain res(mult_xm1(so)) ;
    res *= alpha ;
    return res ;
}
 
Val_domain Domain_polar_compact::laplacian (const Val_domain& so, int m) const {
  Val_domain derr (-alpha*so.der_var(1).mult_xm1().mult_xm1()) ;
  Val_domain dderr (-alpha*derr.der_var(1).mult_xm1().mult_xm1()) ;
  Val_domain dert (so.der_var(2)) ;
  Val_domain res (dderr + div_r(2*derr + div_r(dert.der_var(2) + dert.mult_cos_theta().div_sin_theta()))) ;
  if (m!=0)
    res -= m * m * div_r(div_r(so.div_sin_theta().div_sin_theta())) ;
  return res ;
}
 
Val_domain Domain_polar_compact::laplacian2 (const Val_domain& so, int m) const {
  Val_domain derr (-alpha*so.der_var(1).mult_xm1().mult_xm1()) ;
  Val_domain dderr (-alpha*derr.der_var(1).mult_xm1().mult_xm1()) ;
  Val_domain dert (so.der_var(2)) ;
  Val_domain res (dderr + div_r(derr + div_r(dert.der_var(2)))) ;
  if (m!=0)
    res -= m * m * div_r(div_r(so.div_sin_theta().div_sin_theta())) ;
  return res ;
}
 
Val_domain Domain_polar_compact::der_r (const Val_domain& so) const {
  return (-alpha*so.der_var(1).mult_xm1().mult_xm1()) ;
}
 
 
Val_domain Domain_polar_compact::dt (const Val_domain& so) const {
  return (so.der_var(2)) ;
}
 
Val_domain Domain_polar_compact::der_r_rtwo (const Val_domain& so) const {
  return (-so.der_var(1)/alpha) ;
}
 
 
Val_domain Domain_polar_compact::div_xp1 (const Val_domain& so) const {
    so.coef() ;
    Val_domain res(this) ;
 
    res.base= so.base ;
 
    res.cf = new Array<double> (so.base.ope_1d(div_xp1_1d, 0, *so.cf, res.base)) ;
    res.in_coef = true ;
    return res ;
}
 
double Domain_polar_compact::integrale (const Val_domain& so) const {
  double res = 0 ;
  Val_domain integrant (so) ;
 
  for (int i=0 ; i<3 ; i++) {
    Val_domain auxi (integrant.div_xm1()) ;
    auxi.coef_i() ;
    set_val_inf(auxi, 0.) ; //Filtering
    integrant = auxi ;
  }
 
  integrant.coef() ;
  integrant.get_coef() ;
  Array<double> cf (integrant.get_coef()) ;
 
  int baset = (*integrant.get_base().bases_1d[1]) (0) ;
  switch (baset) {
    case COS_ODD :
    break ;
    case SIN_EVEN :
    break ;
    case COS_EVEN : {
    // Only m=0 :
    double facttheta = M_PI ;
    int baser = (*integrant.get_base().bases_1d[0]) (0) ;
    switch (baser) {
          case CHEB : {
            for (int i=0 ; i<nbr_coefs(0) ; i+=2) {
            res += facttheta * (1./double(i+1) - 1./double(i-1)) *cf(i,0) ;
            }
            break ;
            }
          case LEG : {
           res += facttheta*2*cf(0,0) ;
           break ;
          }
          default :
          cerr << "Case not yet implemented in Domain_polar_compact::integrale" << endl ;
          abort() ;
    }
    break ;
    }
    case SIN_ODD : {
      for (int j=0 ; j<nbr_coefs(1) ; j++) {
        double facttheta = 2./double(2*j+1) ;
        int baser = (*integrant.get_base().bases_1d[0]) (0) ;
      switch (baser) {
          case CHEB : {
            for (int i=0 ; i<nbr_coefs(0) ; i+=2)
            res += facttheta * (1./double(i+1) - 1./double(i-1)) *cf(i,j) ;
            break ;
            }
          case LEG : {
           res += facttheta*2*cf(0,j) ;
           break ;
          }
          default :
          cerr << "Case not yet implemented in Domain_polar_compact::integrale" << endl ;
          abort() ;
        }
      }
      break ;
    }
    default : 
      cerr << "Case not yet implemented in Domain_polar_compact::integrale" << endl ;
      abort() ;
  }
 
  // Phi contribution :
  res *= -1./alpha/alpha ;
  return res ;
}
 
double Domain_polar_compact::integ_volume(const Val_domain& so) const {
  return integrale(so) ;
}
 
  }