void MMM1D_recalcTables()
{
/* polygamma, determine order */
int n;
double err;
double rhomax2nm2, rhomax2 = uz2*mmm1d_params.far_switch_radius_2;
/* rhomax2 < 1, so rhomax2m2 falls monotonously */
n = 1;
rhomax2nm2 = 1.0;
do {
create_mod_psi_up_to(n+1);
/* |uz*z| <= 0.5 */
err = 2*n*fabs(mod_psi_even(n, 0.5))*rhomax2nm2;
rhomax2nm2 *= rhomax2;
n++;
// fprintf(stderr, "%f\n", err);
}
while (err > 0.1*mmm1d_params.maxPWerror);
}
static void prepare_polygamma_series(double maxPWerror, double maxrad2)
{
/* polygamma, determine order */
int n;
double err;
double rhomax2nm2, rhomax2 = uz2*maxrad2;
/* rhomax2 < 1, so rhomax2m2 falls monotonously */
n = 1;
rhomax2nm2 = 1.0;
do {
create_mod_psi_up_to(n+1);
/* |uz*z| <= 0.5 */
err = 2*n*fabs(mod_psi_even(n, 0.5))*rhomax2nm2;
rhomax2nm2 *= rhomax2;
n++;
// fprintf(stderr, "%f\n", err);
}
while (err > 0.1*maxPWerror);
}
double mmm1d_coulomb_pair_energy(Particle *p1, Particle *p2, double d[3], double r2, double r)
{
double chpref = p1->p.q*p2->p.q;
double rxy2, rxy2_d, z_d;
double E;
if (chpref == 0)
return 0;
rxy2 = d[0]*d[0] + d[1]*d[1];
rxy2_d = rxy2*uz2;
z_d = d[2]*uz;
if (rxy2 <= mmm1d_params.far_switch_radius_2) {
/* near range formula */
double r2n, rt, shift_z;
int n;
E = -2*C_GAMMA;
/* polygamma summation */
r2n = 1.0;
for (n = 0; n < n_modPsi; n++) {
double add = mod_psi_even(n, z_d)*r2n;
E -= add;
if (fabs(add) < mmm1d_params.maxPWerror)
break;
r2n *= rxy2_d;
}
E *= coulomb.prefactor*uz;
/* real space parts */
E += coulomb.prefactor/r;
shift_z = d[2] + box_l[2];
rt = sqrt(rxy2 + shift_z*shift_z);
E += coulomb.prefactor/rt;
shift_z = d[2] - box_l[2];
rt = sqrt(rxy2 + shift_z*shift_z);
E += coulomb.prefactor/rt;
}
else {
/* far range formula */
double rxy = sqrt(rxy2);
double rxy_d = rxy*uz;
int bp;
/* The first Bessel term will compensate a little bit the
log term, so add them close together */
E = -0.25*log(rxy2_d) + 0.5*(M_LN2 - C_GAMMA);
for (bp = 1; bp < mmm1d_params.bessel_cutoff; bp++) {
double fq = C_2PI*bp;
E += K0(fq*rxy_d)*cos(fq*z_d);
}
E *= 4*coulomb.prefactor*uz;
}
return chpref*E;
}
void add_mmm1d_coulomb_pair_force(double chpref, double d[3], double r2, double r, double force[3])
{
int dim;
double F[3];
double rxy2, rxy2_d, z_d;
double pref;
double Fx, Fy, Fz;
rxy2 = d[0]*d[0] + d[1]*d[1];
rxy2_d = rxy2*uz2;
z_d = d[2]*uz;
if (rxy2 <= mmm1d_params.far_switch_radius_2) {
/* near range formula */
double sr, sz, r2nm1, rt, rt2, shift_z;
int n;
/* polygamma summation */
sr = 0;
sz = mod_psi_odd(0, z_d);
r2nm1 = 1.0;
for (n = 1; n < n_modPsi; n++) {
double deriv = 2*n;
double mpe = mod_psi_even(n, z_d);
double mpo = mod_psi_odd(n, z_d);
double r2n = r2nm1*rxy2_d;
sz += r2n*mpo;
sr += deriv*r2nm1*mpe;
if (fabs(deriv*r2nm1*mpe) < mmm1d_params.maxPWerror)
break;
r2nm1 = r2n;
}
// fprintf(stderr, "max_n %d\n", n);
Fx = prefL3_i*sr*d[0];
Fy = prefL3_i*sr*d[1];
Fz = prefuz2*sz;
/* real space parts */
pref = coulomb.prefactor/(r2*r);
Fx += pref*d[0];
Fy += pref*d[1];
Fz += pref*d[2];
shift_z = d[2] + box_l[2];
rt2 = rxy2 + shift_z*shift_z;
rt = sqrt(rt2);
pref = coulomb.prefactor/(rt2*rt);
Fx += pref*d[0];
Fy += pref*d[1];
Fz += pref*shift_z;
shift_z = d[2] - box_l[2];
rt2 = rxy2 + shift_z*shift_z;
rt = sqrt(rt2);
pref = coulomb.prefactor/(rt2*rt);
Fx += pref*d[0];
Fy += pref*d[1];
Fz += pref*shift_z;
F[0] = Fx;
F[1] = Fy;
F[2] = Fz;
}
else {
/* far range formula */
double rxy = sqrt(rxy2);
double rxy_d = rxy*uz;
double sr = 0, sz = 0;
int bp;
for (bp = 1; bp < mmm1d_params.bessel_cutoff; bp++) {
double fq = C_2PI*bp, k0, k1;
#ifdef BESSEL_MACHINE_PREC
k0 = K0(fq*rxy_d);
k1 = K1(fq*rxy_d);
#else
LPK01(fq*rxy_d, &k0, &k1);
#endif
sr += bp*k1*cos(fq*z_d);
sz += bp*k0*sin(fq*z_d);
}
sr *= uz2*4*C_2PI;
sz *= uz2*4*C_2PI;
pref = coulomb.prefactor*(sr/rxy + 2*uz/rxy2);
F[0] = pref*d[0];
F[1] = pref*d[1];
F[2] = coulomb.prefactor*sz;
}
for (dim = 0; dim < 3; dim++)
force[dim] += chpref * F[dim];
}
