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lal_tersoff_mod_extra.h
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/// **************************************************************************
// tersoff_mod_extra.h
// -------------------
// Trung Dac Nguyen
//
// Device code for Tersoff math routines
//
// __________________________________________________________________________
// This file is part of the LAMMPS Accelerator Library (LAMMPS_AL)
// __________________________________________________________________________
//
// begin :
// email : ndactrung@gmail.com
// ***************************************************************************/*
#ifndef LAL_TERSOFF_MOD_EXTRA_H
#define LAL_TERSOFF_MOD_EXTRA_H
#ifdef NV_KERNEL
#include "lal_aux_fun1.h"
#else
#endif
#define MY_PI2 (numtyp)1.57079632679489661923
#define MY_PI4 (numtyp)0.78539816339744830962
/* ---------------------------------------------------------------------- */
ucl_inline numtyp vec3_dot(const numtyp x[3], const numtyp y[3])
{
return (x[0]*y[0] + x[1]*y[1] + x[2]*y[2]);
}
ucl_inline void vec3_add(const numtyp x[3], const numtyp y[3], numtyp z[3])
{
z[0] = x[0]+y[0]; z[1] = x[1]+y[1]; z[2] = x[2]+y[2];
}
ucl_inline void vec3_scale(const numtyp k, const numtyp x[3], numtyp y[3])
{
y[0] = k*x[0]; y[1] = k*x[1]; y[2] = k*x[2];
}
ucl_inline void vec3_scaleadd(const numtyp k, const numtyp x[3],
const numtyp y[3], numtyp z[3])
{
z[0] = k*x[0]+y[0]; z[1] = k*x[1]+y[1]; z[2] = k*x[2]+y[2];
}
/* ---------------------------------------------------------------------- */
ucl_inline numtyp ters_gijk_mod(const numtyp costheta,
const numtyp param_c1,
const numtyp param_c2,
const numtyp param_c3,
const numtyp param_c4,
const numtyp param_c5,
const numtyp param_h)
{
const numtyp tmp_h = (param_h - costheta)*(param_h - costheta);
return param_c1 + (param_c2*tmp_h/(param_c3 + tmp_h)) *
((numtyp)1.0 + param_c4*ucl_exp(-param_c5*tmp_h));
}
/* ---------------------------------------------------------------------- */
ucl_inline numtyp ters_gijk_d_mod(const numtyp costheta,
const numtyp param_c2,
const numtyp param_c3,
const numtyp param_c4,
const numtyp param_c5,
const numtyp param_h)
{
const numtyp tmp_h = (param_h - costheta)*(param_h - costheta);
const numtyp g1 = (param_h - costheta)/(param_c3 + tmp_h);
const numtyp g2 = ucl_exp(-param_c5*tmp_h);
return (numtyp)-2.0*param_c2*g1*((1 + param_c4*g2) *
(1 + g1*(costheta - param_h)) - tmp_h*param_c4*param_c5*g2);
}
/* ---------------------------------------------------------------------- */
ucl_inline void costheta_d(const numtyp rij_hat[3],
const numtyp rij,
const numtyp rik_hat[3],
const numtyp rik,
numtyp *dri,
numtyp *drj,
numtyp *drk)
{
// first element is derivative wrt Ri, second wrt Rj, third wrt Rk
numtyp cos_theta = vec3_dot(rij_hat,rik_hat);
vec3_scaleadd(-cos_theta,rij_hat,rik_hat,drj);
vec3_scale(ucl_recip(rij),drj,drj);
vec3_scaleadd(-cos_theta,rik_hat,rij_hat,drk);
vec3_scale(ucl_recip(rik),drk,drk);
vec3_add(drj,drk,dri);
vec3_scale((numtyp)-1.0,dri,dri);
}
/* ---------------------------------------------------------------------- */
ucl_inline numtyp ters_fc(const numtyp r,
const numtyp param_bigr,
const numtyp param_bigd)
{
if (r < param_bigr-param_bigd) return (numtyp)1.0;
if (r > param_bigr+param_bigd) return (numtyp)0.0;
return (numtyp)0.5*((numtyp)1.0 -
(numtyp)1.125*sin(MY_PI2*(r - param_bigr)/param_bigd) -
(numtyp)0.125*sin(3*MY_PI2*(r - param_bigr)/param_bigd));
}
/* ---------------------------------------------------------------------- */
ucl_inline numtyp ters_fc_d(const numtyp r,
const numtyp param_bigr,
const numtyp param_bigd)
{
if (r < param_bigr-param_bigd) return (numtyp)0.0;
if (r > param_bigr+param_bigd) return (numtyp)0.0;
return -((numtyp)0.375*MY_PI4/param_bigd) *
((numtyp)3*cos(MY_PI2*(r - param_bigr)/param_bigd) +
cos((numtyp)3*MY_PI2*(r - param_bigr)/param_bigd));
}
/* ---------------------------------------------------------------------- */
ucl_inline numtyp ters_fa(const numtyp r,
const numtyp param_bigb,
const numtyp param_bigr,
const numtyp param_bigd,
const numtyp param_lam2)
{
if (r > param_bigr + param_bigd) return (numtyp)0.0;
return -param_bigb * ucl_exp(-param_lam2 * r) *
ters_fc(r,param_bigr,param_bigd);
}
/* ---------------------------------------------------------------------- */
ucl_inline numtyp ters_fa_d(const numtyp r,
const numtyp param_bigb,
const numtyp param_bigr,
const numtyp param_bigd,
const numtyp param_lam2)
{
if (r > param_bigr + param_bigd) return (numtyp)0.0;
return param_bigb * ucl_exp(-param_lam2 * r) * (param_lam2 *
ters_fc(r,param_bigr,param_bigd) - ters_fc_d(r,param_bigr,param_bigd));
}
/* ---------------------------------------------------------------------- */
ucl_inline numtyp ters_bij(const numtyp zeta,
const numtyp param_beta,
const numtyp param_powern,
const numtyp param_powern_del,
const numtyp param_ca1,
const numtyp param_ca4)
{
numtyp tmp = param_beta * zeta;
if (tmp > param_ca1)
return ucl_powr(tmp, -param_powern/((numtyp)2.0*param_powern_del));
if (tmp < param_ca4) return (numtyp)1.0;
return ucl_powr((numtyp)1.0 + ucl_powr(tmp,param_powern),
(numtyp)-1.0/((numtyp)2.0*param_powern_del));
}
/* ---------------------------------------------------------------------- */
ucl_inline numtyp ters_bij_d(const numtyp zeta,
const numtyp param_beta,
const numtyp param_powern,
const numtyp param_powern_del,
const numtyp param_ca1,
const numtyp param_ca4)
{
numtyp tmp = param_beta * zeta;
if (tmp > param_ca1) return (numtyp)-0.5*(param_powern/param_powern_del) *
ucl_powr(tmp,(numtyp)-0.5*(param_powern/param_powern_del)) / zeta;
if (tmp < param_ca4) return (numtyp)0.0;
numtyp tmp_n = ucl_powr(tmp,param_powern);
return (numtyp)-0.5 *(param_powern/param_powern_del) *
ucl_powr((numtyp)1.0+tmp_n, (numtyp)-1.0-((numtyp)1.0 /
((numtyp)2.0*param_powern_del)))*tmp_n / zeta;
}
/* ---------------------------------------------------------------------- */
ucl_inline void ters_zetaterm_d(const numtyp prefactor,
const numtyp rij_hat[3],
const numtyp rij,
const numtyp rik_hat[3],
const numtyp rik,
const numtyp param_bigr,
const numtyp param_bigd,
const numtyp param_powermint,
const numtyp param_lam3,
const numtyp param_h,
const numtyp param_c1,
const numtyp param_c2,
const numtyp param_c3,
const numtyp param_c4,
const numtyp param_c5,
numtyp dri[3],
numtyp drj[3],
numtyp drk[3])
{
numtyp gijk,gijk_d,ex_delr,ex_delr_d,fc,dfc,cos_theta,tmp;
numtyp dcosdri[3],dcosdrj[3],dcosdrk[3];
fc = ters_fc(rik,param_bigr,param_bigd);
dfc = ters_fc_d(rik,param_bigr,param_bigd);
numtyp t = param_lam3*(rij-rik);
if ((int)param_powermint == 3) tmp = t*t*t;
else tmp = t;
if (tmp > (numtyp)69.0776) ex_delr = (numtyp)1.e30;
else if (tmp < (numtyp)-69.0776) ex_delr = (numtyp)0.0;
else ex_delr = ucl_exp(tmp);
if ((int)param_powermint == 3)
ex_delr_d = (numtyp)3.0*param_lam3*t*t*ex_delr;
else ex_delr_d = param_lam3 * ex_delr;
cos_theta = vec3_dot(rij_hat,rik_hat);
gijk = ters_gijk_mod(cos_theta,param_c1,param_c2,param_c3,param_c4,param_c5,param_h);
gijk_d = ters_gijk_d_mod(cos_theta,param_c2,param_c3,param_c4,param_c5,param_h);
costheta_d(rij_hat,rij,rik_hat,rik,dcosdri,dcosdrj,dcosdrk);
// compute the derivative wrt Ri
// dri = -dfc*gijk*ex_delr*rik_hat;
// dri += fc*gijk_d*ex_delr*dcosdri;
// dri += fc*gijk*ex_delr_d*(rik_hat - rij_hat);
vec3_scale(-dfc*gijk*ex_delr,rik_hat,dri);
vec3_scaleadd(fc*gijk_d*ex_delr,dcosdri,dri,dri);
vec3_scaleadd(fc*gijk*ex_delr_d,rik_hat,dri,dri);
vec3_scaleadd(-fc*gijk*ex_delr_d,rij_hat,dri,dri);
vec3_scale(prefactor,dri,dri);
// compute the derivative wrt Rj
// drj = fc*gijk_d*ex_delr*dcosdrj;
// drj += fc*gijk*ex_delr_d*rij_hat;
vec3_scale(fc*gijk_d*ex_delr,dcosdrj,drj);
vec3_scaleadd(fc*gijk*ex_delr_d,rij_hat,drj,drj);
vec3_scale(prefactor,drj,drj);
// compute the derivative wrt Rk
// drk = dfc*gijk*ex_delr*rik_hat;
// drk += fc*gijk_d*ex_delr*dcosdrk;
// drk += -fc*gijk*ex_delr_d*rik_hat;
vec3_scale(dfc*gijk*ex_delr,rik_hat,drk);
vec3_scaleadd(fc*gijk_d*ex_delr,dcosdrk,drk,drk);
vec3_scaleadd(-fc*gijk*ex_delr_d,rik_hat,drk,drk);
vec3_scale(prefactor,drk,drk);
}
ucl_inline void ters_zetaterm_d_fi(const numtyp prefactor,
const numtyp rij_hat[3],
const numtyp rij,
const numtyp rik_hat[3],
const numtyp rik,
const numtyp param_bigr,
const numtyp param_bigd,
const numtyp param_powermint,
const numtyp param_lam3,
const numtyp param_h,
const numtyp param_c1,
const numtyp param_c2,
const numtyp param_c3,
const numtyp param_c4,
const numtyp param_c5,
numtyp dri[3])
{
numtyp gijk,gijk_d,ex_delr,ex_delr_d,fc,dfc,cos_theta,tmp;
numtyp dcosdri[3],dcosdrj[3],dcosdrk[3];
fc = ters_fc(rik,param_bigr,param_bigd);
dfc = ters_fc_d(rik,param_bigr,param_bigd);
numtyp t = param_lam3*(rij-rik);
if ((int)param_powermint == 3) tmp = t*t*t;
else tmp = t;
if (tmp > (numtyp)69.0776) ex_delr = (numtyp)1.e30;
else if (tmp < (numtyp)-69.0776) ex_delr = (numtyp)0.0;
else ex_delr = ucl_exp(tmp);
if ((int)param_powermint == 3)
ex_delr_d = (numtyp)3.0*param_lam3*t*t*ex_delr;
else ex_delr_d = param_lam3 * ex_delr;
cos_theta = vec3_dot(rij_hat,rik_hat);
gijk = ters_gijk_mod(cos_theta,param_c1,param_c2,param_c3,param_c4,param_c5,param_h);
gijk_d = ters_gijk_d_mod(cos_theta,param_c2,param_c3,param_c4,param_c5,param_h);
costheta_d(rij_hat,rij,rik_hat,rik,dcosdri,dcosdrj,dcosdrk);
// compute the derivative wrt Ri
// dri = -dfc*gijk*ex_delr*rik_hat;
// dri += fc*gijk_d*ex_delr*dcosdri;
// dri += fc*gijk*ex_delr_d*(rik_hat - rij_hat);
vec3_scale(-dfc*gijk*ex_delr,rik_hat,dri);
vec3_scaleadd(fc*gijk_d*ex_delr,dcosdri,dri,dri);
vec3_scaleadd(fc*gijk*ex_delr_d,rik_hat,dri,dri);
vec3_scaleadd(-fc*gijk*ex_delr_d,rij_hat,dri,dri);
vec3_scale(prefactor,dri,dri);
}
ucl_inline void ters_zetaterm_d_fj(const numtyp prefactor,
const numtyp rij_hat[3],
const numtyp rij,
const numtyp rik_hat[3],
const numtyp rik,
const numtyp param_bigr,
const numtyp param_bigd,
const numtyp param_powermint,
const numtyp param_lam3,
const numtyp param_h,
const numtyp param_c1,
const numtyp param_c2,
const numtyp param_c3,
const numtyp param_c4,
const numtyp param_c5,
numtyp drj[3])
{
numtyp gijk,gijk_d,ex_delr,ex_delr_d,fc,cos_theta,tmp;
numtyp dcosdri[3],dcosdrj[3],dcosdrk[3];
fc = ters_fc(rik,param_bigr,param_bigd);
numtyp t = param_lam3*(rij-rik);
if ((int)param_powermint == 3) tmp = t*t*t;
else tmp = t;
if (tmp > (numtyp)69.0776) ex_delr = (numtyp)1.e30;
else if (tmp < (numtyp)-69.0776) ex_delr = (numtyp)0.0;
else ex_delr = ucl_exp(tmp);
if ((int)param_powermint == 3)
ex_delr_d = (numtyp)3.0*param_lam3*t*t*ex_delr;
else ex_delr_d = param_lam3 * ex_delr;
cos_theta = vec3_dot(rij_hat,rik_hat);
gijk = ters_gijk_mod(cos_theta,param_c1,param_c2,param_c3,param_c4,param_c5,param_h);
gijk_d = ters_gijk_d_mod(cos_theta,param_c2,param_c3,param_c4,param_c5,param_h);
costheta_d(rij_hat,rij,rik_hat,rik,dcosdri,dcosdrj,dcosdrk);
// compute the derivative wrt Rj
// drj = fc*gijk_d*ex_delr*dcosdrj;
// drj += fc*gijk*ex_delr_d*rij_hat;
vec3_scale(fc*gijk_d*ex_delr,dcosdrj,drj);
vec3_scaleadd(fc*gijk*ex_delr_d,rij_hat,drj,drj);
vec3_scale(prefactor,drj,drj);
}
ucl_inline void ters_zetaterm_d_fk(const numtyp prefactor,
const numtyp rij_hat[3],
const numtyp rij,
const numtyp rik_hat[3],
const numtyp rik,
const numtyp param_bigr,
const numtyp param_bigd,
const numtyp param_powermint,
const numtyp param_lam3,
const numtyp param_h,
const numtyp param_c1,
const numtyp param_c2,
const numtyp param_c3,
const numtyp param_c4,
const numtyp param_c5,
numtyp drk[3])
{
numtyp gijk,gijk_d,ex_delr,ex_delr_d,fc,dfc,cos_theta,tmp;
numtyp dcosdri[3],dcosdrj[3],dcosdrk[3];
fc = ters_fc(rik,param_bigr,param_bigd);
dfc = ters_fc_d(rik,param_bigr,param_bigd);
numtyp t = param_lam3*(rij-rik);
if ((int)param_powermint == 3) tmp = t*t*t;
else tmp = t;
if (tmp > (numtyp)69.0776) ex_delr = (numtyp)1.e30;
else if (tmp < (numtyp)-69.0776) ex_delr = (numtyp)0.0;
else ex_delr = ucl_exp(tmp);
if ((int)param_powermint == 3)
ex_delr_d = (numtyp)3.0*param_lam3*t*t*ex_delr;
else ex_delr_d = param_lam3 * ex_delr;
cos_theta = vec3_dot(rij_hat,rik_hat);
gijk = ters_gijk_mod(cos_theta,param_c1,param_c2,param_c3,param_c4,param_c5,param_h);
gijk_d = ters_gijk_d_mod(cos_theta,param_c2,param_c3,param_c4,param_c5,param_h);
costheta_d(rij_hat,rij,rik_hat,rik,dcosdri,dcosdrj,dcosdrk);
// compute the derivative wrt Rk
// drk = dfc*gijk*ex_delr*rik_hat;
// drk += fc*gijk_d*ex_delr*dcosdrk;
// drk += -fc*gijk*ex_delr_d*rik_hat;
vec3_scale(dfc*gijk*ex_delr,rik_hat,drk);
vec3_scaleadd(fc*gijk_d*ex_delr,dcosdrk,drk,drk);
vec3_scaleadd(-fc*gijk*ex_delr_d,rik_hat,drk,drk);
vec3_scale(prefactor,drk,drk);
}
/* ---------------------------------------------------------------------- */
ucl_inline void repulsive(const numtyp param_bigr,
const numtyp param_bigd,
const numtyp param_lam1,
const numtyp param_biga,
const numtyp rsq,
const int eflag,
numtyp *ans)
{
numtyp r,tmp_fc,tmp_fc_d,tmp_exp;
r = ucl_sqrt(rsq);
tmp_fc = ters_fc(r,param_bigr,param_bigd);
tmp_fc_d = ters_fc_d(r,param_bigr,param_bigd);
tmp_exp = ucl_exp(-param_lam1 * r);
// fforce
ans[0] = -param_biga*tmp_exp*(tmp_fc_d - tmp_fc*param_lam1)*ucl_recip(r);
// eng
if (eflag) ans[1] = tmp_fc * param_biga * tmp_exp;
}
/* ---------------------------------------------------------------------- */
ucl_inline numtyp zeta(const numtyp param_powermint,
const numtyp param_lam3,
const numtyp param_bigr,
const numtyp param_bigd,
const numtyp param_h,
const numtyp param_c1,
const numtyp param_c2,
const numtyp param_c3,
const numtyp param_c4,
const numtyp param_c5,
const numtyp rsqij,
const numtyp rsqik,
const numtyp4 delrij,
const numtyp4 delrik)
{
numtyp rij,rik,costheta,arg,ex_delr;
rij = ucl_sqrt(rsqij);
rik = ucl_sqrt(rsqik);
costheta = (delrij.x*delrik.x + delrij.y*delrik.y +
delrij.z*delrik.z) / (rij*rik);
numtyp t = param_lam3*(rij-rik);
if ((int)param_powermint == 3) arg = t*t*t;
else arg = t;
if (arg > (numtyp)69.0776) ex_delr = (numtyp)1.e30;
else if (arg < (numtyp)-69.0776) ex_delr = (numtyp)0.0;
else ex_delr = ucl_exp(arg);
return ters_fc(rik,param_bigr,param_bigd) *
ters_gijk_mod(costheta,param_c1,param_c2,param_c3,param_c4,param_c5,
param_h) * ex_delr;
}
/* ---------------------------------------------------------------------- */
ucl_inline void force_zeta(const numtyp param_bigb,
const numtyp param_bigr,
const numtyp param_bigd,
const numtyp param_lam2,
const numtyp param_beta,
const numtyp param_powern,
const numtyp param_powern_del,
const numtyp param_ca1,
const numtyp param_ca4,
const numtyp rsq,
const numtyp zeta_ij,
const int eflag,
numtyp fpfeng[4])
{
numtyp r,fa,fa_d,bij;
r = ucl_sqrt(rsq);
fa = ters_fa(r,param_bigb,param_bigr,param_bigd,param_lam2);
fa_d = ters_fa_d(r,param_bigb,param_bigr,param_bigd,param_lam2);
bij = ters_bij(zeta_ij,param_beta,param_powern,
param_powern_del,param_ca1,param_ca4);
fpfeng[0] = (numtyp)0.5*bij*fa_d * ucl_recip(r); // fforce
fpfeng[1] = (numtyp)-0.5*fa * ters_bij_d(zeta_ij,param_beta, param_powern,
param_powern_del,param_ca1,param_ca4); // prefactor
if (eflag) fpfeng[2] = (numtyp)0.5*bij*fa; // eng
}
/* ----------------------------------------------------------------------
attractive term
use param_ij cutoff for rij test
use param_ijk cutoff for rik test
------------------------------------------------------------------------- */
ucl_inline void attractive(const numtyp param_bigr,
const numtyp param_bigd,
const numtyp param_powermint,
const numtyp param_lam3,
const numtyp param_h,
const numtyp param_c1,
const numtyp param_c2,
const numtyp param_c3,
const numtyp param_c4,
const numtyp param_c5,
const numtyp prefactor,
const numtyp rij,
const numtyp rijinv,
const numtyp rik,
const numtyp rikinv,
const numtyp delrij[3],
const numtyp delrik[3],
numtyp fi[3],
numtyp fj[3],
numtyp fk[3])
{
numtyp rij_hat[3],rik_hat[3];
vec3_scale(rijinv,delrij,rij_hat);
vec3_scale(rikinv,delrik,rik_hat);
ters_zetaterm_d(prefactor,rij_hat,rij,rik_hat,rik,
param_bigr, param_bigd, param_powermint, param_lam3,
param_h, param_c1, param_c2, param_c3, param_c4, param_c5,
fi, fj, fk);
}
ucl_inline void attractive_fi(const numtyp param_bigr,
const numtyp param_bigd,
const numtyp param_powermint,
const numtyp param_lam3,
const numtyp param_h,
const numtyp param_c1,
const numtyp param_c2,
const numtyp param_c3,
const numtyp param_c4,
const numtyp param_c5,
const numtyp prefactor,
const numtyp rij,
const numtyp rijinv,
const numtyp rik,
const numtyp rikinv,
const numtyp delrij[3],
const numtyp delrik[3],
numtyp fi[3])
{
numtyp rij_hat[3],rik_hat[3];
vec3_scale(rijinv,delrij,rij_hat);
vec3_scale(rikinv,delrik,rik_hat);
ters_zetaterm_d_fi(prefactor,rij_hat,rij,rik_hat,rik,
param_bigr, param_bigd, param_powermint, param_lam3,
param_h, param_c1, param_c2, param_c3, param_c4, param_c5,
fi);
}
ucl_inline void attractive_fj(const numtyp param_bigr,
const numtyp param_bigd,
const numtyp param_powermint,
const numtyp param_lam3,
const numtyp param_h,
const numtyp param_c1,
const numtyp param_c2,
const numtyp param_c3,
const numtyp param_c4,
const numtyp param_c5,
const numtyp prefactor,
const numtyp rij,
const numtyp rijinv,
const numtyp rik,
const numtyp rikinv,
const numtyp delrij[3],
const numtyp delrik[3],
numtyp fj[3])
{
numtyp rij_hat[3],rik_hat[3];
vec3_scale(rijinv,delrij,rij_hat);
vec3_scale(rikinv,delrik,rik_hat);
ters_zetaterm_d_fj(prefactor,rij_hat,rij,rik_hat,rik,
param_bigr, param_bigd, param_powermint, param_lam3,
param_h, param_c1, param_c2, param_c3, param_c4, param_c5,
fj);
}
ucl_inline void attractive_fk(const numtyp param_bigr,
const numtyp param_bigd,
const numtyp param_powermint,
const numtyp param_lam3,
const numtyp param_h,
const numtyp param_c1,
const numtyp param_c2,
const numtyp param_c3,
const numtyp param_c4,
const numtyp param_c5,
const numtyp prefactor,
const numtyp rij,
const numtyp rijinv,
const numtyp rik,
const numtyp rikinv,
const numtyp delrij[3],
const numtyp delrik[3],
numtyp fk[3])
{
numtyp rij_hat[3],rik_hat[3];
vec3_scale(rijinv,delrij,rij_hat);
vec3_scale(rikinv,delrik,rik_hat);
ters_zetaterm_d_fk(prefactor,rij_hat,rij,rik_hat,rik,
param_bigr, param_bigd, param_powermint, param_lam3,
param_h, param_c1, param_c2, param_c3, param_c4, param_c5,
fk);
}
#endif

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