1264 lines
38 KiB
C++
1264 lines
38 KiB
C++
// clang-format off
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/* ----------------------------------------------------------------------
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LAMMPS - Large-scale Atomic/Molecular Massively Parallel Simulator
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https://www.lammps.org/, Sandia National Laboratories
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Steve Plimpton, sjplimp@sandia.gov
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Copyright (2003) Sandia Corporation. Under the terms of Contract
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DE-AC04-94AL85000 with Sandia Corporation, the U.S. Government retains
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certain rights in this software. This software is distributed under
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the GNU General Public License.
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See the README file in the top-level LAMMPS directory.
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------------------------------------------------------------------------- */
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/* ----------------------------------------------------------------------
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Contributing Authors : Germain Clavier (TUe), Aidan Thompson (Sandia)
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------------------------------------------------------------------------- */
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#include "compute_born_matrix.h"
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#include "angle.h"
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#include "atom.h"
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#include "atom_vec.h"
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#include "bond.h"
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#include "comm.h"
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#include "compute.h"
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#include "dihedral.h"
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#include "domain.h"
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#include "error.h"
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#include "force.h"
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#include "improper.h"
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#include "kspace.h"
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#include "memory.h"
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#include "modify.h"
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#include "molecule.h"
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#include "neigh_list.h"
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#include "neigh_request.h"
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#include "neighbor.h"
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#include "pair.h"
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#include "update.h"
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#include "universe.h"
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#include <cmath>
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#include <cstring>
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using namespace LAMMPS_NS;
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#define BIG 1000000000
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// This table is used to pick the 3d rij vector indices used to
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// compute the 6 indices long Voigt stress vector
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static int constexpr sigma_albe[6][2] = {
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{0, 0}, // s11
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{1, 1}, // s22
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{2, 2}, // s33
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{1, 2}, // s44
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{0, 2}, // s55
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{0, 1}, // s66
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};
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// This table is used to pick the correct indices from the Voigt
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// stress vector to compute the Cij matrix (21 terms, see doc) contribution
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static int constexpr C_albe[21][2] = {
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{0, 0}, // C11
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{1, 1}, // C22
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{2, 2}, // C33
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{3, 3}, // C44
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{4, 4}, // C55
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{5, 5}, // C66
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{0, 1}, // C12
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{0, 2}, // C13
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{0, 3}, // C14
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{0, 4}, // C15
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{0, 5}, // C16
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{1, 2}, // C23
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{1, 3}, // C24
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{1, 4}, // C25
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{1, 5}, // C26
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{2, 3}, // C34
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{2, 4}, // C35
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{2, 5}, // C36
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{3, 4}, // C45
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{3, 5}, // C46
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{4, 5} // C56
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};
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// This table is used to pick the 3d rij vector indices used to
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// compute the 21 indices long Cij matrix
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static int constexpr albemunu[21][4] = {
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{0, 0, 0, 0}, // C11
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{1, 1, 1, 1}, // C22
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{2, 2, 2, 2}, // C33
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{1, 2, 1, 2}, // C44
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{0, 2, 0, 2}, // C55
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{0, 1, 0, 1}, // C66
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{0, 0, 1, 1}, // C12
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{0, 0, 2, 2}, // C13
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{0, 0, 1, 2}, // C14
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{0, 0, 0, 2}, // C15
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{0, 0, 0, 1}, // C16
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{1, 1, 2, 2}, // C23
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{1, 1, 1, 2}, // C24
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{1, 1, 0, 2}, // C25
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{1, 1, 0, 1}, // C26
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{2, 2, 1, 2}, // C34
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{2, 2, 0, 2}, // C35
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{2, 2, 0, 1}, // C36
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{1, 2, 0, 2}, // C45
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{1, 2, 0, 1}, // C46
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{0, 1, 0, 2} // C56
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};
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/* ---------------------------------------------------------------------- */
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ComputeBornMatrix::ComputeBornMatrix(LAMMPS *lmp, int narg, char **arg) :
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Compute(lmp, narg, arg), id_virial(nullptr), temp_x(nullptr),
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temp_f(nullptr)
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{
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if (narg < 3) error->all(FLERR,"Illegal compute born/matrix command");
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MPI_Comm_rank(world, &me);
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// For now the matrix can be computed as a 21 element vector
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nvalues = 21;
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// Error check
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numflag = 0;
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numdelta = 0.0;
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pairflag = 0;
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bondflag = 0;
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angleflag = 0;
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dihedflag = 0;
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impflag = 0;
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if (narg == 3) {
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pairflag = 1;
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bondflag = 1;
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angleflag = 1;
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dihedflag = 1;
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impflag = 1;
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} else {
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int iarg = 3;
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while (iarg < narg) {
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if (strcmp(arg[iarg],"numdiff") == 0) {
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if (iarg+3 > narg) error->all(FLERR,"Illegal compute born/matrix command");
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numflag = 1;
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numdelta = utils::numeric(FLERR,arg[iarg+1],false,lmp);
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if (numdelta <= 0.0) error->all(FLERR, "Illegal compute born/matrix command");
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id_virial = utils::strdup(arg[iarg+2]);
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int icompute = modify->find_compute(id_virial);
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if (icompute < 0) error->all(FLERR,"Could not find compute born/matrix pressure ID");
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compute_virial = modify->compute[icompute];
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if (compute_virial->pressflag == 0)
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error->all(FLERR,"Compute born/matrix pressure ID does not compute pressure");
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iarg += 3;
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} else if (strcmp(arg[iarg],"pair") == 0) pairflag = 1;
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else if (strcmp(arg[iarg],"bond") == 0) bondflag = 1;
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else if (strcmp(arg[iarg],"angle") == 0) angleflag = 1;
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else if (strcmp(arg[iarg],"dihedral") == 0) dihedflag = 1;
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else if (strcmp(arg[iarg],"improper") == 0) impflag = 1;
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else error->all(FLERR,"Illegal compute born/matrix command");
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++iarg;
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}
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}
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if (pairflag) {
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if (numflag) error->all(FLERR, "Illegal compute born/matrix command: cannot mix numflag and other flags");
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if (force->pair) {
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if (force->pair->born_matrix_enable == 0) {
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if (comm->me == 0) error->warning(FLERR, "Pair style does not support compute born/matrix");
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}
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} else {
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pairflag = 0;
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}
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}
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if (bondflag) {
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if (numflag) error->all(FLERR, "Illegal compute born/matrix command: cannot mix numflag and other flags");
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if (force->bond) {
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if (force->bond->born_matrix_enable == 0) {
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if (comm->me == 0) error->warning(FLERR, "Bond style does not support compute born/matrix");
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}
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} else {
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bondflag = 0;
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}
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}
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if (angleflag) {
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if (numflag) error->all(FLERR, "Illegal compute born/matrix command: cannot mix numflag and other flags");
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if (force->angle) {
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if (force->angle->born_matrix_enable == 0) {
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if (comm->me == 0) error->warning(FLERR, "Angle style does not support compute born/matrix");
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}
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} else {
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angleflag = 0;
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}
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}
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if (dihedflag) {
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if (numflag) error->all(FLERR, "Illegal compute born/matrix command: cannot mix numflag and other flags");
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if (force->dihedral) {
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if (force->dihedral->born_matrix_enable == 0) {
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if (comm->me == 0) error->warning(FLERR, "Dihedral style does not support compute born/matrix");
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}
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} else {
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dihedflag = 0;
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}
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}
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if (impflag) {
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if (numflag) error->all(FLERR, "Illegal compute born/matrix command: cannot mix numflag and other flags");
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if (force->improper) {
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if (force->improper->born_matrix_enable == 0) {
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if (comm->me == 0) error->warning(FLERR, "Improper style does not support compute born/matrix");
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}
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} else {
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impflag = 0;
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}
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}
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if (force->kspace) {
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if (!numflag) error->warning(FLERR, "KSPACE contribution not supported by compute born/matrix");
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}
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// Initialize some variables
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values_local = values_global = vector = nullptr;
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// this fix produces a global vector
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memory->create(vector, nvalues, "born_matrix:vector");
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memory->create(values_global, nvalues, "born_matrix:values_global");
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size_vector = nvalues;
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vector_flag = 1;
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extvector = 0;
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maxatom = 0;
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if (!numflag) {
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memory->create(values_local, nvalues, "born_matrix:values_local");
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} else {
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reallocate();
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// set fixed-point to default = center of cell
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fixedpoint[0] = 0.5 * (domain->boxlo[0] + domain->boxhi[0]);
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fixedpoint[1] = 0.5 * (domain->boxlo[1] + domain->boxhi[1]);
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fixedpoint[2] = 0.5 * (domain->boxlo[2] + domain->boxhi[2]);
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// define the cartesian indices for each strain (Voigt order)
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dirlist[0][0] = 0;
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dirlist[0][1] = 0;
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dirlist[1][0] = 1;
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dirlist[1][1] = 1;
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dirlist[2][0] = 2;
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dirlist[2][1] = 2;
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dirlist[3][0] = 1;
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dirlist[3][1] = 2;
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dirlist[4][0] = 0;
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dirlist[4][1] = 2;
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dirlist[5][0] = 0;
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dirlist[5][1] = 1;
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}
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}
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/* ---------------------------------------------------------------------- */
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ComputeBornMatrix::~ComputeBornMatrix()
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{
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memory->destroy(values_global);
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memory->destroy(vector);
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if (!numflag) {
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memory->destroy(values_local);
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} else {
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memory->destroy(temp_x);
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memory->destroy(temp_f);
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delete[] id_virial;
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}
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}
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/* ---------------------------------------------------------------------- */
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void ComputeBornMatrix::init()
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{
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//Timestep value
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dt = update->dt;
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if (!numflag) {
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// need an occasional half neighbor list
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int irequest = neighbor->request((void *) this);
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neighbor->requests[irequest]->pair = 0;
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neighbor->requests[irequest]->compute = 1;
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neighbor->requests[irequest]->occasional = 1;
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} else {
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// check for virial compute
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int icompute = modify->find_compute(id_virial);
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if (icompute < 0) error->all(FLERR, "Virial compute ID for compute born/matrix does not exist");
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compute_virial = modify->compute[icompute];
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// set up reverse index lookup
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for (int m = 0; m < nvalues; m++) {
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int a = C_albe[m][0];
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int b = C_albe[m][1];
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revalbe[a][b] = m;
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revalbe[b][a] = m;
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}
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// for (int a = 0; a < NDIR_VIRIAL; a++) {
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// for (int b = 0; b < NDIR_VIRIAL; b++) {
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// printf("%d ",revalbe[a][b]);
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// }
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// printf("\n");
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// }
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// voigt3VtoM notation in normal physics sense,
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// 3x3 matrix and vector indexing
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// i-j: (1-1), (2-2), (3-3), (2-3), (1-3), (1-2)
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// voigt3VtoM: 1 2 3 4 5 6
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voigt3VtoM[0][0]=0; // for 1
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voigt3VtoM[0][1]=0;
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voigt3VtoM[1][0]=1; // for 2
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voigt3VtoM[1][1]=1;
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voigt3VtoM[2][0]=2; // for 3
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voigt3VtoM[2][1]=2;
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voigt3VtoM[3][0]=1; // for 4
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voigt3VtoM[3][1]=2;
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voigt3VtoM[4][0]=0; // for 5
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voigt3VtoM[4][1]=2;
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voigt3VtoM[5][0]=0; // for 6
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voigt3VtoM[5][1]=1;
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// to convert to vector indexing:
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// matrix index to vector index, double -> single index
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// this is not used at all
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voigt3MtoV[0][0]=0; voigt3MtoV[0][1]=5; voigt3MtoV[0][2]=4;
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voigt3MtoV[1][0]=5; voigt3MtoV[1][1]=1; voigt3MtoV[1][2]=3;
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voigt3MtoV[2][0]=4; voigt3MtoV[2][1]=3; voigt3MtoV[2][2]=2;
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// this is just for the virial.
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// since they use the xx,yy,zz,xy,xz,yz
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// order not the ordinary voigt
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virialMtoV[0][0]=0; virialMtoV[0][1]=3; virialMtoV[0][2]=4;
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virialMtoV[1][0]=3; virialMtoV[1][1]=1; virialMtoV[1][2]=5;
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virialMtoV[2][0]=4; virialMtoV[2][1]=5; virialMtoV[2][2]=2;
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// reorder LAMMPS virial vector to Voigt order
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virialVtoV[0] = 0;
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virialVtoV[1] = 1;
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virialVtoV[2] = 2;
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virialVtoV[3] = 5;
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virialVtoV[4] = 4;
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virialVtoV[5] = 3;
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// the following is for 6x6 matrix and vector indexing converter
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// this is clearly different order form albe[][] and revalbe[]
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// should not be used
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int indcounter = 0;
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for(int row = 0; row < NDIR_VIRIAL; row++)
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for(int col = row; col< NDIR_VIRIAL; col++) {
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voigt6MtoV[row][col] = voigt6MtoV[col][row] = indcounter;
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indcounter++;
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}
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// printf("Voigt6MtoV:\n");
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// for (int a = 0; a < NDIR_VIRIAL; a++) {
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// for (int b = 0; b < NDIR_VIRIAL; b++) {
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// printf("%d ", voigt6MtoV[a][b]);
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// }
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// printf("\n");
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// }
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// set up 3x3 kronecker deltas
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for(int row = 0; row < NXYZ_VIRIAL; row++)
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for(int col = 0; col < NXYZ_VIRIAL; col++)
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kronecker[row][col] = 0;
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for(int row = 0; row < NXYZ_VIRIAL; row++)
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kronecker[row][row] = 1;
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}
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}
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/* ---------------------------------------------------------------------- */
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void ComputeBornMatrix::init_list(int /* id */, NeighList *ptr)
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{
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list = ptr;
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}
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/* ----------------------------------------------------------------------
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compute output vector
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------------------------------------------------------------------------- */
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void ComputeBornMatrix::compute_vector()
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{
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invoked_vector = update->ntimestep;
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if (!numflag) {
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// zero out arrays for one sample
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for (int m = 0; m < nvalues; m++) values_local[m] = 0.0;
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// Compute Born contribution
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if (pairflag) compute_pairs();
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if (bondflag) compute_bonds();
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if (angleflag) compute_angles();
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if (dihedflag) compute_dihedrals();
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// sum Born contributions over all procs
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MPI_Allreduce(values_local, values_global, nvalues, MPI_DOUBLE, MPI_SUM, world);
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// convert to pressure units
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// As discussed, it might be better to keep it as energy units.
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// but this is to be defined
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// double nktv2p = force->nktv2p;
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// double inv_volume = 1.0 / (domain->xprd * domain->yprd * domain->zprd);
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// for (int m = 0; m < nvalues; m++) {
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// values_global[m] *= (nktv2p * inv_volume);
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// }
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} else {
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// calculate Born matrix using stress finite differences
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compute_numdiff();
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// for consistency this is returned in energy units
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double inv_nktv2p = 1.0/force->nktv2p;
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double volume = domain->xprd * domain->yprd * domain->zprd;
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for (int m = 0; m < nvalues; m++) {
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values_global[m] *= inv_nktv2p * volume;
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}
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}
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for (int m = 0; m < nvalues; m++) vector[m] = values_global[m];
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}
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/* ----------------------------------------------------------------------
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compute Born contribution of local proc
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------------------------------------------------------------------------- */
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void ComputeBornMatrix::compute_pairs()
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{
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int i, j, ii, jj, inum, jnum, itype, jtype;
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double rsq, factor_coul, factor_lj;
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double dupair, du2pair, rinv;
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int *ilist, *jlist, *numneigh, **firstneigh;
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int *type = atom->type;
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int *mask = atom->mask;
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int nlocal = atom->nlocal;
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double *special_coul = force->special_coul;
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double *special_lj = force->special_lj;
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int newton_pair = force->newton_pair;
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// invoke half neighbor list (will copy or build if necessary)
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neighbor->build_one(list);
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inum = list->inum;
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ilist = list->ilist;
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numneigh = list->numneigh;
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firstneigh = list->firstneigh;
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// loop over neighbors of my atoms
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Pair *pair = force->pair;
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double **cutsq = force->pair->cutsq;
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// Declares born values
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int a, b, c, d;
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double xi1, xi2, xi3;
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double fi1, fi2, fi3;
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double xj1, xj2, xj3;
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double rij[3];
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double pair_pref;
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double r2inv;
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for (ii = 0; ii < inum; ii++) {
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i = ilist[ii];
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if (!(mask[i] & groupbit)) continue;
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xi1 = atom->x[i][0];
|
|
xi2 = atom->x[i][1];
|
|
xi3 = atom->x[i][2];
|
|
itype = type[i];
|
|
jlist = firstneigh[i];
|
|
jnum = numneigh[i];
|
|
|
|
for (jj = 0; jj < jnum; jj++) {
|
|
j = jlist[jj];
|
|
factor_lj = special_lj[sbmask(j)];
|
|
factor_coul = special_coul[sbmask(j)];
|
|
j &= NEIGHMASK;
|
|
|
|
if (!(mask[j] & groupbit)) continue;
|
|
|
|
xj1 = atom->x[j][0];
|
|
xj2 = atom->x[j][1];
|
|
xj3 = atom->x[j][2];
|
|
rij[0] = xj1 - xi1;
|
|
rij[1] = xj2 - xi2;
|
|
rij[2] = xj3 - xi3;
|
|
rsq = rij[0] * rij[0] + rij[1] * rij[1] + rij[2] * rij[2];
|
|
r2inv = 1.0 / rsq;
|
|
rinv = sqrt(r2inv);
|
|
jtype = type[j];
|
|
|
|
if (rsq >= cutsq[itype][jtype]) continue;
|
|
|
|
if (newton_pair || j < nlocal) {
|
|
|
|
// Add contribution to Born tensor
|
|
|
|
pair->born_matrix(i, j, itype, jtype, rsq, factor_coul, factor_lj, dupair, du2pair);
|
|
pair_pref = du2pair - dupair * rinv;
|
|
|
|
// See albemunu in compute_born_matrix.h for indices order.
|
|
|
|
a = 0;
|
|
b = 0;
|
|
c = 0;
|
|
d = 0;
|
|
for (int m = 0; m < nvalues; m++) {
|
|
a = albemunu[m][0];
|
|
b = albemunu[m][1];
|
|
c = albemunu[m][2];
|
|
d = albemunu[m][3];
|
|
values_local[m] += pair_pref * rij[a] * rij[b] * rij[c] * rij[d] * r2inv;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
/* ----------------------------------------------------------------------
|
|
compute Born matrix using virial stress finite differences
|
|
------------------------------------------------------------------------- */
|
|
|
|
void ComputeBornMatrix::compute_numdiff()
|
|
{
|
|
double energy;
|
|
int vec_indice;
|
|
|
|
// grow arrays if necessary
|
|
|
|
int nall = atom->nlocal + atom->nghost;
|
|
if (nall > maxatom) reallocate();
|
|
|
|
// store copy of current forces for owned and ghost atoms
|
|
|
|
double **x = atom->x;
|
|
double **f = atom->f;
|
|
|
|
for (int i = 0; i < nall; i++)
|
|
for (int k = 0; k < 3; k++) {
|
|
temp_x[i][k] = x[i][k];
|
|
temp_f[i][k] = f[i][k];
|
|
}
|
|
|
|
// loop over 6 strain directions
|
|
// compute stress finite difference in each direction
|
|
// It must be noted that, as stated in Yoshimoto's eq. 15, eq 16.
|
|
// and eq. A3, this tensor is NOT the true Cijkl tensor.
|
|
// We have the relationship
|
|
// C_ijkl=1./4.(\hat{C}_ijkl+\hat{C}_jikl+\hat{C}_ijlk+\hat{C}_jilk)
|
|
|
|
int flag, allflag;
|
|
|
|
for (int idir = 0; idir < NDIR_VIRIAL; idir++) {
|
|
displace_atoms(nall, idir, 1.0);
|
|
force_clear(nall);
|
|
update_virial();
|
|
for (int jdir = 0; jdir < NDIR_VIRIAL; jdir++) {
|
|
vec_indice = revalbe[idir][jdir];
|
|
values_global[vec_indice] = compute_virial->vector[virialVtoV[jdir]];
|
|
}
|
|
restore_atoms(nall, idir);
|
|
|
|
displace_atoms(nall, idir, -1.0);
|
|
force_clear(nall);
|
|
update_virial();
|
|
for (int jdir = 0; jdir < NDIR_VIRIAL; jdir++) {
|
|
vec_indice = revalbe[idir][jdir];
|
|
values_global[vec_indice] -= compute_virial->vector[virialVtoV[jdir]];
|
|
}
|
|
|
|
// End of the strain
|
|
restore_atoms(nall, idir);
|
|
}
|
|
|
|
// apply derivative factor
|
|
|
|
double denominator = -0.5 / numdelta;
|
|
for (int m = 0; m < nvalues; m++) values_global[m] *= denominator;
|
|
|
|
// recompute virial so all virial and energy contributions are as before
|
|
// also needed for virial stress addon contributions to Born matrix
|
|
// this will possibly break compute stress/atom, need to test
|
|
|
|
update_virial();
|
|
|
|
virial_addon();
|
|
|
|
// restore original forces for owned and ghost atoms
|
|
|
|
for (int i = 0; i < nall; i++)
|
|
for (int k = 0; k < 3; k++)
|
|
f[i][k] = temp_f[i][k];
|
|
|
|
}
|
|
|
|
/* ----------------------------------------------------------------------
|
|
displace position of all owned and ghost atoms
|
|
------------------------------------------------------------------------- */
|
|
|
|
void ComputeBornMatrix::displace_atoms(int nall, int idir, double magnitude)
|
|
{
|
|
double **x = atom->x;
|
|
|
|
// A.T.
|
|
// this works for vector indices 7, 8, 9, 12, 14, 18 and 15, 16, 17
|
|
// corresponding i,j indices 12, 13, 14, 23, 25, 36 and 26, 34, 35
|
|
int k = dirlist[idir][1];
|
|
int l = dirlist[idir][0];
|
|
|
|
// A.T.
|
|
// this works for vector indices 7, 8, 9, 12, 14, 18 and 10, 11, 13
|
|
// corresponding i,j indices 12, 13, 14, 23, 25, 36 and 15, 16, 24
|
|
// G.C.:
|
|
// I see no difference with a 0 step simulation between both
|
|
// methods.
|
|
// int k = dirlist[idir][0];
|
|
// int l = dirlist[idir][1];
|
|
for (int i = 0; i < nall; i++)
|
|
x[i][k] = temp_x[i][k] + numdelta * magnitude * (temp_x[i][l] - fixedpoint[l]);
|
|
}
|
|
|
|
/* ----------------------------------------------------------------------
|
|
restore position of all owned and ghost atoms
|
|
------------------------------------------------------------------------- */
|
|
|
|
void ComputeBornMatrix::restore_atoms(int nall, int idir)
|
|
{
|
|
|
|
// reset all coords, just to be safe, ignore idir
|
|
|
|
double **x = atom->x;
|
|
for (int i = 0; i < nall; i++)
|
|
for (int k = 0; k < 3; k++)
|
|
x[i][k] = temp_x[i][k];
|
|
}
|
|
|
|
/* ----------------------------------------------------------------------
|
|
evaluate potential forces and virial
|
|
same logic as in Verlet
|
|
------------------------------------------------------------------------- */
|
|
|
|
void ComputeBornMatrix::update_virial()
|
|
{
|
|
int eflag = 0;
|
|
// int vflag = VIRIAL_FDOTR; // Need to generalize this
|
|
int vflag = 1;
|
|
|
|
if (force->pair) force->pair->compute(eflag, vflag);
|
|
|
|
if (atom->molecular != Atom::ATOMIC) {
|
|
if (force->bond) force->bond->compute(eflag, vflag);
|
|
if (force->angle) force->angle->compute(eflag, vflag);
|
|
if (force->dihedral) force->dihedral->compute(eflag, vflag);
|
|
if (force->improper) force->improper->compute(eflag, vflag);
|
|
}
|
|
|
|
if (force->kspace) force->kspace->compute(eflag, vflag);
|
|
|
|
compute_virial->compute_vector();
|
|
}
|
|
|
|
/* ----------------------------------------------------------------------
|
|
calculate virial stress addon terms to the Born matrix
|
|
this is based on original code of Dr. Yubao Zhen
|
|
described here: Comp. Phys. Comm. 183 (2012) 261-265
|
|
------------------------------------------------------------------------- */
|
|
|
|
void ComputeBornMatrix::virial_addon()
|
|
{
|
|
// compute the contribution due to perturbation
|
|
// here the addon parts are put into born
|
|
// delta_il sigv_jk + delta_ik sigv_jl +
|
|
// delta_jl sigv_ik + delta_jk sigv_il
|
|
// Note: in calculation kl is all there from 0 to 6, and ij=(id,jd)
|
|
// each time there are six numbers passed for (Dijkl+Djikl)
|
|
// and the term I need should be div by 2.
|
|
// Job is to arrange the 6 numbers with ij indexing to the 21
|
|
// element data structure.
|
|
// the sigv is the virial stress at current time. It is never touched.
|
|
// Note the symmetry of (i-j), (k-n), and (ij, kn)
|
|
// so we only need to evaluate 6x6 matrix with symmetry
|
|
|
|
int kd, nd, id, jd;
|
|
int m;
|
|
|
|
double* sigv = compute_virial->vector;
|
|
double modefactor[6] = {1.0, 1.0, 1.0, 0.5, 0.5, 0.5};
|
|
|
|
for (int idir = 0; idir < NDIR_VIRIAL; idir++) {
|
|
int ijvgt = idir; // this is it.
|
|
double addon;
|
|
|
|
// extract the two indices composing the voigt representation
|
|
|
|
id = voigt3VtoM[ijvgt][0];
|
|
jd = voigt3VtoM[ijvgt][1];
|
|
|
|
for (int knvgt=ijvgt; knvgt < NDIR_VIRIAL; knvgt++) {
|
|
kd = voigt3VtoM[knvgt][0];
|
|
nd = voigt3VtoM[knvgt][1];
|
|
addon = kronecker[id][nd]*sigv[virialMtoV[jd][kd]] +
|
|
kronecker[id][kd]*sigv[virialMtoV[jd][nd]];
|
|
if(id != jd)
|
|
addon += kronecker[jd][nd]*sigv[virialMtoV[id][kd]] +
|
|
kronecker[jd][kd]*sigv[virialMtoV[id][nd]];
|
|
|
|
m = revalbe[ijvgt][knvgt];
|
|
|
|
values_global[revalbe[ijvgt][knvgt]] += 0.5*modefactor[idir]*addon;
|
|
}
|
|
}
|
|
}
|
|
|
|
/* ----------------------------------------------------------------------
|
|
clear forces needed
|
|
------------------------------------------------------------------------- */
|
|
|
|
void ComputeBornMatrix::force_clear(int nall)
|
|
{
|
|
double **forces = atom->f;
|
|
size_t nbytes = 3 * sizeof(double) * nall;
|
|
if (nbytes) memset(&forces[0][0], 0, nbytes);
|
|
}
|
|
|
|
/* ----------------------------------------------------------------------
|
|
reallocated local per-atoms arrays
|
|
------------------------------------------------------------------------- */
|
|
|
|
void ComputeBornMatrix::reallocate()
|
|
{
|
|
memory->destroy(temp_x);
|
|
memory->destroy(temp_f);
|
|
maxatom = atom->nmax;
|
|
memory->create(temp_x, maxatom, 3, "born/matrix:temp_x");
|
|
memory->create(temp_f, maxatom, 3, "born/matrix:temp_f");
|
|
}
|
|
|
|
/* ----------------------------------------------------------------------
|
|
memory usage of local atom-based arrays
|
|
------------------------------------------------------------------------- */
|
|
|
|
double ComputeBornMatrix::memory_usage()
|
|
{
|
|
double bytes = 0.0;
|
|
bytes += (double) 2 * maxatom * 3 * sizeof(double);
|
|
return bytes;
|
|
}
|
|
|
|
/* ----------------------------------------------------------------------
|
|
Count bonds and compute bond info on this proc
|
|
only count bond once if newton_bond is off
|
|
all atoms in interaction must be in group
|
|
all atoms in interaction must be known to proc
|
|
if bond is deleted or turned off (type <= 0)
|
|
do not count or count contribution
|
|
---------------------------------------------------------------------- */
|
|
void ComputeBornMatrix::compute_bonds()
|
|
{
|
|
int i,m,n,nb,atom1,atom2,imol,iatom,btype,ivar;
|
|
tagint tagprev;
|
|
double dx,dy,dz,rsq;
|
|
|
|
double **x = atom->x;
|
|
double **v = atom->v;
|
|
int *type = atom->type;
|
|
tagint *tag = atom->tag;
|
|
int *num_bond = atom->num_bond;
|
|
tagint **bond_atom = atom->bond_atom;
|
|
int **bond_type = atom->bond_type;
|
|
int *mask = atom->mask;
|
|
|
|
int *molindex = atom->molindex;
|
|
int *molatom = atom->molatom;
|
|
Molecule **onemols = atom->avec->onemols;
|
|
|
|
int nlocal = atom->nlocal;
|
|
int newton_bond = force->newton_bond;
|
|
int molecular = atom->molecular;
|
|
|
|
Bond *bond = force->bond;
|
|
|
|
int a,b,c,d;
|
|
double rij[3];
|
|
double rinv, r2inv;
|
|
double pair_pref, dupair, du2pair;
|
|
|
|
// loop over all atoms and their bonds
|
|
|
|
m = 0;
|
|
while (m<nvalues) {
|
|
|
|
for (atom1 = 0; atom1 < nlocal; atom1++) {
|
|
if (!(mask[atom1] & groupbit)) continue;
|
|
|
|
if (molecular == 1) nb = num_bond[atom1];
|
|
else {
|
|
if (molindex[atom1] < 0) continue;
|
|
imol = molindex[atom1];
|
|
iatom = molatom[atom1];
|
|
nb = onemols[imol]->num_bond[iatom];
|
|
}
|
|
|
|
for (i = 0; i < nb; i++) {
|
|
if (molecular == 1) {
|
|
btype = bond_type[atom1][i];
|
|
atom2 = atom->map(bond_atom[atom1][i]);
|
|
} else {
|
|
tagprev = tag[atom1] - iatom - 1;
|
|
btype = onemols[imol]->bond_type[iatom][i];
|
|
atom2 = atom->map(onemols[imol]->bond_atom[iatom][i]+tagprev);
|
|
}
|
|
|
|
if (atom2 < 0 || !(mask[atom2] & groupbit)) continue;
|
|
if (newton_bond == 0 && tag[atom1] > tag[atom2]) continue;
|
|
if (btype <= 0) continue;
|
|
|
|
dx = x[atom2][0] - x[atom1][0];
|
|
dy = x[atom2][1] - x[atom1][1];
|
|
dz = x[atom2][2] - x[atom1][2];
|
|
domain->minimum_image(dx,dy,dz);
|
|
rsq = dx*dx + dy*dy + dz*dz;
|
|
rij[0] = dx;
|
|
rij[1] = dy;
|
|
rij[2] = dz;
|
|
r2inv = 1.0/rsq;
|
|
rinv = sqrt(r2inv);
|
|
|
|
pair_pref = 0.0;
|
|
dupair = 0.0;
|
|
du2pair = 0.0;
|
|
bond->born_matrix(btype,rsq,atom1,atom2,dupair,du2pair);
|
|
pair_pref = du2pair - dupair*rinv;
|
|
|
|
a = 0;
|
|
b = 0;
|
|
c = 0;
|
|
d = 0;
|
|
for (i = 0; i<21; i++) {
|
|
a = albemunu[i][0];
|
|
b = albemunu[i][1];
|
|
c = albemunu[i][2];
|
|
d = albemunu[i][3];
|
|
values_local[m+i] += pair_pref*rij[a]*rij[b]*rij[c]*rij[d]*r2inv;
|
|
}
|
|
}
|
|
}
|
|
m += 21;
|
|
}
|
|
}
|
|
|
|
/* ----------------------------------------------------------------------
|
|
count angles and compute angle info on this proc
|
|
only count if 2nd atom is the one storing the angle
|
|
all atoms in interaction must be in group
|
|
all atoms in interaction must be known to proc
|
|
if bond is deleted or turned off (type <= 0)
|
|
do not count or count contribution
|
|
---------------------------------------------------------------------- */
|
|
void ComputeBornMatrix::compute_angles()
|
|
{
|
|
int i,m,n,na,atom1,atom2,atom3,imol,iatom,atype,ivar;
|
|
tagint tagprev;
|
|
double delx1,dely1,delz1,delx2,dely2,delz2;
|
|
double rsq1,rsq2,r1,r2,cost;
|
|
double r1r2, r1r2inv;
|
|
double rsq1inv,rsq2inv,r1inv,r2inv,cinv;
|
|
double *ptr;
|
|
|
|
double **x = atom->x;
|
|
tagint *tag = atom->tag;
|
|
int *num_angle = atom->num_angle;
|
|
tagint **angle_atom1 = atom->angle_atom1;
|
|
tagint **angle_atom2 = atom->angle_atom2;
|
|
tagint **angle_atom3 = atom->angle_atom3;
|
|
int **angle_type = atom->angle_type;
|
|
int *mask = atom->mask;
|
|
|
|
int *molindex = atom->molindex;
|
|
int *molatom = atom->molatom;
|
|
Molecule **onemols = atom->avec->onemols;
|
|
|
|
int nlocal = atom->nlocal;
|
|
int molecular = atom->molecular;
|
|
|
|
// loop over all atoms and their angles
|
|
|
|
Angle *angle = force->angle;
|
|
|
|
int a,b,c,d,e,f;
|
|
double duang, du2ang;
|
|
double del1[3], del2[3];
|
|
double dcos[6];
|
|
double d2cos[21];
|
|
double d2lncos[21];
|
|
|
|
// Initializing array for intermediate cos derivatives
|
|
// w regard to strain
|
|
for (i = 0; i < 6; i++) {
|
|
dcos[i] = 0;
|
|
}
|
|
for (i = 0; i < 21; i++) {
|
|
d2cos[i] = 0;
|
|
d2lncos[i] = 0;
|
|
}
|
|
|
|
m = 0;
|
|
while (m < nvalues) {
|
|
for (atom2 = 0; atom2 < nlocal; atom2++) {
|
|
if (!(mask[atom2] & groupbit)) continue;
|
|
|
|
if (molecular == 1) na = num_angle[atom2];
|
|
else {
|
|
if (molindex[atom2] < 0) continue;
|
|
imol = molindex[atom2];
|
|
iatom = molatom[atom2];
|
|
na = onemols[imol]->num_angle[iatom];
|
|
}
|
|
|
|
for (i = 0; i < na; i++) {
|
|
if (molecular == 1) {
|
|
if (tag[atom2] != angle_atom2[atom2][i]) continue;
|
|
atype = angle_type[atom2][i];
|
|
atom1 = atom->map(angle_atom1[atom2][i]);
|
|
atom3 = atom->map(angle_atom3[atom2][i]);
|
|
} else {
|
|
if (tag[atom2] != onemols[imol]->angle_atom2[atom2][i]) continue;
|
|
atype = onemols[imol]->angle_type[atom2][i];
|
|
tagprev = tag[atom2] - iatom - 1;
|
|
atom1 = atom->map(onemols[imol]->angle_atom1[atom2][i]+tagprev);
|
|
atom3 = atom->map(onemols[imol]->angle_atom3[atom2][i]+tagprev);
|
|
}
|
|
|
|
if (atom1 < 0 || !(mask[atom1] & groupbit)) continue;
|
|
if (atom3 < 0 || !(mask[atom3] & groupbit)) continue;
|
|
if (atype <= 0) continue;
|
|
|
|
delx1 = x[atom1][0] - x[atom2][0];
|
|
dely1 = x[atom1][1] - x[atom2][1];
|
|
delz1 = x[atom1][2] - x[atom2][2];
|
|
domain->minimum_image(delx1,dely1,delz1);
|
|
del1[0] = delx1;
|
|
del1[1] = dely1;
|
|
del1[2] = delz1;
|
|
|
|
rsq1 = delx1*delx1 + dely1*dely1 + delz1*delz1;
|
|
rsq1inv = 1.0/rsq1;
|
|
r1 = sqrt(rsq1);
|
|
r1inv = 1.0/r1;
|
|
|
|
delx2 = x[atom3][0] - x[atom2][0];
|
|
dely2 = x[atom3][1] - x[atom2][1];
|
|
delz2 = x[atom3][2] - x[atom2][2];
|
|
domain->minimum_image(delx2,dely2,delz2);
|
|
del2[0] = delx2;
|
|
del2[1] = dely2;
|
|
del2[2] = delz2;
|
|
|
|
rsq2 = delx2*delx2 + dely2*dely2 + delz2*delz2;
|
|
rsq2inv = 1.0/rsq2;
|
|
r2 = sqrt(rsq2);
|
|
r2inv = 1.0/r2;
|
|
|
|
r1r2 = delx1*delx2 + dely1*dely2 + delz1*delz2;
|
|
r1r2inv = 1/r1r2;
|
|
// cost = cosine of angle
|
|
|
|
cost = delx1*delx2 + dely1*dely2 + delz1*delz2;
|
|
cost /= r1*r2;
|
|
if (cost > 1.0) cost = 1.0;
|
|
if (cost < -1.0) cost = -1.0;
|
|
cinv = 1.0/cost;
|
|
|
|
// The method must return derivative with regards
|
|
// to cos(theta)!
|
|
// Use the chain rule if needed:
|
|
// dU(t)/de = dt/dcos(t)*dU(t)/dt*dcos(t)/de
|
|
// with dt/dcos(t) = -1/sin(t)
|
|
angle->born_matrix(atype,atom1,atom2,atom3,duang,du2ang);
|
|
|
|
// Voigt notation
|
|
// 1 = 11, 2 = 22, 3 = 33
|
|
// 4 = 23, 5 = 13, 6 = 12
|
|
a = 0;
|
|
b = 0;
|
|
c = 0;
|
|
d = 0;
|
|
for (i = 0; i<6; i++) {
|
|
a = sigma_albe[i][0];
|
|
b = sigma_albe[i][1];
|
|
dcos[i] = cost*(del1[a]*del2[b]+del1[b]*del2[a]*r1r2inv -
|
|
del1[a]*del1[b]*rsq1inv - del2[a]*del2[b]*rsq2inv);
|
|
}
|
|
for (i = 0; i<21; i++) {
|
|
a = albemunu[i][0];
|
|
b = albemunu[i][1];
|
|
c = albemunu[i][2];
|
|
d = albemunu[i][3];
|
|
e = C_albe[i][0];
|
|
f = C_albe[i][1];
|
|
d2lncos[i] = 2*(del1[a]*del1[b]*del1[c]*del1[d]*rsq1inv*rsq1inv +
|
|
del2[a]*del2[b]*del2[c]*del2[d]*rsq2inv*rsq2inv) -
|
|
(del1[a]*del2[b]+del1[b]*del2[a]) *
|
|
(del1[c]*del2[d]+del1[d]*del2[c]) *
|
|
r1r2inv*r1r2inv;
|
|
d2cos[i] = cost*d2lncos[i] + dcos[e]*dcos[f]*cinv;
|
|
values_local[m+i] += duang*d2cos[i] + du2ang*dcos[e]*dcos[f];
|
|
}
|
|
}
|
|
}
|
|
m+=21;
|
|
}
|
|
}
|
|
|
|
/* ----------------------------------------------------------------------
|
|
count dihedrals on this proc
|
|
only count if 2nd atom is the one storing the dihedral
|
|
all atoms in interaction must be in group
|
|
all atoms in interaction must be known to proc
|
|
if flag is set, compute requested info about dihedral
|
|
------------------------------------------------------------------------- */
|
|
|
|
void ComputeBornMatrix::compute_dihedrals()
|
|
{
|
|
int i,m,n,nd,atom1,atom2,atom3,atom4,imol,iatom,dtype,ivar;
|
|
tagint tagprev;
|
|
double vb1x,vb1y,vb1z,vb2x,vb2y,vb2z,vb3x,vb3y,vb3z,vb2xm,vb2ym,vb2zm;
|
|
double ax,ay,az,bx,by,bz,rasq,rbsq,rgsq,rg,ra2inv,rb2inv,rabinv;
|
|
double si,co,phi;
|
|
double *ptr;
|
|
|
|
double **x = atom->x;
|
|
tagint *tag = atom->tag;
|
|
int *num_dihedral = atom->num_dihedral;
|
|
tagint **dihedral_atom1 = atom->dihedral_atom1;
|
|
tagint **dihedral_atom2 = atom->dihedral_atom2;
|
|
tagint **dihedral_atom3 = atom->dihedral_atom3;
|
|
tagint **dihedral_atom4 = atom->dihedral_atom4;
|
|
int *mask = atom->mask;
|
|
|
|
int *molindex = atom->molindex;
|
|
int *molatom = atom->molatom;
|
|
Molecule **onemols = atom->avec->onemols;
|
|
|
|
int nlocal = atom->nlocal;
|
|
int molecular = atom->molecular;
|
|
|
|
// loop over all atoms and their dihedrals
|
|
|
|
Dihedral *dihedral = force->dihedral;
|
|
|
|
double dudih,du2dih;
|
|
int a,b,c,d,e,f;
|
|
double b1sq;
|
|
double b2sq;
|
|
double b3sq;
|
|
double b1b2;
|
|
double b1b3;
|
|
double b2b3;
|
|
double b1[3];
|
|
double b2[3];
|
|
double b3[3];
|
|
|
|
// Actually derivatives of the square of the
|
|
// vectors dot product.
|
|
double dmn[6];
|
|
double dmm[6];
|
|
double dnn[6];
|
|
double d2mn[21];
|
|
double d2mm[21];
|
|
double d2nn[21];
|
|
|
|
double dcos[6];
|
|
double d2cos[21];
|
|
|
|
for (i = 0; i < 6; i++) {
|
|
dmn[i] =0;
|
|
dmm[i] = 0;
|
|
dnn[i] = 0;
|
|
dcos[i] = 0;
|
|
}
|
|
for (i = 0; i < 21; i++) {
|
|
d2mn[i] = 0;
|
|
d2mm[i] = 0;
|
|
d2nn[i] = 0;
|
|
d2cos[i] = 0;
|
|
}
|
|
|
|
m = 0;
|
|
while (m < nvalues) {
|
|
for (atom2 = 0; atom2 < nlocal; atom2++) {
|
|
if (!(mask[atom2] & groupbit)) continue;
|
|
|
|
if (molecular == 1) nd = num_dihedral[atom2];
|
|
else {
|
|
if (molindex[atom2] < 0) continue;
|
|
imol = molindex[atom2];
|
|
iatom = molatom[atom2];
|
|
nd = onemols[imol]->num_dihedral[iatom];
|
|
}
|
|
|
|
for (i = 0; i < nd; i++) {
|
|
if (molecular == 1) {
|
|
if (tag[atom2] != dihedral_atom2[atom2][i]) continue;
|
|
atom1 = atom->map(dihedral_atom1[atom2][i]);
|
|
atom3 = atom->map(dihedral_atom3[atom2][i]);
|
|
atom4 = atom->map(dihedral_atom4[atom2][i]);
|
|
} else {
|
|
if (tag[atom2] != onemols[imol]->dihedral_atom2[atom2][i]) continue;
|
|
tagprev = tag[atom2] - iatom - 1;
|
|
atom1 = atom->map(onemols[imol]->dihedral_atom1[atom2][i]+tagprev);
|
|
atom3 = atom->map(onemols[imol]->dihedral_atom3[atom2][i]+tagprev);
|
|
atom4 = atom->map(onemols[imol]->dihedral_atom4[atom2][i]+tagprev);
|
|
}
|
|
|
|
if (atom1 < 0 || !(mask[atom1] & groupbit)) continue;
|
|
if (atom3 < 0 || !(mask[atom3] & groupbit)) continue;
|
|
if (atom4 < 0 || !(mask[atom4] & groupbit)) continue;
|
|
|
|
// phi calculation from dihedral style harmonic
|
|
|
|
// The method must return derivative with regards
|
|
// to cos(phi)!
|
|
// Use the chain rule if needed:
|
|
// dU(t)/de = dt/dcos(t)*dU(t)/dt*dcos(t)/de
|
|
// with dt/dcos(t) = -1/sin(t)
|
|
|
|
dihedral->born_matrix(nd,atom1,atom2,atom3,atom4,dudih,du2dih);
|
|
|
|
vb1x = x[atom1][0] - x[atom2][0];
|
|
vb1y = x[atom1][1] - x[atom2][1];
|
|
vb1z = x[atom1][2] - x[atom2][2];
|
|
domain->minimum_image(vb1x,vb1y,vb1z);
|
|
b1[0] = vb1x;
|
|
b1[1] = vb1y;
|
|
b1[2] = vb1z;
|
|
b1sq = b1[0]*b1[0]+b1[1]*b1[1]+b1[2]*b1[2];
|
|
|
|
vb2x = x[atom3][0] - x[atom2][0];
|
|
vb2y = x[atom3][1] - x[atom2][1];
|
|
vb2z = x[atom3][2] - x[atom2][2];
|
|
domain->minimum_image(vb2x,vb2y,vb2z);
|
|
b2[0] = vb2x;
|
|
b2[1] = vb2y;
|
|
b2[2] = vb2z;
|
|
b2sq = b2[0]*b2[0]+b2[1]*b2[1]+b2[2]*b2[2];
|
|
|
|
vb2xm = -vb2x;
|
|
vb2ym = -vb2y;
|
|
vb2zm = -vb2z;
|
|
domain->minimum_image(vb2xm,vb2ym,vb2zm);
|
|
|
|
vb3x = x[atom4][0] - x[atom3][0];
|
|
vb3y = x[atom4][1] - x[atom3][1];
|
|
vb3z = x[atom4][2] - x[atom3][2];
|
|
domain->minimum_image(vb3x,vb3y,vb3z);
|
|
b3[0] = vb3x;
|
|
b3[1] = vb3y;
|
|
b3[2] = vb3z;
|
|
b3sq = b3[0]*b3[0]+b3[1]*b3[1]+b3[2]*b3[2];
|
|
|
|
b1b2 = b1[0]*b2[0]+b1[1]*b2[1]+b1[2]*b2[2];
|
|
b1b3 = b1[0]*b3[0]+b1[1]*b3[1]+b1[2]*b3[2];
|
|
b2b3 = b2[0]*b3[0]+b2[1]*b3[1]+b2[2]*b3[2];
|
|
|
|
ax = vb1y*vb2zm - vb1z*vb2ym;
|
|
ay = vb1z*vb2xm - vb1x*vb2zm;
|
|
az = vb1x*vb2ym - vb1y*vb2xm;
|
|
bx = vb3y*vb2zm - vb3z*vb2ym;
|
|
by = vb3z*vb2xm - vb3x*vb2zm;
|
|
bz = vb3x*vb2ym - vb3y*vb2xm;
|
|
|
|
rasq = ax*ax + ay*ay + az*az;
|
|
rbsq = bx*bx + by*by + bz*bz;
|
|
rgsq = vb2xm*vb2xm + vb2ym*vb2ym + vb2zm*vb2zm;
|
|
rg = sqrt(rgsq);
|
|
|
|
ra2inv = rb2inv = 0.0;
|
|
if (rasq > 0) ra2inv = 1.0/rasq;
|
|
if (rbsq > 0) rb2inv = 1.0/rbsq;
|
|
rabinv = sqrt(ra2inv*rb2inv);
|
|
|
|
co = (ax*bx + ay*by + az*bz)*rabinv;
|
|
si = rg*rabinv*(ax*vb3x + ay*vb3y + az*vb3z);
|
|
|
|
if (co > 1.0) co = 1.0;
|
|
if (co < -1.0) co = -1.0;
|
|
phi = atan2(si,co);
|
|
|
|
// above a and b are m and n vectors
|
|
// here they are integers indices
|
|
a = 0;
|
|
b = 0;
|
|
c = 0;
|
|
d = 0;
|
|
e = 0;
|
|
f = 0;
|
|
for (i = 0; i<6; i++) {
|
|
a = sigma_albe[i][0];
|
|
b = sigma_albe[i][1];
|
|
dmm[i] = 2*(b2sq*b1[a]*b1[b]+b1sq*b2[a]*b2[b] - b1b2*(b1[a]*b2[b]+b1[b]*b2[a]));
|
|
dnn[i] = 2*(b3sq*b2[a]*b2[b]+b2sq*b3[a]*b3[b] - b2b3*(b2[a]*b3[b]+b2[b]*b3[a]));
|
|
dmn[i] = b1b2*(b2[a]*b3[b]+b2[b]*b3[a]) + b2b3*(b1[a]*b2[b]+b1[b]*b2[a])
|
|
- 2*(b1b3*b2[a]*b2[b]) - b2sq*(b1[a]*b3[b]+b1[b]*b3[a]);
|
|
dcos[i] = co*(rabinv*rabinv*dmn[i] - ra2inv*dmm[i] - rb2inv*dnn[i])/2.;
|
|
}
|
|
for (i = 0; i<21; i++) {
|
|
a = albemunu[i][0];
|
|
b = albemunu[i][1];
|
|
c = albemunu[i][2];
|
|
d = albemunu[i][3];
|
|
e = C_albe[i][0];
|
|
f = C_albe[i][1];
|
|
d2mm[i] = 4*(b1[a]*b1[b]*b2[c]*b2[d] + b1[c]*b1[d]*b2[a]*b2[b])
|
|
- 8*(b1[a]*b2[b]+b1[b]*b2[a])*(b1[c]*b2[d]+b1[d]*b2[c]);
|
|
d2nn[i] = 4*(b2[a]*b2[b]*b3[c]*b3[d] + b2[c]*b2[d]*b3[a]*b3[b])
|
|
- 8*(b2[a]*b3[b]+b2[b]*b3[a])*(b2[c]*b3[d]+b2[d]*b3[c]);
|
|
d2mn[i] = (b1[a]*b2[b]+b1[b]*b2[a])*(b2[c]*b3[d]+b2[d]*b3[c])
|
|
+ (b2[a]*b3[b]+b2[b]*b3[a])*(b1[c]*b2[d]+b1[d]*b2[d])
|
|
- (b1[a]*b3[b]+b1[b]*b3[a])*(b2[c]*b2[d]+b2[c]*b2[d])
|
|
- (b1[c]*b3[d]+b1[d]*b3[c])*(b2[a]*b2[b]+b2[a]*b2[b]);
|
|
d2cos[i] = co/2.*(
|
|
rabinv*rabinv*d2mn[i]
|
|
- rabinv*rabinv*rabinv*rabinv*dmn[e]*dmn[f]
|
|
+ ra2inv*ra2inv*dmm[e]*dmm[f]
|
|
- ra2inv*d2mm[i]
|
|
+ rb2inv*rb2inv*dnn[e]*dnn[f]
|
|
- rb2inv*d2nn[i]);
|
|
values_local[m+i] += dudih*d2cos[i] + du2dih*dcos[e]*dcos[f];
|
|
}
|
|
}
|
|
}
|
|
m+=21;
|
|
}
|
|
}
|