// ---------------------------------------------------------------------------------------------------------------------
//! Project local densities only (Frozen species)
// ---------------------------------------------------------------------------------------------------------------------
void Projector3D4Order::basic( double *rhoj, Particles &particles, unsigned int ipart, unsigned int type )
{
//Warning : this function is used for frozen species or initialization only and doesn't use the standard scheme.
//rho type = 0
//Jx type = 1
//Jy type = 2
//Jz type = 3
// -------------------------------------
// Variable declaration & initialization
// -------------------------------------
int iloc, jloc;
int ny( nprimy ), nz( nprimz ), nyz;
// (x,y,z) components of the current density for the macro-particle
double charge_weight = inv_cell_volume * ( double )( particles.charge( ipart ) )*particles.weight( ipart );
if( type > 0 ) {
charge_weight *= 1./sqrt( 1.0 + particles.momentum( 0, ipart )*particles.momentum( 0, ipart )
+ particles.momentum( 1, ipart )*particles.momentum( 1, ipart )
+ particles.momentum( 2, ipart )*particles.momentum( 2, ipart ) );
if( type == 1 ) {
charge_weight *= particles.momentum( 0, ipart );
} else if( type == 2 ) {
charge_weight *= particles.momentum( 1, ipart );
ny ++;
} else {
charge_weight *= particles.momentum( 2, ipart );
nz ++;
}
}
nyz = ny*nz;
// variable declaration
double xpn, ypn, zpn;
double delta, delta2, delta3, delta4;
double Sx1[7], Sy1[7], Sz1[7]; // arrays used for the Esirkepov projection method
// Initialize all current-related arrays to zero
for( unsigned int i=0; i<7; i++ ) {
Sx1[i] = 0.;
Sy1[i] = 0.;
Sz1[i] = 0.;
}
// --------------------------------------------------------
// Locate particles & Calculate Esirkepov coef. S, DS and W
// --------------------------------------------------------
// locate the particle on the primal grid at current time-step & calculate coeff. S1
xpn = particles.position( 0, ipart ) * dx_inv_;
int ip = round( xpn+ 0.5*( type==1 ) );
delta = xpn - ( double )ip;
delta2 = delta*delta;
delta3 = delta2*delta;
delta4 = delta3*delta;
Sx1[1] = dble_1_ov_384 - dble_1_ov_48 * delta + dble_1_ov_16 * delta2 - dble_1_ov_12 * delta3 + dble_1_ov_24 * delta4;
Sx1[2] = dble_19_ov_96 - dble_11_ov_24 * delta + dble_1_ov_4 * delta2 + dble_1_ov_6 * delta3 - dble_1_ov_6 * delta4;
Sx1[3] = dble_115_ov_192 - dble_5_ov_8 * delta2 + dble_1_ov_4 * delta4;
Sx1[4] = dble_19_ov_96 + dble_11_ov_24 * delta + dble_1_ov_4 * delta2 - dble_1_ov_6 * delta3 - dble_1_ov_6 * delta4;
Sx1[5] = dble_1_ov_384 + dble_1_ov_48 * delta + dble_1_ov_16 * delta2 + dble_1_ov_12 * delta3 + dble_1_ov_24 * delta4;
ypn = particles.position( 1, ipart ) * dy_inv_;
int jp = round( ypn+ 0.5*( type==2 ) );
delta = ypn - ( double )jp;
delta2 = delta*delta;
delta3 = delta2*delta;
delta4 = delta3*delta;
Sy1[1] = dble_1_ov_384 - dble_1_ov_48 * delta + dble_1_ov_16 * delta2 - dble_1_ov_12 * delta3 + dble_1_ov_24 * delta4;
Sy1[2] = dble_19_ov_96 - dble_11_ov_24 * delta + dble_1_ov_4 * delta2 + dble_1_ov_6 * delta3 - dble_1_ov_6 * delta4;
Sy1[3] = dble_115_ov_192 - dble_5_ov_8 * delta2 + dble_1_ov_4 * delta4;
Sy1[4] = dble_19_ov_96 + dble_11_ov_24 * delta + dble_1_ov_4 * delta2 - dble_1_ov_6 * delta3 - dble_1_ov_6 * delta4;
Sy1[5] = dble_1_ov_384 + dble_1_ov_48 * delta + dble_1_ov_16 * delta2 + dble_1_ov_12 * delta3 + dble_1_ov_24 * delta4;
zpn = particles.position( 2, ipart ) * dz_inv_;
int kp = round( zpn+ 0.5*( type==3 ) );
delta = zpn - ( double )kp;
delta2 = delta*delta;
delta3 = delta2*delta;
delta4 = delta3*delta;
Sz1[1] = dble_1_ov_384 - dble_1_ov_48 * delta + dble_1_ov_16 * delta2 - dble_1_ov_12 * delta3 + dble_1_ov_24 * delta4;
Sz1[2] = dble_19_ov_96 - dble_11_ov_24 * delta + dble_1_ov_4 * delta2 + dble_1_ov_6 * delta3 - dble_1_ov_6 * delta4;
Sz1[3] = dble_115_ov_192 - dble_5_ov_8 * delta2 + dble_1_ov_4 * delta4;
Sz1[4] = dble_19_ov_96 + dble_11_ov_24 * delta + dble_1_ov_4 * delta2 - dble_1_ov_6 * delta3 - dble_1_ov_6 * delta4;
Sz1[5] = dble_1_ov_384 + dble_1_ov_48 * delta + dble_1_ov_16 * delta2 + dble_1_ov_12 * delta3 + dble_1_ov_24 * delta4;
// ---------------------------
// Calculate the total charge
// ---------------------------
ip -= i_domain_begin + 3;
jp -= j_domain_begin + 3;
kp -= k_domain_begin + 3;
for( unsigned int i=0 ; i<7 ; i++ ) {
iloc = ( i+ip )*nyz;
for( unsigned int j=0 ; j<7 ; j++ ) {
jloc = ( jp+j )*nz;
for( unsigned int k=0 ; k<7 ; k++ ) {
rhoj[iloc+jloc+kp+k] += charge_weight * Sx1[i]*Sy1[j]*Sz1[k];
}
}
}//i
} // END Project local current densities (Frozen species)
// ---------------------------------------------------------------------------------------------------------------------
//! Project local current densities (sort)
// ---------------------------------------------------------------------------------------------------------------------
void Projector3D4Order::currentsAndDensity( double *Jx, double *Jy, double *Jz, double *rho, Particles &particles, unsigned int ipart, double invgf, int *iold, double *deltaold )
{
int nparts = particles.size();
// -------------------------------------
// Variable declaration & initialization
// -------------------------------------
// (x,y,z) components of the current density for the macro-particle
double charge_weight = inv_cell_volume * ( double )( particles.charge( ipart ) )*particles.weight( ipart );
double crx_p = charge_weight*dx_ov_dt;
double cry_p = charge_weight*dy_ov_dt;
double crz_p = charge_weight*dz_ov_dt;
// variable declaration
double xpn, ypn, zpn;
double delta, delta2, delta3, delta4;
// arrays used for the Esirkepov projection method
double Sx0[7], Sx1[7], Sy0[7], Sy1[7], Sz0[7], Sz1[7], DSx[7], DSy[7], DSz[7];
double tmpJx[7][7], tmpJy[7][7], tmpJz[7][7];
for( unsigned int i=0; i<7; i++ ) {
Sx1[i] = 0.;
Sy1[i] = 0.;
Sz1[i] = 0.;
}
for( unsigned int j=0; j<7; j++ )
for( unsigned int k=0; k<7; k++ ) {
tmpJx[j][k] = 0.;
}
for( unsigned int i=0; i<7; i++ )
for( unsigned int k=0; k<7; k++ ) {
tmpJy[i][k] = 0.;
}
for( unsigned int i=0; i<7; i++ )
for( unsigned int j=0; j<7; j++ ) {
tmpJz[i][j] = 0.;
}
// --------------------------------------------------------
// Locate particles & Calculate Esirkepov coef. S, DS and W
// --------------------------------------------------------
// locate the particle on the primal grid at former time-step & calculate coeff. S0
delta = deltaold[0*nparts];
delta2 = delta*delta;
delta3 = delta2*delta;
delta4 = delta3*delta;
Sx0[0] = 0.;
Sx0[1] = dble_1_ov_384 - dble_1_ov_48 * delta + dble_1_ov_16 * delta2 - dble_1_ov_12 * delta3 + dble_1_ov_24 * delta4;
Sx0[2] = dble_19_ov_96 - dble_11_ov_24 * delta + dble_1_ov_4 * delta2 + dble_1_ov_6 * delta3 - dble_1_ov_6 * delta4;
Sx0[3] = dble_115_ov_192 - dble_5_ov_8 * delta2 + dble_1_ov_4 * delta4;
Sx0[4] = dble_19_ov_96 + dble_11_ov_24 * delta + dble_1_ov_4 * delta2 - dble_1_ov_6 * delta3 - dble_1_ov_6 * delta4;
Sx0[5] = dble_1_ov_384 + dble_1_ov_48 * delta + dble_1_ov_16 * delta2 + dble_1_ov_12 * delta3 + dble_1_ov_24 * delta4;
Sx0[6] = 0.;
delta = deltaold[1*nparts];
delta2 = delta*delta;
delta3 = delta2*delta;
delta4 = delta3*delta;
Sy0[0] = 0.;
Sy0[1] = dble_1_ov_384 - dble_1_ov_48 * delta + dble_1_ov_16 * delta2 - dble_1_ov_12 * delta3 + dble_1_ov_24 * delta4;
Sy0[2] = dble_19_ov_96 - dble_11_ov_24 * delta + dble_1_ov_4 * delta2 + dble_1_ov_6 * delta3 - dble_1_ov_6 * delta4;
Sy0[3] = dble_115_ov_192 - dble_5_ov_8 * delta2 + dble_1_ov_4 * delta4;
Sy0[4] = dble_19_ov_96 + dble_11_ov_24 * delta + dble_1_ov_4 * delta2 - dble_1_ov_6 * delta3 - dble_1_ov_6 * delta4;
Sy0[5] = dble_1_ov_384 + dble_1_ov_48 * delta + dble_1_ov_16 * delta2 + dble_1_ov_12 * delta3 + dble_1_ov_24 * delta4;
Sy0[6] = 0.;
delta = deltaold[2*nparts];
delta2 = delta*delta;
delta3 = delta2*delta;
delta4 = delta3*delta;
Sz0[0] = 0.;
Sz0[1] = dble_1_ov_384 - dble_1_ov_48 * delta + dble_1_ov_16 * delta2 - dble_1_ov_12 * delta3 + dble_1_ov_24 * delta4;
Sz0[2] = dble_19_ov_96 - dble_11_ov_24 * delta + dble_1_ov_4 * delta2 + dble_1_ov_6 * delta3 - dble_1_ov_6 * delta4;
Sz0[3] = dble_115_ov_192 - dble_5_ov_8 * delta2 + dble_1_ov_4 * delta4;
Sz0[4] = dble_19_ov_96 + dble_11_ov_24 * delta + dble_1_ov_4 * delta2 - dble_1_ov_6 * delta3 - dble_1_ov_6 * delta4;
Sz0[5] = dble_1_ov_384 + dble_1_ov_48 * delta + dble_1_ov_16 * delta2 + dble_1_ov_12 * delta3 + dble_1_ov_24 * delta4;
Sz0[6] = 0.;
// locate the particle on the primal grid at current time-step & calculate coeff. S1
xpn = particles.position( 0, ipart ) * dx_inv_;
int ip = round( xpn );
int ipo = iold[0*nparts];
int ip_m_ipo = ip-ipo-i_domain_begin;
delta = xpn - ( double )ip;
delta2 = delta*delta;
delta3 = delta2*delta;
delta4 = delta3*delta;
Sx1[ip_m_ipo+1] = dble_1_ov_384 - dble_1_ov_48 * delta + dble_1_ov_16 * delta2 - dble_1_ov_12 * delta3 + dble_1_ov_24 * delta4;
Sx1[ip_m_ipo+2] = dble_19_ov_96 - dble_11_ov_24 * delta + dble_1_ov_4 * delta2 + dble_1_ov_6 * delta3 - dble_1_ov_6 * delta4;
Sx1[ip_m_ipo+3] = dble_115_ov_192 - dble_5_ov_8 * delta2 + dble_1_ov_4 * delta4;
Sx1[ip_m_ipo+4] = dble_19_ov_96 + dble_11_ov_24 * delta + dble_1_ov_4 * delta2 - dble_1_ov_6 * delta3 - dble_1_ov_6 * delta4;
Sx1[ip_m_ipo+5] = dble_1_ov_384 + dble_1_ov_48 * delta + dble_1_ov_16 * delta2 + dble_1_ov_12 * delta3 + dble_1_ov_24 * delta4;
ypn = particles.position( 1, ipart ) * dy_inv_;
int jp = round( ypn );
int jpo = iold[1*nparts];
int jp_m_jpo = jp-jpo-j_domain_begin;
delta = ypn - ( double )jp;
delta2 = delta*delta;
delta3 = delta2*delta;
delta4 = delta3*delta;
Sy1[jp_m_jpo+1] = dble_1_ov_384 - dble_1_ov_48 * delta + dble_1_ov_16 * delta2 - dble_1_ov_12 * delta3 + dble_1_ov_24 * delta4;
Sy1[jp_m_jpo+2] = dble_19_ov_96 - dble_11_ov_24 * delta + dble_1_ov_4 * delta2 + dble_1_ov_6 * delta3 - dble_1_ov_6 * delta4;
Sy1[jp_m_jpo+3] = dble_115_ov_192 - dble_5_ov_8 * delta2 + dble_1_ov_4 * delta4;
Sy1[jp_m_jpo+4] = dble_19_ov_96 + dble_11_ov_24 * delta + dble_1_ov_4 * delta2 - dble_1_ov_6 * delta3 - dble_1_ov_6 * delta4;
Sy1[jp_m_jpo+5] = dble_1_ov_384 + dble_1_ov_48 * delta + dble_1_ov_16 * delta2 + dble_1_ov_12 * delta3 + dble_1_ov_24 * delta4;
zpn = particles.position( 2, ipart ) * dz_inv_;
int kp = round( zpn );
int kpo = iold[2*nparts];
int kp_m_kpo = kp-kpo-k_domain_begin;
delta = zpn - ( double )kp;
delta2 = delta*delta;
delta3 = delta2*delta;
delta4 = delta3*delta;
Sz1[kp_m_kpo+1] = dble_1_ov_384 - dble_1_ov_48 * delta + dble_1_ov_16 * delta2 - dble_1_ov_12 * delta3 + dble_1_ov_24 * delta4;
Sz1[kp_m_kpo+2] = dble_19_ov_96 - dble_11_ov_24 * delta + dble_1_ov_4 * delta2 + dble_1_ov_6 * delta3 - dble_1_ov_6 * delta4;
Sz1[kp_m_kpo+3] = dble_115_ov_192 - dble_5_ov_8 * delta2 + dble_1_ov_4 * delta4;
Sz1[kp_m_kpo+4] = dble_19_ov_96 + dble_11_ov_24 * delta + dble_1_ov_4 * delta2 - dble_1_ov_6 * delta3 - dble_1_ov_6 * delta4;
Sz1[kp_m_kpo+5] = dble_1_ov_384 + dble_1_ov_48 * delta + dble_1_ov_16 * delta2 + dble_1_ov_12 * delta3 + dble_1_ov_24 * delta4;
// computes Esirkepov coefficients
for( unsigned int i=0; i < 7; i++ ) {
DSx[i] = Sx1[i] - Sx0[i];
DSy[i] = Sy1[i] - Sy0[i];
DSz[i] = Sz1[i] - Sz0[i];
}
// ---------------------------
// Calculate the total current
// ---------------------------
ipo -= 3; //This minus 3 come from the order 3 scheme, based on a 7 points stencil from -3 to +3.
// i/j/kpo stored with - i/j/k_domain_begin in Interpolator
jpo -= 3;
kpo -= 3;
int iloc, jloc, kloc, linindex;
// Jx^(d,p,p)
for( unsigned int i=1 ; i<7 ; i++ ) {
iloc = i+ipo;
for( unsigned int j=0 ; j<7 ; j++ ) {
jloc = j+jpo;
for( unsigned int k=0 ; k<7 ; k++ ) {
tmpJx[j][k] -= crx_p * DSx[i-1] * ( Sy0[j]*Sz0[k] + 0.5*DSy[j]*Sz0[k] + 0.5*DSz[k]*Sy0[j] + one_third*DSy[j]*DSz[k] );
kloc = k+kpo;
linindex = iloc*nprimz*nprimy+jloc*nprimz+kloc;
Jx [linindex] += tmpJx[j][k]; // iloc = (i+ipo)*nprimy;
}
}
}//i
// Jy^(p,d,p)
for( unsigned int i=0 ; i<7 ; i++ ) {
iloc = i+ipo;
for( unsigned int j=1 ; j<7 ; j++ ) {
jloc = j+jpo;
for( unsigned int k=0 ; k<7 ; k++ ) {
tmpJy[i][k] -= cry_p * DSy[j-1] * ( Sz0[k]*Sx0[i] + 0.5*DSz[k]*Sx0[i] + 0.5*DSx[i]*Sz0[k] + one_third*DSz[k]*DSx[i] );
kloc = k+kpo;
linindex = iloc*nprimz*( nprimy+1 )+jloc*nprimz+kloc;
Jy [linindex] += tmpJy[i][k]; //
}
}
}//i
// Jz^(p,p,d)
for( unsigned int i=0 ; i<7 ; i++ ) {
iloc = i+ipo;
for( unsigned int j=0 ; j<7 ; j++ ) {
jloc = j+jpo;
for( unsigned int k=1 ; k<7 ; k++ ) {
tmpJz[i][j] -= crz_p * DSz[k-1] * ( Sx0[i]*Sy0[j] + 0.5*DSx[i]*Sy0[j] + 0.5*DSy[j]*Sx0[i] + one_third*DSx[i]*DSy[j] );
kloc = k+kpo;
linindex = iloc*( nprimz+1 )*nprimy+jloc*( nprimz+1 )+kloc;
Jz [linindex] += tmpJz[i][j]; //
}
}
}//i
// Rho^(p,p,p)
for( unsigned int i=0 ; i<7 ; i++ ) {
iloc = i+ipo;
for( unsigned int j=0 ; j<7 ; j++ ) {
jloc = j+jpo;
for( unsigned int k=0 ; k<7 ; k++ ) {
kloc = k+kpo;
linindex = iloc*nprimz*nprimy+jloc*nprimz+kloc;
rho[linindex] += charge_weight * Sx1[i]*Sy1[j]*Sz1[k];
}
}
}//i
} // END Project local densities (Jx, Jy, Jz, rho, sort)