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|
/// **************************************************************************
// tersoff_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_EXTRA_H
#define LAL_TERSOFF_EXTRA_H
#if defined(NV_KERNEL) || defined(USE_HIP)
#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(const numtyp costheta,
const numtyp param_c,
const numtyp param_d,
const numtyp param_h,
const numtyp param_gamma)
{
const numtyp hcth = param_h - costheta;
return param_gamma*((numtyp)1.0 + param_c*ucl_recip(param_d) -
param_c *ucl_recip(param_d + hcth*hcth));
}
/* ---------------------------------------------------------------------- */
ucl_inline numtyp ters_gijk_d(const numtyp costheta,
const numtyp param_c,
const numtyp param_d,
const numtyp param_h,
const numtyp param_gamma,
numtyp *ans_d)
{
const numtyp hcth = param_h - costheta;
const numtyp idhh=ucl_recip(param_d + hcth*hcth);
const numtyp numerator = (numtyp)-2.0 * param_c * hcth;
*ans_d=param_gamma*numerator*idhh*idhh;
return param_gamma*((numtyp)1.0+param_c*ucl_recip(param_d)-param_c*idhh);
}
/* ---------------------------------------------------------------------- */
ucl_inline void costheta_d(const numtyp cos_theta,
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
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;
#ifndef ONETYPE
if (r > param_bigr+param_bigd) return (numtyp)0.0;
#endif
return (numtyp)0.5*((numtyp)1.0 - sin(MY_PI2*(r - param_bigr)/param_bigd));
}
/* ---------------------------------------------------------------------- */
ucl_inline numtyp ters_fc_d(const numtyp r,
const numtyp param_bigr,
const numtyp param_bigd,
numtyp *ans_d)
{
if (r < param_bigr-param_bigd) {
*ans_d=(numtyp)0.0;
return (numtyp)1.0;
}
#ifndef ONETYPE
if (r > param_bigr+param_bigd) {
*ans_d=(numtyp)0.0;
return (numtyp)0.0;
}
#endif
const numtyp ibigd = ucl_recip(param_bigd);
const numtyp angle = MY_PI2*(r - param_bigr)*ibigd;
*ans_d=-(MY_PI4*ibigd) * cos(angle);
return (numtyp)0.5*((numtyp)1.0 - sin(angle));
}
/* ---------------------------------------------------------------------- */
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,
numtyp *ans_d)
{
#ifndef ONETYPE
if (r > param_bigr + param_bigd) {
*ans_d = (numtyp)0.0;
return (numtyp)0.0;
}
#endif
numtyp dfc;
const numtyp fc=ters_fc_d(r,param_bigr,param_bigd,&dfc);
const numtyp blr = param_bigb * ucl_exp(-param_lam2 * r);
*ans_d = blr * (param_lam2 * fc - dfc);
return -blr * fc;
}
/* ---------------------------------------------------------------------- */
ucl_inline numtyp ters_bij_d(const numtyp zeta,
const numtyp param_beta,
const numtyp param_powern,
const numtyp param_c1,
const numtyp param_c2,
const numtyp param_c3,
const numtyp param_c4,
numtyp *ans_d)
{
const numtyp tmp = param_beta * zeta;
if (tmp > param_c1) {
*ans_d = param_beta * (numtyp)-0.5*ucl_powr(tmp,(numtyp)-1.5);
return ucl_rsqrt(tmp);
}
if (tmp > param_c2) {
const numtyp ptmp = ucl_powr(tmp,-param_powern);
const numtyp i2n = ucl_recip((numtyp)2.0 * param_powern);
*ans_d = param_beta * ((numtyp)-0.5*ucl_powr(tmp,(numtyp)-1.5) *
((numtyp)1.0 - ((numtyp)1.0 + (numtyp)1.0 * i2n) *
ptmp));
return ((numtyp)1.0 - ptmp * i2n)*ucl_rsqrt(tmp);
}
if (tmp < param_c4) {
*ans_d = (numtyp)0.0;
return (numtyp)1.0;
}
if (tmp < param_c3) {
*ans_d = (numtyp)-0.5*param_beta * ucl_powr(tmp,param_powern-(numtyp)1.0);
return (numtyp)1.0 - ucl_powr(tmp,param_powern)/((numtyp)2.0*param_powern);
}
const numtyp tmp_n = (numtyp)1.0+ucl_powr(tmp,param_powern);
const numtyp i2n = -ucl_recip((numtyp)2.0*param_powern);
*ans_d = (numtyp)-0.5*ucl_powr(tmp_n,(numtyp)-1.0+i2n)*(tmp_n-(numtyp)1.0)/
zeta;
return ucl_powr(tmp_n, i2n);
}
/* ---------------------------------------------------------------------- */
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 int param_powermint,
const numtyp param_lam3,
const numtyp param_c,
const numtyp param_d,
const numtyp param_h,
const numtyp param_gamma,
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_d(rik,param_bigr,param_bigd,&dfc);
numtyp t = param_lam3*(rij-rik);
if (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 (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_d(cos_theta,param_c,param_d,param_h,param_gamma,&gijk_d);
costheta_d(cos_theta,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 int param_powermint,
const numtyp param_lam3,
const numtyp param_c,
const numtyp param_d,
const numtyp param_h,
const numtyp param_gamma,
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_d(rik,param_bigr,param_bigd,&dfc);
numtyp t = param_lam3*(rij-rik);
if (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 (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_d(cos_theta,param_c,param_d,param_h,param_gamma,&gijk_d);
costheta_d(cos_theta,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 int param_powermint,
const numtyp param_lam3,
const numtyp param_c,
const numtyp param_d,
const numtyp param_h,
const numtyp param_gamma,
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 (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 (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_d(cos_theta,param_c,param_d,param_h,param_gamma,&gijk_d);
costheta_d(cos_theta,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 int param_powermint,
const numtyp param_lam3,
const numtyp param_c,
const numtyp param_d,
const numtyp param_h,
const numtyp param_gamma,
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_d(rik,param_bigr,param_bigd,&dfc);
numtyp t = param_lam3*(rij-rik);
if (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 (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_d(cos_theta,param_c,param_d,param_h,param_gamma,&gijk_d);
costheta_d(cos_theta,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_d(r,param_bigr,param_bigd,&tmp_fc_d);
tmp_exp = param_biga * ucl_exp(-param_lam1 * r);
// fforce
ans[0] = -tmp_exp*(tmp_fc_d - tmp_fc*param_lam1)*ucl_recip(r);
// eng
if (EVFLAG && eflag) ans[1] = tmp_fc * tmp_exp;
}
/* ---------------------------------------------------------------------- */
ucl_inline numtyp zeta(const int param_powermint,
const numtyp param_lam3,
const numtyp param_bigr,
const numtyp param_bigd,
const numtyp param_c,
const numtyp param_d,
const numtyp param_h,
const numtyp param_gamma,
const numtyp rij,
const numtyp rsqik,
const numtyp4 delrij,
const numtyp4 delrik)
{
numtyp rik,costheta,arg,ex_delr;
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 (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(costheta,param_c, param_d, param_h, param_gamma) * 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_c1,
const numtyp param_c2,
const numtyp param_c3,
const numtyp param_c4,
const numtyp r,
const numtyp zeta_ij,
const int eflag,
numtyp fpfeng[4])
{
numtyp fa,fa_d,bij,bij_d;
fa = ters_fa_d(r,param_bigb,param_bigr,param_bigd,param_lam2,&fa_d);
bij = ters_bij_d(zeta_ij,param_beta,param_powern,
param_c1,param_c2, param_c3, param_c4, &bij_d);
fpfeng[0] = (numtyp)0.5*bij*fa_d*ucl_recip(r); // fforce
fpfeng[1] = (numtyp)-0.5*fa*bij_d; // prefactor
if (EVFLAG && 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 int param_powermint,
const numtyp param_lam3,
const numtyp param_c,
const numtyp param_d,
const numtyp param_h,
const numtyp param_gamma,
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_c, param_d, param_h, param_gamma, fi, fj, fk);
}
ucl_inline void attractive_fi(const numtyp param_bigr,
const numtyp param_bigd,
const int param_powermint,
const numtyp param_lam3,
const numtyp param_c,
const numtyp param_d,
const numtyp param_h,
const numtyp param_gamma,
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_c, param_d, param_h, param_gamma, fi);
}
ucl_inline void attractive_fj(const numtyp param_bigr,
const numtyp param_bigd,
const int param_powermint,
const numtyp param_lam3,
const numtyp param_c,
const numtyp param_d,
const numtyp param_h,
const numtyp param_gamma,
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_c, param_d, param_h, param_gamma, fj);
}
ucl_inline void attractive_fk(const numtyp param_bigr,
const numtyp param_bigd,
const int param_powermint,
const numtyp param_lam3,
const numtyp param_c,
const numtyp param_d,
const numtyp param_h,
const numtyp param_gamma,
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_c, param_d, param_h, param_gamma, fk);
}
#endif
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