593 lines
22 KiB
C
593 lines
22 KiB
C
/// **************************************************************************
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// tersoff_extra.h
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// -------------------
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// Trung Dac Nguyen
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//
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// Device code for Tersoff math routines
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//
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// __________________________________________________________________________
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// This file is part of the LAMMPS Accelerator Library (LAMMPS_AL)
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// __________________________________________________________________________
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//
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// begin :
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// email : ndactrung@gmail.com
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// ***************************************************************************/*
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#ifndef LAL_TERSOFF_EXTRA_H
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#define LAL_TERSOFF_EXTRA_H
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#if defined(NV_KERNEL) || defined(USE_HIP)
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#include "lal_aux_fun1.h"
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#else
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#endif
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#define MY_PI2 (numtyp)1.57079632679489661923
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#define MY_PI4 (numtyp)0.78539816339744830962
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/* ---------------------------------------------------------------------- */
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ucl_inline numtyp vec3_dot(const numtyp x[3], const numtyp y[3])
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{
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return (x[0]*y[0] + x[1]*y[1] + x[2]*y[2]);
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}
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ucl_inline void vec3_add(const numtyp x[3], const numtyp y[3], numtyp z[3])
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{
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z[0] = x[0]+y[0]; z[1] = x[1]+y[1]; z[2] = x[2]+y[2];
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}
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ucl_inline void vec3_scale(const numtyp k, const numtyp x[3], numtyp y[3])
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{
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y[0] = k*x[0]; y[1] = k*x[1]; y[2] = k*x[2];
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}
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ucl_inline void vec3_scaleadd(const numtyp k, const numtyp x[3],
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const numtyp y[3], numtyp z[3])
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{
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z[0] = k*x[0]+y[0]; z[1] = k*x[1]+y[1]; z[2] = k*x[2]+y[2];
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}
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/* ---------------------------------------------------------------------- */
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ucl_inline numtyp ters_gijk(const numtyp costheta,
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const numtyp param_c,
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const numtyp param_d,
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const numtyp param_h,
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const numtyp param_gamma)
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{
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const numtyp hcth = param_h - costheta;
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return param_gamma*((numtyp)1.0 + param_c*ucl_recip(param_d) -
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param_c *ucl_recip(param_d + hcth*hcth));
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}
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/* ---------------------------------------------------------------------- */
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ucl_inline numtyp ters_gijk_d(const numtyp costheta,
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const numtyp param_c,
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const numtyp param_d,
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const numtyp param_h,
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const numtyp param_gamma,
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numtyp *ans_d)
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{
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const numtyp hcth = param_h - costheta;
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const numtyp idhh=ucl_recip(param_d + hcth*hcth);
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const numtyp numerator = (numtyp)-2.0 * param_c * hcth;
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*ans_d=param_gamma*numerator*idhh*idhh;
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return param_gamma*((numtyp)1.0+param_c*ucl_recip(param_d)-param_c*idhh);
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}
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/* ---------------------------------------------------------------------- */
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ucl_inline void costheta_d(const numtyp cos_theta,
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const numtyp rij_hat[3],
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const numtyp rij,
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const numtyp rik_hat[3],
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const numtyp rik,
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numtyp *dri,
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numtyp *drj,
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numtyp *drk)
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{
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// first element is derivative wrt Ri, second wrt Rj, third wrt Rk
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vec3_scaleadd(-cos_theta,rij_hat,rik_hat,drj);
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vec3_scale(ucl_recip(rij),drj,drj);
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vec3_scaleadd(-cos_theta,rik_hat,rij_hat,drk);
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vec3_scale(ucl_recip(rik),drk,drk);
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vec3_add(drj,drk,dri);
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vec3_scale((numtyp)-1.0,dri,dri);
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}
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/* ---------------------------------------------------------------------- */
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ucl_inline numtyp ters_fc(const numtyp r,
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const numtyp param_bigr,
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const numtyp param_bigd)
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{
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if (r < param_bigr-param_bigd) return (numtyp)1.0;
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#ifndef ONETYPE
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if (r > param_bigr+param_bigd) return (numtyp)0.0;
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#endif
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return (numtyp)0.5*((numtyp)1.0 - sin(MY_PI2*(r - param_bigr)/param_bigd));
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}
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/* ---------------------------------------------------------------------- */
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ucl_inline numtyp ters_fc_d(const numtyp r,
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const numtyp param_bigr,
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const numtyp param_bigd,
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numtyp *ans_d)
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{
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if (r < param_bigr-param_bigd) {
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*ans_d=(numtyp)0.0;
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return (numtyp)1.0;
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}
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#ifndef ONETYPE
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if (r > param_bigr+param_bigd) {
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*ans_d=(numtyp)0.0;
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return (numtyp)0.0;
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}
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#endif
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const numtyp ibigd = ucl_recip(param_bigd);
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const numtyp angle = MY_PI2*(r - param_bigr)*ibigd;
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*ans_d=-(MY_PI4*ibigd) * cos(angle);
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return (numtyp)0.5*((numtyp)1.0 - sin(angle));
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}
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/* ---------------------------------------------------------------------- */
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ucl_inline numtyp ters_fa_d(const numtyp r,
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const numtyp param_bigb,
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const numtyp param_bigr,
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const numtyp param_bigd,
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const numtyp param_lam2,
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numtyp *ans_d)
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{
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#ifndef ONETYPE
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if (r > param_bigr + param_bigd) return (numtyp)0.0;
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#endif
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numtyp dfc;
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const numtyp fc=ters_fc_d(r,param_bigr,param_bigd,&dfc);
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const numtyp blr = param_bigb * ucl_exp(-param_lam2 * r);
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*ans_d = blr * (param_lam2 * fc - dfc);
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return -blr * fc;
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}
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/* ---------------------------------------------------------------------- */
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ucl_inline numtyp ters_bij_d(const numtyp zeta,
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const numtyp param_beta,
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const numtyp param_powern,
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const numtyp param_c1,
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const numtyp param_c2,
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const numtyp param_c3,
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const numtyp param_c4,
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numtyp *ans_d)
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{
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const numtyp tmp = param_beta * zeta;
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if (tmp > param_c1) {
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*ans_d = param_beta * (numtyp)-0.5*ucl_powr(tmp,(numtyp)-1.5);
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return ucl_rsqrt(tmp);
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}
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if (tmp > param_c2) {
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const numtyp ptmp = ucl_powr(tmp,-param_powern);
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const numtyp i2n = ucl_recip((numtyp)2.0 * param_powern);
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*ans_d = param_beta * ((numtyp)-0.5*ucl_powr(tmp,(numtyp)-1.5) *
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((numtyp)1.0 - ((numtyp)1.0 + (numtyp)1.0 * i2n) *
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ptmp));
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return ((numtyp)1.0 - ptmp * i2n)*ucl_rsqrt(tmp);
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}
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if (tmp < param_c4) {
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*ans_d = (numtyp)0.0;
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return (numtyp)1.0;
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}
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if (tmp < param_c3) {
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*ans_d = (numtyp)-0.5*param_beta * ucl_powr(tmp,param_powern-(numtyp)1.0);
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return (numtyp)1.0 - ucl_powr(tmp,param_powern)/((numtyp)2.0*param_powern);
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}
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const numtyp tmp_n = (numtyp)1.0+ucl_powr(tmp,param_powern);
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const numtyp i2n = -ucl_recip((numtyp)2.0*param_powern);
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*ans_d = (numtyp)-0.5*ucl_powr(tmp_n,(numtyp)-1.0+i2n)*(tmp_n-(numtyp)1.0)/
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zeta;
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return ucl_powr(tmp_n, i2n);
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}
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/* ---------------------------------------------------------------------- */
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ucl_inline void ters_zetaterm_d(const numtyp prefactor,
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const numtyp rij_hat[3],
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const numtyp rij,
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const numtyp rik_hat[3],
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const numtyp rik,
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const numtyp param_bigr,
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const numtyp param_bigd,
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const int param_powermint,
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const numtyp param_lam3,
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const numtyp param_c,
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const numtyp param_d,
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const numtyp param_h,
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const numtyp param_gamma,
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numtyp dri[3],
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numtyp drj[3],
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numtyp drk[3])
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{
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numtyp gijk,gijk_d,ex_delr,ex_delr_d,fc,dfc,cos_theta,tmp;
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numtyp dcosdri[3],dcosdrj[3],dcosdrk[3];
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fc = ters_fc_d(rik,param_bigr,param_bigd,&dfc);
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numtyp t = param_lam3*(rij-rik);
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if (param_powermint == 3) tmp = t*t*t;
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else tmp = t;
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if (tmp > (numtyp)69.0776) ex_delr = (numtyp)1.e30;
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else if (tmp < (numtyp)-69.0776) ex_delr = (numtyp)0.0;
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else ex_delr = ucl_exp(tmp);
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if (param_powermint == 3)
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ex_delr_d = (numtyp)3.0*param_lam3*t*t*ex_delr;
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else ex_delr_d = param_lam3 * ex_delr;
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cos_theta = vec3_dot(rij_hat,rik_hat);
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gijk = ters_gijk_d(cos_theta,param_c,param_d,param_h,param_gamma,&gijk_d);
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costheta_d(cos_theta,rij_hat,rij,rik_hat,rik,dcosdri,dcosdrj,dcosdrk);
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// compute the derivative wrt Ri
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// dri = -dfc*gijk*ex_delr*rik_hat;
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// dri += fc*gijk_d*ex_delr*dcosdri;
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// dri += fc*gijk*ex_delr_d*(rik_hat - rij_hat);
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vec3_scale(-dfc*gijk*ex_delr,rik_hat,dri);
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vec3_scaleadd(fc*gijk_d*ex_delr,dcosdri,dri,dri);
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vec3_scaleadd(fc*gijk*ex_delr_d,rik_hat,dri,dri);
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vec3_scaleadd(-fc*gijk*ex_delr_d,rij_hat,dri,dri);
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vec3_scale(prefactor,dri,dri);
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// compute the derivative wrt Rj
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// drj = fc*gijk_d*ex_delr*dcosdrj;
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// drj += fc*gijk*ex_delr_d*rij_hat;
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vec3_scale(fc*gijk_d*ex_delr,dcosdrj,drj);
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vec3_scaleadd(fc*gijk*ex_delr_d,rij_hat,drj,drj);
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vec3_scale(prefactor,drj,drj);
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// compute the derivative wrt Rk
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// drk = dfc*gijk*ex_delr*rik_hat;
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// drk += fc*gijk_d*ex_delr*dcosdrk;
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// drk += -fc*gijk*ex_delr_d*rik_hat;
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vec3_scale(dfc*gijk*ex_delr,rik_hat,drk);
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vec3_scaleadd(fc*gijk_d*ex_delr,dcosdrk,drk,drk);
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vec3_scaleadd(-fc*gijk*ex_delr_d,rik_hat,drk,drk);
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vec3_scale(prefactor,drk,drk);
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}
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ucl_inline void ters_zetaterm_d_fi(const numtyp prefactor,
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const numtyp rij_hat[3],
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const numtyp rij,
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const numtyp rik_hat[3],
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const numtyp rik,
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const numtyp param_bigr,
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const numtyp param_bigd,
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const int param_powermint,
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const numtyp param_lam3,
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const numtyp param_c,
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const numtyp param_d,
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const numtyp param_h,
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const numtyp param_gamma,
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numtyp dri[3])
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{
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numtyp gijk,gijk_d,ex_delr,ex_delr_d,fc,dfc,cos_theta,tmp;
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numtyp dcosdri[3],dcosdrj[3],dcosdrk[3];
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fc = ters_fc_d(rik,param_bigr,param_bigd,&dfc);
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numtyp t = param_lam3*(rij-rik);
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if (param_powermint == 3) tmp = t*t*t;
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else tmp = t;
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if (tmp > (numtyp)69.0776) ex_delr = (numtyp)1.e30;
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else if (tmp < (numtyp)-69.0776) ex_delr = (numtyp)0.0;
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else ex_delr = ucl_exp(tmp);
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if (param_powermint == 3)
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ex_delr_d = (numtyp)3.0*param_lam3*t*t*ex_delr;
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else ex_delr_d = param_lam3 * ex_delr;
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cos_theta = vec3_dot(rij_hat,rik_hat);
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gijk = ters_gijk_d(cos_theta,param_c,param_d,param_h,param_gamma,&gijk_d);
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costheta_d(cos_theta,rij_hat,rij,rik_hat,rik,dcosdri,dcosdrj,dcosdrk);
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// compute the derivative wrt Ri
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// dri = -dfc*gijk*ex_delr*rik_hat;
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// dri += fc*gijk_d*ex_delr*dcosdri;
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// dri += fc*gijk*ex_delr_d*(rik_hat - rij_hat);
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vec3_scale(-dfc*gijk*ex_delr,rik_hat,dri);
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vec3_scaleadd(fc*gijk_d*ex_delr,dcosdri,dri,dri);
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vec3_scaleadd(fc*gijk*ex_delr_d,rik_hat,dri,dri);
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vec3_scaleadd(-fc*gijk*ex_delr_d,rij_hat,dri,dri);
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vec3_scale(prefactor,dri,dri);
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}
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ucl_inline void ters_zetaterm_d_fj(const numtyp prefactor,
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const numtyp rij_hat[3],
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const numtyp rij,
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const numtyp rik_hat[3],
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const numtyp rik,
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const numtyp param_bigr,
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const numtyp param_bigd,
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const int param_powermint,
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const numtyp param_lam3,
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const numtyp param_c,
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const numtyp param_d,
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const numtyp param_h,
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const numtyp param_gamma,
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numtyp drj[3])
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{
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numtyp gijk,gijk_d,ex_delr,ex_delr_d,fc,cos_theta,tmp;
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numtyp dcosdri[3],dcosdrj[3],dcosdrk[3];
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fc = ters_fc(rik,param_bigr,param_bigd);
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numtyp t = param_lam3*(rij-rik);
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if (param_powermint == 3) tmp = t*t*t;
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else tmp = t;
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if (tmp > (numtyp)69.0776) ex_delr = (numtyp)1.e30;
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else if (tmp < (numtyp)-69.0776) ex_delr = (numtyp)0.0;
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else ex_delr = ucl_exp(tmp);
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if (param_powermint == 3)
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ex_delr_d = (numtyp)3.0*param_lam3*t*t*ex_delr;
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else ex_delr_d = param_lam3 * ex_delr;
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cos_theta = vec3_dot(rij_hat,rik_hat);
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gijk = ters_gijk_d(cos_theta,param_c,param_d,param_h,param_gamma,&gijk_d);
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costheta_d(cos_theta,rij_hat,rij,rik_hat,rik,dcosdri,dcosdrj,dcosdrk);
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// compute the derivative wrt Rj
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// drj = fc*gijk_d*ex_delr*dcosdrj;
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// drj += fc*gijk*ex_delr_d*rij_hat;
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vec3_scale(fc*gijk_d*ex_delr,dcosdrj,drj);
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vec3_scaleadd(fc*gijk*ex_delr_d,rij_hat,drj,drj);
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vec3_scale(prefactor,drj,drj);
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}
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ucl_inline void ters_zetaterm_d_fk(const numtyp prefactor,
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const numtyp rij_hat[3],
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const numtyp rij,
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const numtyp rik_hat[3],
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const numtyp rik,
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const numtyp param_bigr,
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const numtyp param_bigd,
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const int param_powermint,
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const numtyp param_lam3,
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const numtyp param_c,
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const numtyp param_d,
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const numtyp param_h,
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const numtyp param_gamma,
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numtyp drk[3])
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{
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numtyp gijk,gijk_d,ex_delr,ex_delr_d,fc,dfc,cos_theta,tmp;
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numtyp dcosdri[3],dcosdrj[3],dcosdrk[3];
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fc = ters_fc_d(rik,param_bigr,param_bigd,&dfc);
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numtyp t = param_lam3*(rij-rik);
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if (param_powermint == 3) tmp = t*t*t;
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else tmp = t;
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if (tmp > (numtyp)69.0776) ex_delr = (numtyp)1.e30;
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else if (tmp < (numtyp)-69.0776) ex_delr = (numtyp)0.0;
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else ex_delr = ucl_exp(tmp);
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if (param_powermint == 3)
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ex_delr_d = (numtyp)3.0*param_lam3*t*t*ex_delr;
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else ex_delr_d = param_lam3 * ex_delr;
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cos_theta = vec3_dot(rij_hat,rik_hat);
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gijk = ters_gijk_d(cos_theta,param_c,param_d,param_h,param_gamma,&gijk_d);
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costheta_d(cos_theta,rij_hat,rij,rik_hat,rik,dcosdri,dcosdrj,dcosdrk);
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// compute the derivative wrt Rk
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// drk = dfc*gijk*ex_delr*rik_hat;
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// drk += fc*gijk_d*ex_delr*dcosdrk;
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// drk += -fc*gijk*ex_delr_d*rik_hat;
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vec3_scale(dfc*gijk*ex_delr,rik_hat,drk);
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vec3_scaleadd(fc*gijk_d*ex_delr,dcosdrk,drk,drk);
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vec3_scaleadd(-fc*gijk*ex_delr_d,rik_hat,drk,drk);
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vec3_scale(prefactor,drk,drk);
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}
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/* ---------------------------------------------------------------------- */
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ucl_inline void repulsive(const numtyp param_bigr,
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const numtyp param_bigd,
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const numtyp param_lam1,
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const numtyp param_biga,
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const numtyp rsq,
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const int eflag,
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numtyp *ans)
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{
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numtyp r,tmp_fc,tmp_fc_d,tmp_exp;
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r = ucl_sqrt(rsq);
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tmp_fc = ters_fc_d(r,param_bigr,param_bigd,&tmp_fc_d);
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tmp_exp = param_biga * ucl_exp(-param_lam1 * r);
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// fforce
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ans[0] = -tmp_exp*(tmp_fc_d - tmp_fc*param_lam1)*ucl_recip(r);
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// eng
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if (EVFLAG && eflag) ans[1] = tmp_fc * tmp_exp;
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}
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/* ---------------------------------------------------------------------- */
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ucl_inline numtyp zeta(const int param_powermint,
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const numtyp param_lam3,
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const numtyp param_bigr,
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const numtyp param_bigd,
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const numtyp param_c,
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const numtyp param_d,
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const numtyp param_h,
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const numtyp param_gamma,
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const numtyp rij,
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const numtyp rsqik,
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const numtyp4 delrij,
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const numtyp4 delrik)
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{
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numtyp rik,costheta,arg,ex_delr;
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rik = ucl_sqrt(rsqik);
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costheta = (delrij.x*delrik.x + delrij.y*delrik.y +
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delrij.z*delrik.z) / (rij*rik);
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numtyp t = param_lam3*(rij-rik);
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if (param_powermint == 3) arg = t*t*t;
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else arg = t;
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if (arg > (numtyp)69.0776) ex_delr = (numtyp)1.e30;
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else if (arg < (numtyp)-69.0776) ex_delr = (numtyp)0.0;
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else ex_delr = ucl_exp(arg);
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return ters_fc(rik,param_bigr,param_bigd) *
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ters_gijk(costheta,param_c, param_d, param_h, param_gamma) * ex_delr;
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}
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/* ---------------------------------------------------------------------- */
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ucl_inline void force_zeta(const numtyp param_bigb,
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const numtyp param_bigr,
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const numtyp param_bigd,
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const numtyp param_lam2,
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const numtyp param_beta,
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const numtyp param_powern,
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const numtyp param_c1,
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const numtyp param_c2,
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const numtyp param_c3,
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const numtyp param_c4,
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const numtyp r,
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const numtyp zeta_ij,
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const int eflag,
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numtyp fpfeng[4])
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{
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numtyp fa,fa_d,bij,bij_d;
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fa = ters_fa_d(r,param_bigb,param_bigr,param_bigd,param_lam2,&fa_d);
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bij = ters_bij_d(zeta_ij,param_beta,param_powern,
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param_c1,param_c2, param_c3, param_c4, &bij_d);
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fpfeng[0] = (numtyp)0.5*bij*fa_d*ucl_recip(r); // fforce
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fpfeng[1] = (numtyp)-0.5*fa*bij_d; // prefactor
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if (EVFLAG && eflag) fpfeng[2] = (numtyp)0.5*bij*fa; // eng
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}
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/* ----------------------------------------------------------------------
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attractive term
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use param_ij cutoff for rij test
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use param_ijk cutoff for rik test
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------------------------------------------------------------------------- */
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ucl_inline void attractive(const numtyp param_bigr,
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const numtyp param_bigd,
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const int param_powermint,
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const numtyp param_lam3,
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const numtyp param_c,
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const numtyp param_d,
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const numtyp param_h,
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const numtyp param_gamma,
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const numtyp prefactor,
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const numtyp rij,
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const numtyp rijinv,
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const numtyp rik,
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const numtyp rikinv,
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const numtyp delrij[3],
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const numtyp delrik[3],
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numtyp fi[3],
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numtyp fj[3],
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numtyp fk[3])
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{
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numtyp rij_hat[3],rik_hat[3];
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vec3_scale(rijinv,delrij,rij_hat);
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vec3_scale(rikinv,delrik,rik_hat);
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ters_zetaterm_d(prefactor,rij_hat,rij,rik_hat,rik,
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param_bigr, param_bigd, param_powermint, param_lam3,
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param_c, param_d, param_h, param_gamma, fi, fj, fk);
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}
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ucl_inline void attractive_fi(const numtyp param_bigr,
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const numtyp param_bigd,
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const int param_powermint,
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const numtyp param_lam3,
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const numtyp param_c,
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const numtyp param_d,
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const numtyp param_h,
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const numtyp param_gamma,
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const numtyp prefactor,
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const numtyp rij,
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const numtyp rijinv,
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const numtyp rik,
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const numtyp rikinv,
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const numtyp delrij[3],
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const numtyp delrik[3],
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numtyp fi[3])
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{
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numtyp rij_hat[3],rik_hat[3];
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vec3_scale(rijinv,delrij,rij_hat);
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vec3_scale(rikinv,delrik,rik_hat);
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ters_zetaterm_d_fi(prefactor,rij_hat,rij,rik_hat,rik,
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param_bigr, param_bigd, param_powermint, param_lam3,
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param_c, param_d, param_h, param_gamma, fi);
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}
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ucl_inline void attractive_fj(const numtyp param_bigr,
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const numtyp param_bigd,
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const int param_powermint,
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const numtyp param_lam3,
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const numtyp param_c,
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const numtyp param_d,
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const numtyp param_h,
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const numtyp param_gamma,
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const numtyp prefactor,
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const numtyp rij,
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const numtyp rijinv,
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const numtyp rik,
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const numtyp rikinv,
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const numtyp delrij[3],
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const numtyp delrik[3],
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numtyp fj[3])
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{
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numtyp rij_hat[3],rik_hat[3];
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vec3_scale(rijinv,delrij,rij_hat);
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vec3_scale(rikinv,delrik,rik_hat);
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ters_zetaterm_d_fj(prefactor,rij_hat,rij,rik_hat,rik,
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param_bigr, param_bigd, param_powermint, param_lam3,
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param_c, param_d, param_h, param_gamma, fj);
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}
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ucl_inline void attractive_fk(const numtyp param_bigr,
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const numtyp param_bigd,
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const int param_powermint,
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const numtyp param_lam3,
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const numtyp param_c,
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const numtyp param_d,
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const numtyp param_h,
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const numtyp param_gamma,
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const numtyp prefactor,
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const numtyp rij,
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const numtyp rijinv,
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const numtyp rik,
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const numtyp rikinv,
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const numtyp delrij[3],
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const numtyp delrik[3],
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numtyp fk[3])
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{
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numtyp rij_hat[3],rik_hat[3];
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vec3_scale(rijinv,delrij,rij_hat);
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vec3_scale(rikinv,delrik,rik_hat);
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ters_zetaterm_d_fk(prefactor,rij_hat,rij,rik_hat,rik,
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param_bigr, param_bigd, param_powermint, param_lam3,
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param_c, param_d, param_h, param_gamma, fk);
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}
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#endif
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