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meam_force.cpp
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Thu, Jun 6, 12:24

meam_force.cpp
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#include "meam.h"
#include "math_special.h"
#include <algorithm>
using namespace LAMMPS_NS;
void
MEAM::meam_force(int i, int eflag_either, int eflag_global, int eflag_atom, int vflag_atom, double* eng_vdwl,
double* eatom, int ntype, int* type, int* fmap, double** x, int numneigh, int* firstneigh,
int numneigh_full, int* firstneigh_full, int fnoffset, double** f, double** vatom,
int* errorflag)
{
int j, jn, k, kn, kk, m, n, p, q;
int nv2, nv3, elti, eltj, eltk, ind;
double xitmp, yitmp, zitmp, delij[3], rij2, rij, rij3;
double delik[3], deljk[3], v[6], fi[3], fj[3];
double third, sixth;
double pp, dUdrij, dUdsij, dUdrijm[3], force, forcem;
double r, recip, phi, phip;
double sij;
double a1, a1i, a1j, a2, a2i, a2j;
double a3i, a3j;
double shpi[3], shpj[3];
double ai, aj, ro0i, ro0j, invrei, invrej;
double rhoa0j, drhoa0j, rhoa0i, drhoa0i;
double rhoa1j, drhoa1j, rhoa1i, drhoa1i;
double rhoa2j, drhoa2j, rhoa2i, drhoa2i;
double a3, a3a, rhoa3j, drhoa3j, rhoa3i, drhoa3i;
double drho0dr1, drho0dr2, drho0ds1, drho0ds2;
double drho1dr1, drho1dr2, drho1ds1, drho1ds2;
double drho1drm1[3], drho1drm2[3];
double drho2dr1, drho2dr2, drho2ds1, drho2ds2;
double drho2drm1[3], drho2drm2[3];
double drho3dr1, drho3dr2, drho3ds1, drho3ds2;
double drho3drm1[3], drho3drm2[3];
double dt1dr1, dt1dr2, dt1ds1, dt1ds2;
double dt2dr1, dt2dr2, dt2ds1, dt2ds2;
double dt3dr1, dt3dr2, dt3ds1, dt3ds2;
double drhodr1, drhodr2, drhods1, drhods2, drhodrm1[3], drhodrm2[3];
double arg;
double arg1i1, arg1j1, arg1i2, arg1j2, arg1i3, arg1j3, arg3i3, arg3j3;
double dsij1, dsij2, force1, force2;
double t1i, t2i, t3i, t1j, t2j, t3j;
*errorflag = 0;
third = 1.0 / 3.0;
sixth = 1.0 / 6.0;
// Compute forces atom i
elti = fmap[type[i]];
if (elti < 0) return;
xitmp = x[i][0];
yitmp = x[i][1];
zitmp = x[i][2];
// Treat each pair
for (jn = 0; jn < numneigh; jn++) {
j = firstneigh[jn];
eltj = fmap[type[j]];
if (!iszero(scrfcn[fnoffset + jn]) && eltj >= 0) {
sij = scrfcn[fnoffset + jn] * fcpair[fnoffset + jn];
delij[0] = x[j][0] - xitmp;
delij[1] = x[j][1] - yitmp;
delij[2] = x[j][2] - zitmp;
rij2 = delij[0] * delij[0] + delij[1] * delij[1] + delij[2] * delij[2];
if (rij2 < this->cutforcesq) {
rij = sqrt(rij2);
r = rij;
// Compute phi and phip
ind = this->eltind[elti][eltj];
pp = rij * this->rdrar;
kk = (int)pp;
kk = std::min(kk, this->nrar - 2);
pp = pp - kk;
pp = std::min(pp, 1.0);
phi = ((this->phirar3[ind][kk] * pp + this->phirar2[ind][kk]) * pp + this->phirar1[ind][kk]) * pp +
this->phirar[ind][kk];
phip = (this->phirar6[ind][kk] * pp + this->phirar5[ind][kk]) * pp + this->phirar4[ind][kk];
recip = 1.0 / r;
if (eflag_either != 0) {
if (eflag_global != 0)
*eng_vdwl = *eng_vdwl + phi * sij;
if (eflag_atom != 0) {
eatom[i] = eatom[i] + 0.5 * phi * sij;
eatom[j] = eatom[j] + 0.5 * phi * sij;
}
}
// write(1,*) "force_meamf: phi: ",phi
// write(1,*) "force_meamf: phip: ",phip
// Compute pair densities and derivatives
invrei = 1.0 / this->re_meam[elti][elti];
ai = rij * invrei - 1.0;
ro0i = this->rho0_meam[elti];
rhoa0i = ro0i * MathSpecial::fm_exp(-this->beta0_meam[elti] * ai);
drhoa0i = -this->beta0_meam[elti] * invrei * rhoa0i;
rhoa1i = ro0i * MathSpecial::fm_exp(-this->beta1_meam[elti] * ai);
drhoa1i = -this->beta1_meam[elti] * invrei * rhoa1i;
rhoa2i = ro0i * MathSpecial::fm_exp(-this->beta2_meam[elti] * ai);
drhoa2i = -this->beta2_meam[elti] * invrei * rhoa2i;
rhoa3i = ro0i * MathSpecial::fm_exp(-this->beta3_meam[elti] * ai);
drhoa3i = -this->beta3_meam[elti] * invrei * rhoa3i;
if (elti != eltj) {
invrej = 1.0 / this->re_meam[eltj][eltj];
aj = rij * invrej - 1.0;
ro0j = this->rho0_meam[eltj];
rhoa0j = ro0j * MathSpecial::fm_exp(-this->beta0_meam[eltj] * aj);
drhoa0j = -this->beta0_meam[eltj] * invrej * rhoa0j;
rhoa1j = ro0j * MathSpecial::fm_exp(-this->beta1_meam[eltj] * aj);
drhoa1j = -this->beta1_meam[eltj] * invrej * rhoa1j;
rhoa2j = ro0j * MathSpecial::fm_exp(-this->beta2_meam[eltj] * aj);
drhoa2j = -this->beta2_meam[eltj] * invrej * rhoa2j;
rhoa3j = ro0j * MathSpecial::fm_exp(-this->beta3_meam[eltj] * aj);
drhoa3j = -this->beta3_meam[eltj] * invrej * rhoa3j;
} else {
rhoa0j = rhoa0i;
drhoa0j = drhoa0i;
rhoa1j = rhoa1i;
drhoa1j = drhoa1i;
rhoa2j = rhoa2i;
drhoa2j = drhoa2i;
rhoa3j = rhoa3i;
drhoa3j = drhoa3i;
}
const double t1mi = this->t1_meam[elti];
const double t2mi = this->t2_meam[elti];
const double t3mi = this->t3_meam[elti];
const double t1mj = this->t1_meam[eltj];
const double t2mj = this->t2_meam[eltj];
const double t3mj = this->t3_meam[eltj];
if (this->ialloy == 1) {
rhoa1j *= t1mj;
rhoa2j *= t2mj;
rhoa3j *= t3mj;
rhoa1i *= t1mi;
rhoa2i *= t2mi;
rhoa3i *= t3mi;
drhoa1j *= t1mj;
drhoa2j *= t2mj;
drhoa3j *= t3mj;
drhoa1i *= t1mi;
drhoa2i *= t2mi;
drhoa3i *= t3mi;
}
nv2 = 0;
nv3 = 0;
arg1i1 = 0.0;
arg1j1 = 0.0;
arg1i2 = 0.0;
arg1j2 = 0.0;
arg1i3 = 0.0;
arg1j3 = 0.0;
arg3i3 = 0.0;
arg3j3 = 0.0;
for (n = 0; n < 3; n++) {
for (p = n; p < 3; p++) {
for (q = p; q < 3; q++) {
arg = delij[n] * delij[p] * delij[q] * this->v3D[nv3];
arg1i3 = arg1i3 + arho3[i][nv3] * arg;
arg1j3 = arg1j3 - arho3[j][nv3] * arg;
nv3 = nv3 + 1;
}
arg = delij[n] * delij[p] * this->v2D[nv2];
arg1i2 = arg1i2 + arho2[i][nv2] * arg;
arg1j2 = arg1j2 + arho2[j][nv2] * arg;
nv2 = nv2 + 1;
}
arg1i1 = arg1i1 + arho1[i][n] * delij[n];
arg1j1 = arg1j1 - arho1[j][n] * delij[n];
arg3i3 = arg3i3 + arho3b[i][n] * delij[n];
arg3j3 = arg3j3 - arho3b[j][n] * delij[n];
}
// rho0 terms
drho0dr1 = drhoa0j * sij;
drho0dr2 = drhoa0i * sij;
// rho1 terms
a1 = 2 * sij / rij;
drho1dr1 = a1 * (drhoa1j - rhoa1j / rij) * arg1i1;
drho1dr2 = a1 * (drhoa1i - rhoa1i / rij) * arg1j1;
a1 = 2.0 * sij / rij;
for (m = 0; m < 3; m++) {
drho1drm1[m] = a1 * rhoa1j * arho1[i][m];
drho1drm2[m] = -a1 * rhoa1i * arho1[j][m];
}
// rho2 terms
a2 = 2 * sij / rij2;
drho2dr1 = a2 * (drhoa2j - 2 * rhoa2j / rij) * arg1i2 - 2.0 / 3.0 * arho2b[i] * drhoa2j * sij;
drho2dr2 = a2 * (drhoa2i - 2 * rhoa2i / rij) * arg1j2 - 2.0 / 3.0 * arho2b[j] * drhoa2i * sij;
a2 = 4 * sij / rij2;
for (m = 0; m < 3; m++) {
drho2drm1[m] = 0.0;
drho2drm2[m] = 0.0;
for (n = 0; n < 3; n++) {
drho2drm1[m] = drho2drm1[m] + arho2[i][this->vind2D[m][n]] * delij[n];
drho2drm2[m] = drho2drm2[m] - arho2[j][this->vind2D[m][n]] * delij[n];
}
drho2drm1[m] = a2 * rhoa2j * drho2drm1[m];
drho2drm2[m] = -a2 * rhoa2i * drho2drm2[m];
}
// rho3 terms
rij3 = rij * rij2;
a3 = 2 * sij / rij3;
a3a = 6.0 / 5.0 * sij / rij;
drho3dr1 = a3 * (drhoa3j - 3 * rhoa3j / rij) * arg1i3 - a3a * (drhoa3j - rhoa3j / rij) * arg3i3;
drho3dr2 = a3 * (drhoa3i - 3 * rhoa3i / rij) * arg1j3 - a3a * (drhoa3i - rhoa3i / rij) * arg3j3;
a3 = 6 * sij / rij3;
a3a = 6 * sij / (5 * rij);
for (m = 0; m < 3; m++) {
drho3drm1[m] = 0.0;
drho3drm2[m] = 0.0;
nv2 = 0;
for (n = 0; n < 3; n++) {
for (p = n; p < 3; p++) {
arg = delij[n] * delij[p] * this->v2D[nv2];
drho3drm1[m] = drho3drm1[m] + arho3[i][this->vind3D[m][n][p]] * arg;
drho3drm2[m] = drho3drm2[m] + arho3[j][this->vind3D[m][n][p]] * arg;
nv2 = nv2 + 1;
}
}
drho3drm1[m] = (a3 * drho3drm1[m] - a3a * arho3b[i][m]) * rhoa3j;
drho3drm2[m] = (-a3 * drho3drm2[m] + a3a * arho3b[j][m]) * rhoa3i;
}
// Compute derivatives of weighting functions t wrt rij
t1i = t_ave[i][0];
t2i = t_ave[i][1];
t3i = t_ave[i][2];
t1j = t_ave[j][0];
t2j = t_ave[j][1];
t3j = t_ave[j][2];
if (this->ialloy == 1) {
a1i = 0.0;
a1j = 0.0;
a2i = 0.0;
a2j = 0.0;
a3i = 0.0;
a3j = 0.0;
if (!iszero(tsq_ave[i][0]))
a1i = drhoa0j * sij / tsq_ave[i][0];
if (!iszero(tsq_ave[j][0]))
a1j = drhoa0i * sij / tsq_ave[j][0];
if (!iszero(tsq_ave[i][1]))
a2i = drhoa0j * sij / tsq_ave[i][1];
if (!iszero(tsq_ave[j][1]))
a2j = drhoa0i * sij / tsq_ave[j][1];
if (!iszero(tsq_ave[i][2]))
a3i = drhoa0j * sij / tsq_ave[i][2];
if (!iszero(tsq_ave[j][2]))
a3j = drhoa0i * sij / tsq_ave[j][2];
dt1dr1 = a1i * (t1mj - t1i * t1mj*t1mj);
dt1dr2 = a1j * (t1mi - t1j * t1mi*t1mi);
dt2dr1 = a2i * (t2mj - t2i * t2mj*t2mj);
dt2dr2 = a2j * (t2mi - t2j * t2mi*t2mi);
dt3dr1 = a3i * (t3mj - t3i * t3mj*t3mj);
dt3dr2 = a3j * (t3mi - t3j * t3mi*t3mi);
} else if (this->ialloy == 2) {
dt1dr1 = 0.0;
dt1dr2 = 0.0;
dt2dr1 = 0.0;
dt2dr2 = 0.0;
dt3dr1 = 0.0;
dt3dr2 = 0.0;
} else {
ai = 0.0;
if (!iszero(rho0[i]))
ai = drhoa0j * sij / rho0[i];
aj = 0.0;
if (!iszero(rho0[j]))
aj = drhoa0i * sij / rho0[j];
dt1dr1 = ai * (t1mj - t1i);
dt1dr2 = aj * (t1mi - t1j);
dt2dr1 = ai * (t2mj - t2i);
dt2dr2 = aj * (t2mi - t2j);
dt3dr1 = ai * (t3mj - t3i);
dt3dr2 = aj * (t3mi - t3j);
}
// Compute derivatives of total density wrt rij, sij and rij(3)
get_shpfcn(this->lattce_meam[elti][elti], shpi);
get_shpfcn(this->lattce_meam[eltj][eltj], shpj);
drhodr1 = dgamma1[i] * drho0dr1 +
dgamma2[i] * (dt1dr1 * rho1[i] + t1i * drho1dr1 + dt2dr1 * rho2[i] + t2i * drho2dr1 +
dt3dr1 * rho3[i] + t3i * drho3dr1) -
dgamma3[i] * (shpi[0] * dt1dr1 + shpi[1] * dt2dr1 + shpi[2] * dt3dr1);
drhodr2 = dgamma1[j] * drho0dr2 +
dgamma2[j] * (dt1dr2 * rho1[j] + t1j * drho1dr2 + dt2dr2 * rho2[j] + t2j * drho2dr2 +
dt3dr2 * rho3[j] + t3j * drho3dr2) -
dgamma3[j] * (shpj[0] * dt1dr2 + shpj[1] * dt2dr2 + shpj[2] * dt3dr2);
for (m = 0; m < 3; m++) {
drhodrm1[m] = 0.0;
drhodrm2[m] = 0.0;
drhodrm1[m] = dgamma2[i] * (t1i * drho1drm1[m] + t2i * drho2drm1[m] + t3i * drho3drm1[m]);
drhodrm2[m] = dgamma2[j] * (t1j * drho1drm2[m] + t2j * drho2drm2[m] + t3j * drho3drm2[m]);
}
// Compute derivatives wrt sij, but only if necessary
if (!iszero(dscrfcn[fnoffset + jn])) {
drho0ds1 = rhoa0j;
drho0ds2 = rhoa0i;
a1 = 2.0 / rij;
drho1ds1 = a1 * rhoa1j * arg1i1;
drho1ds2 = a1 * rhoa1i * arg1j1;
a2 = 2.0 / rij2;
drho2ds1 = a2 * rhoa2j * arg1i2 - 2.0 / 3.0 * arho2b[i] * rhoa2j;
drho2ds2 = a2 * rhoa2i * arg1j2 - 2.0 / 3.0 * arho2b[j] * rhoa2i;
a3 = 2.0 / rij3;
a3a = 6.0 / (5.0 * rij);
drho3ds1 = a3 * rhoa3j * arg1i3 - a3a * rhoa3j * arg3i3;
drho3ds2 = a3 * rhoa3i * arg1j3 - a3a * rhoa3i * arg3j3;
if (this->ialloy == 1) {
a1i = 0.0;
a1j = 0.0;
a2i = 0.0;
a2j = 0.0;
a3i = 0.0;
a3j = 0.0;
if (!iszero(tsq_ave[i][0]))
a1i = rhoa0j / tsq_ave[i][0];
if (!iszero(tsq_ave[j][0]))
a1j = rhoa0i / tsq_ave[j][0];
if (!iszero(tsq_ave[i][1]))
a2i = rhoa0j / tsq_ave[i][1];
if (!iszero(tsq_ave[j][1]))
a2j = rhoa0i / tsq_ave[j][1];
if (!iszero(tsq_ave[i][2]))
a3i = rhoa0j / tsq_ave[i][2];
if (!iszero(tsq_ave[j][2]))
a3j = rhoa0i / tsq_ave[j][2];
dt1ds1 = a1i * (t1mj - t1i * pow(t1mj, 2));
dt1ds2 = a1j * (t1mi - t1j * pow(t1mi, 2));
dt2ds1 = a2i * (t2mj - t2i * pow(t2mj, 2));
dt2ds2 = a2j * (t2mi - t2j * pow(t2mi, 2));
dt3ds1 = a3i * (t3mj - t3i * pow(t3mj, 2));
dt3ds2 = a3j * (t3mi - t3j * pow(t3mi, 2));
} else if (this->ialloy == 2) {
dt1ds1 = 0.0;
dt1ds2 = 0.0;
dt2ds1 = 0.0;
dt2ds2 = 0.0;
dt3ds1 = 0.0;
dt3ds2 = 0.0;
} else {
ai = 0.0;
if (!iszero(rho0[i]))
ai = rhoa0j / rho0[i];
aj = 0.0;
if (!iszero(rho0[j]))
aj = rhoa0i / rho0[j];
dt1ds1 = ai * (t1mj - t1i);
dt1ds2 = aj * (t1mi - t1j);
dt2ds1 = ai * (t2mj - t2i);
dt2ds2 = aj * (t2mi - t2j);
dt3ds1 = ai * (t3mj - t3i);
dt3ds2 = aj * (t3mi - t3j);
}
drhods1 = dgamma1[i] * drho0ds1 +
dgamma2[i] * (dt1ds1 * rho1[i] + t1i * drho1ds1 + dt2ds1 * rho2[i] + t2i * drho2ds1 +
dt3ds1 * rho3[i] + t3i * drho3ds1) -
dgamma3[i] * (shpi[0] * dt1ds1 + shpi[1] * dt2ds1 + shpi[2] * dt3ds1);
drhods2 = dgamma1[j] * drho0ds2 +
dgamma2[j] * (dt1ds2 * rho1[j] + t1j * drho1ds2 + dt2ds2 * rho2[j] + t2j * drho2ds2 +
dt3ds2 * rho3[j] + t3j * drho3ds2) -
dgamma3[j] * (shpj[0] * dt1ds2 + shpj[1] * dt2ds2 + shpj[2] * dt3ds2);
}
// Compute derivatives of energy wrt rij, sij and rij[3]
dUdrij = phip * sij + frhop[i] * drhodr1 + frhop[j] * drhodr2;
dUdsij = 0.0;
if (!iszero(dscrfcn[fnoffset + jn])) {
dUdsij = phi + frhop[i] * drhods1 + frhop[j] * drhods2;
}
for (m = 0; m < 3; m++) {
dUdrijm[m] = frhop[i] * drhodrm1[m] + frhop[j] * drhodrm2[m];
}
// Add the part of the force due to dUdrij and dUdsij
force = dUdrij * recip + dUdsij * dscrfcn[fnoffset + jn];
for (m = 0; m < 3; m++) {
forcem = delij[m] * force + dUdrijm[m];
f[i][m] = f[i][m] + forcem;
f[j][m] = f[j][m] - forcem;
}
// Tabulate per-atom virial as symmetrized stress tensor
if (vflag_atom != 0) {
fi[0] = delij[0] * force + dUdrijm[0];
fi[1] = delij[1] * force + dUdrijm[1];
fi[2] = delij[2] * force + dUdrijm[2];
v[0] = -0.5 * (delij[0] * fi[0]);
v[1] = -0.5 * (delij[1] * fi[1]);
v[2] = -0.5 * (delij[2] * fi[2]);
v[3] = -0.25 * (delij[0] * fi[1] + delij[1] * fi[0]);
v[4] = -0.25 * (delij[0] * fi[2] + delij[2] * fi[0]);
v[5] = -0.25 * (delij[1] * fi[2] + delij[2] * fi[1]);
for (m = 0; m < 6; m++) {
vatom[i][m] = vatom[i][m] + v[m];
vatom[j][m] = vatom[j][m] + v[m];
}
}
// Now compute forces on other atoms k due to change in sij
if (iszero(sij) || iszero(sij - 1.0)) continue; //: cont jn loop
double dxik(0), dyik(0), dzik(0);
double dxjk(0), dyjk(0), dzjk(0);
for (kn = 0; kn < numneigh_full; kn++) {
k = firstneigh_full[kn];
eltk = fmap[type[k]];
if (k != j && eltk >= 0) {
double xik, xjk, cikj, sikj, dfc, a;
double dCikj1, dCikj2;
double delc, rik2, rjk2;
sij = scrfcn[jn+fnoffset] * fcpair[jn+fnoffset];
const double Cmax = this->Cmax_meam[elti][eltj][eltk];
const double Cmin = this->Cmin_meam[elti][eltj][eltk];
dsij1 = 0.0;
dsij2 = 0.0;
if (!iszero(sij) && !iszero(sij - 1.0)) {
const double rbound = rij2 * this->ebound_meam[elti][eltj];
delc = Cmax - Cmin;
dxjk = x[k][0] - x[j][0];
dyjk = x[k][1] - x[j][1];
dzjk = x[k][2] - x[j][2];
rjk2 = dxjk * dxjk + dyjk * dyjk + dzjk * dzjk;
if (rjk2 <= rbound) {
dxik = x[k][0] - x[i][0];
dyik = x[k][1] - x[i][1];
dzik = x[k][2] - x[i][2];
rik2 = dxik * dxik + dyik * dyik + dzik * dzik;
if (rik2 <= rbound) {
xik = rik2 / rij2;
xjk = rjk2 / rij2;
a = 1 - (xik - xjk) * (xik - xjk);
if (!iszero(a)) {
cikj = (2.0 * (xik + xjk) + a - 2.0) / a;
if (cikj >= Cmin && cikj <= Cmax) {
cikj = (cikj - Cmin) / delc;
sikj = dfcut(cikj, dfc);
dCfunc2(rij2, rik2, rjk2, dCikj1, dCikj2);
a = sij / delc * dfc / sikj;
dsij1 = a * dCikj1;
dsij2 = a * dCikj2;
}
}
}
}
}
if (!iszero(dsij1) || !iszero(dsij2)) {
force1 = dUdsij * dsij1;
force2 = dUdsij * dsij2;
f[i][0] += force1 * dxik;
f[i][1] += force1 * dyik;
f[i][2] += force1 * dzik;
f[j][0] += force2 * dxjk;
f[j][1] += force2 * dyjk;
f[j][2] += force2 * dzjk;
f[k][0] -= force1 * dxik + force2 * dxjk;
f[k][1] -= force1 * dyik + force2 * dyjk;
f[k][2] -= force1 * dzik + force2 * dzjk;
// Tabulate per-atom virial as symmetrized stress tensor
if (vflag_atom != 0) {
fi[0] = force1 * dxik;
fi[1] = force1 * dyik;
fi[2] = force1 * dzik;
fj[0] = force2 * dxjk;
fj[1] = force2 * dyjk;
fj[2] = force2 * dzjk;
v[0] = -third * (dxik * fi[0] + dxjk * fj[0]);
v[1] = -third * (dyik * fi[1] + dyjk * fj[1]);
v[2] = -third * (dzik * fi[2] + dzjk * fj[2]);
v[3] = -sixth * (dxik * fi[1] + dxjk * fj[1] + dyik * fi[0] + dyjk * fj[0]);
v[4] = -sixth * (dxik * fi[2] + dxjk * fj[2] + dzik * fi[0] + dzjk * fj[0]);
v[5] = -sixth * (dyik * fi[2] + dyjk * fj[2] + dzik * fi[1] + dzjk * fj[1]);
for (m = 0; m < 6; m++) {
vatom[i][m] = vatom[i][m] + v[m];
vatom[j][m] = vatom[j][m] + v[m];
vatom[k][m] = vatom[k][m] + v[m];
}
}
}
}
// end of k loop
}
}
}
// end of j loop
}
}

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