| 1 |
module eam |
| 2 |
use definitions, ONLY : DP,default_error |
| 3 |
use simulation |
| 4 |
use force_globals |
| 5 |
use status |
| 6 |
use atype_module |
| 7 |
use Vector_class |
| 8 |
#ifdef IS_MPI |
| 9 |
use mpiSimulation |
| 10 |
#endif |
| 11 |
implicit none |
| 12 |
PRIVATE |
| 13 |
|
| 14 |
|
| 15 |
logical, save :: EAM_FF_initialized = .false. |
| 16 |
integer, save :: EAM_Mixing_Policy |
| 17 |
real(kind = dp), save :: EAM_rcut |
| 18 |
logical, save :: haveRcut = .false. |
| 19 |
|
| 20 |
character(len = statusMsgSize) :: errMesg |
| 21 |
integer :: eam_err |
| 22 |
|
| 23 |
character(len = 200) :: errMsg |
| 24 |
character(len=*), parameter :: RoutineName = "EAM MODULE" |
| 25 |
!! Logical that determines if eam arrays should be zeroed |
| 26 |
logical :: cleanme = .true. |
| 27 |
logical :: nmflag = .false. |
| 28 |
|
| 29 |
|
| 30 |
type, private :: EAMtype |
| 31 |
integer :: eam_atype |
| 32 |
real( kind = DP ) :: eam_dr |
| 33 |
integer :: eam_nr |
| 34 |
integer :: eam_nrho |
| 35 |
real( kind = DP ) :: eam_lattice |
| 36 |
real( kind = DP ) :: eam_drho |
| 37 |
real( kind = DP ) :: eam_rcut |
| 38 |
integer :: eam_atype_map |
| 39 |
|
| 40 |
real( kind = DP ), pointer, dimension(:) :: eam_rvals => null() |
| 41 |
real( kind = DP ), pointer, dimension(:) :: eam_rhovals => null() |
| 42 |
real( kind = DP ), pointer, dimension(:) :: eam_F_rho => null() |
| 43 |
real( kind = DP ), pointer, dimension(:) :: eam_Z_r => null() |
| 44 |
real( kind = DP ), pointer, dimension(:) :: eam_rho_r => null() |
| 45 |
real( kind = DP ), pointer, dimension(:) :: eam_phi_r => null() |
| 46 |
real( kind = DP ), pointer, dimension(:) :: eam_F_rho_pp => null() |
| 47 |
real( kind = DP ), pointer, dimension(:) :: eam_Z_r_pp => null() |
| 48 |
real( kind = DP ), pointer, dimension(:) :: eam_rho_r_pp => null() |
| 49 |
real( kind = DP ), pointer, dimension(:) :: eam_phi_r_pp => null() |
| 50 |
end type EAMtype |
| 51 |
|
| 52 |
|
| 53 |
!! Arrays for derivatives used in force calculation |
| 54 |
real( kind = dp), dimension(:), allocatable :: frho |
| 55 |
real( kind = dp), dimension(:), allocatable :: rho |
| 56 |
|
| 57 |
real( kind = dp), dimension(:), allocatable :: dfrhodrho |
| 58 |
real( kind = dp), dimension(:), allocatable :: d2frhodrhodrho |
| 59 |
|
| 60 |
|
| 61 |
!! Arrays for MPI storage |
| 62 |
#ifdef IS_MPI |
| 63 |
real( kind = dp),save, dimension(:), allocatable :: dfrhodrho_col |
| 64 |
real( kind = dp),save, dimension(:), allocatable :: dfrhodrho_row |
| 65 |
real( kind = dp),save, dimension(:), allocatable :: frho_row |
| 66 |
real( kind = dp),save, dimension(:), allocatable :: frho_col |
| 67 |
real( kind = dp),save, dimension(:), allocatable :: rho_row |
| 68 |
real( kind = dp),save, dimension(:), allocatable :: rho_col |
| 69 |
real( kind = dp),save, dimension(:), allocatable :: rho_tmp |
| 70 |
real( kind = dp),save, dimension(:), allocatable :: d2frhodrhodrho_col |
| 71 |
real( kind = dp),save, dimension(:), allocatable :: d2frhodrhodrho_row |
| 72 |
#endif |
| 73 |
|
| 74 |
type, private :: EAMTypeList |
| 75 |
integer :: n_eam_types = 0 |
| 76 |
integer :: currentAddition = 0 |
| 77 |
|
| 78 |
type (EAMtype), pointer :: EAMParams(:) => null() |
| 79 |
end type EAMTypeList |
| 80 |
|
| 81 |
|
| 82 |
type (eamTypeList), save :: EAMList |
| 83 |
|
| 84 |
!! standard eam stuff |
| 85 |
|
| 86 |
|
| 87 |
public :: init_EAM_FF |
| 88 |
public :: setCutoffEAM |
| 89 |
public :: do_eam_pair |
| 90 |
public :: newEAMtype |
| 91 |
public :: calc_eam_prepair_rho |
| 92 |
public :: calc_eam_preforce_Frho |
| 93 |
public :: clean_EAM |
| 94 |
|
| 95 |
contains |
| 96 |
|
| 97 |
|
| 98 |
subroutine newEAMtype(lattice_constant,eam_nrho,eam_drho,eam_nr,& |
| 99 |
eam_dr,rcut,eam_Z_r,eam_rho_r,eam_F_rho,& |
| 100 |
eam_ident,status) |
| 101 |
real (kind = dp ) :: lattice_constant |
| 102 |
integer :: eam_nrho |
| 103 |
real (kind = dp ) :: eam_drho |
| 104 |
integer :: eam_nr |
| 105 |
real (kind = dp ) :: eam_dr |
| 106 |
real (kind = dp ) :: rcut |
| 107 |
real (kind = dp ), dimension(eam_nr) :: eam_Z_r |
| 108 |
real (kind = dp ), dimension(eam_nr) :: eam_rho_r |
| 109 |
real (kind = dp ), dimension(eam_nrho) :: eam_F_rho |
| 110 |
integer :: eam_ident |
| 111 |
integer :: status |
| 112 |
|
| 113 |
integer :: nAtypes |
| 114 |
integer :: maxVals |
| 115 |
integer :: alloc_stat |
| 116 |
integer :: current |
| 117 |
integer,pointer :: Matchlist(:) => null() |
| 118 |
|
| 119 |
status = 0 |
| 120 |
|
| 121 |
|
| 122 |
!! Assume that atypes has already been set and get the total number of types in atypes |
| 123 |
!! Also assume that every member of atypes is a EAM model. |
| 124 |
|
| 125 |
|
| 126 |
! check to see if this is the first time into |
| 127 |
if (.not.associated(EAMList%EAMParams)) then |
| 128 |
call getMatchingElementList(atypes, "is_EAM", .true., nAtypes, MatchList) |
| 129 |
EAMList%n_eam_types = nAtypes |
| 130 |
allocate(EAMList%EAMParams(nAtypes)) |
| 131 |
end if |
| 132 |
|
| 133 |
EAMList%currentAddition = EAMList%currentAddition + 1 |
| 134 |
current = EAMList%currentAddition |
| 135 |
|
| 136 |
|
| 137 |
call allocate_EAMType(eam_nrho,eam_nr,EAMList%EAMParams(current),stat=alloc_stat) |
| 138 |
if (alloc_stat /= 0) then |
| 139 |
status = -1 |
| 140 |
return |
| 141 |
end if |
| 142 |
|
| 143 |
! this is a possible bug, we assume a correspondence between the vector atypes and |
| 144 |
! EAMAtypes |
| 145 |
|
| 146 |
EAMList%EAMParams(current)%eam_atype = eam_ident |
| 147 |
EAMList%EAMParams(current)%eam_lattice = lattice_constant |
| 148 |
EAMList%EAMParams(current)%eam_nrho = eam_nrho |
| 149 |
EAMList%EAMParams(current)%eam_drho = eam_drho |
| 150 |
EAMList%EAMParams(current)%eam_nr = eam_nr |
| 151 |
EAMList%EAMParams(current)%eam_dr = eam_dr |
| 152 |
EAMList%EAMParams(current)%eam_rcut = rcut |
| 153 |
EAMList%EAMParams(current)%eam_Z_r = eam_Z_r |
| 154 |
EAMList%EAMParams(current)%eam_rho_r = eam_rho_r |
| 155 |
EAMList%EAMParams(current)%eam_F_rho = eam_F_rho |
| 156 |
|
| 157 |
end subroutine newEAMtype |
| 158 |
|
| 159 |
|
| 160 |
|
| 161 |
subroutine init_EAM_FF(status) |
| 162 |
integer :: status |
| 163 |
integer :: i,j |
| 164 |
real(kind=dp) :: current_rcut_max |
| 165 |
integer :: alloc_stat |
| 166 |
integer :: number_r, number_rho |
| 167 |
|
| 168 |
|
| 169 |
status = 0 |
| 170 |
if (EAMList%currentAddition == 0) then |
| 171 |
call handleError("init_EAM_FF","No members in EAMList") |
| 172 |
status = -1 |
| 173 |
return |
| 174 |
end if |
| 175 |
|
| 176 |
|
| 177 |
do i = 1, EAMList%currentAddition |
| 178 |
|
| 179 |
! Build array of r values |
| 180 |
|
| 181 |
do j = 1,EAMList%EAMParams(i)%eam_nr |
| 182 |
EAMList%EAMParams(i)%eam_rvals(j) = & |
| 183 |
real(j-1,kind=dp)* & |
| 184 |
EAMList%EAMParams(i)%eam_dr |
| 185 |
end do |
| 186 |
! Build array of rho values |
| 187 |
do j = 1,EAMList%EAMParams(i)%eam_nrho |
| 188 |
EAMList%EAMParams(i)%eam_rhovals(j) = & |
| 189 |
real(j-1,kind=dp)* & |
| 190 |
EAMList%EAMParams(i)%eam_drho |
| 191 |
end do |
| 192 |
! convert from eV to kcal / mol: |
| 193 |
EAMList%EAMParams(i)%eam_F_rho = EAMList%EAMParams(i)%eam_F_rho * 23.06054E0_DP |
| 194 |
|
| 195 |
! precompute the pair potential and get it into kcal / mol: |
| 196 |
EAMList%EAMParams(i)%eam_phi_r(1) = 0.0E0_DP |
| 197 |
do j = 2, EAMList%EAMParams(i)%eam_nr |
| 198 |
EAMList%EAMParams(i)%eam_phi_r(j) = (EAMList%EAMParams(i)%eam_Z_r(j)**2)/EAMList%EAMParams(i)%eam_rvals(j) |
| 199 |
EAMList%EAMParams(i)%eam_phi_r(j) = EAMList%EAMParams(i)%eam_phi_r(j)*331.999296E0_DP |
| 200 |
enddo |
| 201 |
end do |
| 202 |
|
| 203 |
|
| 204 |
do i = 1, EAMList%currentAddition |
| 205 |
number_r = EAMList%EAMParams(i)%eam_nr |
| 206 |
number_rho = EAMList%EAMParams(i)%eam_nrho |
| 207 |
|
| 208 |
call eam_spline(number_r, EAMList%EAMParams(i)%eam_rvals, & |
| 209 |
EAMList%EAMParams(i)%eam_rho_r, & |
| 210 |
EAMList%EAMParams(i)%eam_rho_r_pp, & |
| 211 |
0.0E0_DP, 0.0E0_DP, 'N') |
| 212 |
call eam_spline(number_r, EAMList%EAMParams(i)%eam_rvals, & |
| 213 |
EAMList%EAMParams(i)%eam_Z_r, & |
| 214 |
EAMList%EAMParams(i)%eam_Z_r_pp, & |
| 215 |
0.0E0_DP, 0.0E0_DP, 'N') |
| 216 |
call eam_spline(number_rho, EAMList%EAMParams(i)%eam_rhovals, & |
| 217 |
EAMList%EAMParams(i)%eam_F_rho, & |
| 218 |
EAMList%EAMParams(i)%eam_F_rho_pp, & |
| 219 |
0.0E0_DP, 0.0E0_DP, 'N') |
| 220 |
call eam_spline(number_r, EAMList%EAMParams(i)%eam_rvals, & |
| 221 |
EAMList%EAMParams(i)%eam_phi_r, & |
| 222 |
EAMList%EAMParams(i)%eam_phi_r_pp, & |
| 223 |
0.0E0_DP, 0.0E0_DP, 'N') |
| 224 |
enddo |
| 225 |
|
| 226 |
! current_rcut_max = EAMList%EAMParams(1)%eam_rcut |
| 227 |
!! find the smallest rcut for any eam atype |
| 228 |
! do i = 2, EAMList%currentAddition |
| 229 |
! current_rcut_max =max(current_rcut_max,EAMList%EAMParams(i)%eam_rcut) |
| 230 |
! end do |
| 231 |
|
| 232 |
! EAM_rcut = current_rcut_max |
| 233 |
! EAM_rcut_orig = current_rcut_max |
| 234 |
! do i = 1, EAMList%currentAddition |
| 235 |
! EAMList%EAMParam(i)s%eam_atype_map(eam_atype(i)) = i |
| 236 |
! end do |
| 237 |
!! Allocate arrays for force calculation |
| 238 |
|
| 239 |
call allocateEAM(alloc_stat) |
| 240 |
if (alloc_stat /= 0 ) then |
| 241 |
write(*,*) "allocateEAM failed" |
| 242 |
status = -1 |
| 243 |
return |
| 244 |
endif |
| 245 |
|
| 246 |
end subroutine init_EAM_FF |
| 247 |
|
| 248 |
!! routine checks to see if array is allocated, deallocates array if allocated |
| 249 |
!! and then creates the array to the required size |
| 250 |
subroutine allocateEAM(status) |
| 251 |
integer, intent(out) :: status |
| 252 |
|
| 253 |
#ifdef IS_MPI |
| 254 |
integer :: nrow |
| 255 |
integer :: ncol |
| 256 |
#endif |
| 257 |
integer :: alloc_stat |
| 258 |
|
| 259 |
|
| 260 |
status = 0 |
| 261 |
#ifdef IS_MPI |
| 262 |
nrow = getNrow(plan_row) |
| 263 |
ncol = getNcol(plan_col) |
| 264 |
#endif |
| 265 |
|
| 266 |
if (allocated(frho)) deallocate(frho) |
| 267 |
allocate(frho(nlocal),stat=alloc_stat) |
| 268 |
if (alloc_stat /= 0) then |
| 269 |
status = -1 |
| 270 |
return |
| 271 |
end if |
| 272 |
if (allocated(rho)) deallocate(rho) |
| 273 |
allocate(rho(nlocal),stat=alloc_stat) |
| 274 |
if (alloc_stat /= 0) then |
| 275 |
status = -1 |
| 276 |
return |
| 277 |
end if |
| 278 |
|
| 279 |
if (allocated(dfrhodrho)) deallocate(dfrhodrho) |
| 280 |
allocate(dfrhodrho(nlocal),stat=alloc_stat) |
| 281 |
if (alloc_stat /= 0) then |
| 282 |
status = -1 |
| 283 |
return |
| 284 |
end if |
| 285 |
|
| 286 |
if (allocated(d2frhodrhodrho)) deallocate(d2frhodrhodrho) |
| 287 |
allocate(d2frhodrhodrho(nlocal),stat=alloc_stat) |
| 288 |
if (alloc_stat /= 0) then |
| 289 |
status = -1 |
| 290 |
return |
| 291 |
end if |
| 292 |
|
| 293 |
#ifdef IS_MPI |
| 294 |
|
| 295 |
if (allocated(rho_tmp)) deallocate(rho_tmp) |
| 296 |
allocate(rho_tmp(nlocal),stat=alloc_stat) |
| 297 |
if (alloc_stat /= 0) then |
| 298 |
status = -1 |
| 299 |
return |
| 300 |
end if |
| 301 |
|
| 302 |
|
| 303 |
if (allocated(frho_row)) deallocate(frho_row) |
| 304 |
allocate(frho_row(nrow),stat=alloc_stat) |
| 305 |
if (alloc_stat /= 0) then |
| 306 |
status = -1 |
| 307 |
return |
| 308 |
end if |
| 309 |
if (allocated(rho_row)) deallocate(rho_row) |
| 310 |
allocate(rho_row(nrow),stat=alloc_stat) |
| 311 |
if (alloc_stat /= 0) then |
| 312 |
status = -1 |
| 313 |
return |
| 314 |
end if |
| 315 |
if (allocated(dfrhodrho_row)) deallocate(dfrhodrho_row) |
| 316 |
allocate(dfrhodrho_row(nrow),stat=alloc_stat) |
| 317 |
if (alloc_stat /= 0) then |
| 318 |
status = -1 |
| 319 |
return |
| 320 |
end if |
| 321 |
if (allocated(d2frhodrhodrho_row)) deallocate(d2frhodrhodrho_row) |
| 322 |
allocate(d2frhodrhodrho_row(nrow),stat=alloc_stat) |
| 323 |
if (alloc_stat /= 0) then |
| 324 |
status = -1 |
| 325 |
return |
| 326 |
end if |
| 327 |
|
| 328 |
|
| 329 |
! Now do column arrays |
| 330 |
|
| 331 |
if (allocated(frho_col)) deallocate(frho_col) |
| 332 |
allocate(frho_col(ncol),stat=alloc_stat) |
| 333 |
if (alloc_stat /= 0) then |
| 334 |
status = -1 |
| 335 |
return |
| 336 |
end if |
| 337 |
if (allocated(rho_col)) deallocate(rho_col) |
| 338 |
allocate(rho_col(ncol),stat=alloc_stat) |
| 339 |
if (alloc_stat /= 0) then |
| 340 |
status = -1 |
| 341 |
return |
| 342 |
end if |
| 343 |
if (allocated(dfrhodrho_col)) deallocate(dfrhodrho_col) |
| 344 |
allocate(dfrhodrho_col(ncol),stat=alloc_stat) |
| 345 |
if (alloc_stat /= 0) then |
| 346 |
status = -1 |
| 347 |
return |
| 348 |
end if |
| 349 |
if (allocated(d2frhodrhodrho_col)) deallocate(d2frhodrhodrho_col) |
| 350 |
allocate(d2frhodrhodrho_col(ncol),stat=alloc_stat) |
| 351 |
if (alloc_stat /= 0) then |
| 352 |
status = -1 |
| 353 |
return |
| 354 |
end if |
| 355 |
|
| 356 |
#endif |
| 357 |
|
| 358 |
end subroutine allocateEAM |
| 359 |
|
| 360 |
!! C sets rcut to be the largest cutoff of any atype |
| 361 |
!! present in this simulation. Doesn't include all atypes |
| 362 |
!! sim knows about, just those in the simulation. |
| 363 |
subroutine setCutoffEAM(rcut, status) |
| 364 |
real(kind=dp) :: rcut |
| 365 |
integer :: status |
| 366 |
status = 0 |
| 367 |
|
| 368 |
EAM_rcut = rcut |
| 369 |
|
| 370 |
end subroutine setCutoffEAM |
| 371 |
|
| 372 |
|
| 373 |
|
| 374 |
subroutine clean_EAM() |
| 375 |
|
| 376 |
! clean non-IS_MPI first |
| 377 |
frho = 0.0_dp |
| 378 |
rho = 0.0_dp |
| 379 |
dfrhodrho = 0.0_dp |
| 380 |
! clean MPI if needed |
| 381 |
#ifdef IS_MPI |
| 382 |
frho_row = 0.0_dp |
| 383 |
frho_col = 0.0_dp |
| 384 |
rho_row = 0.0_dp |
| 385 |
rho_col = 0.0_dp |
| 386 |
rho_tmp = 0.0_dp |
| 387 |
dfrhodrho_row = 0.0_dp |
| 388 |
dfrhodrho_col = 0.0_dp |
| 389 |
#endif |
| 390 |
end subroutine clean_EAM |
| 391 |
|
| 392 |
|
| 393 |
|
| 394 |
subroutine allocate_EAMType(eam_n_rho,eam_n_r,thisEAMType,stat) |
| 395 |
integer, intent(in) :: eam_n_rho |
| 396 |
integer, intent(in) :: eam_n_r |
| 397 |
type (EAMType) :: thisEAMType |
| 398 |
integer, optional :: stat |
| 399 |
integer :: alloc_stat |
| 400 |
|
| 401 |
|
| 402 |
|
| 403 |
if (present(stat)) stat = 0 |
| 404 |
|
| 405 |
allocate(thisEAMType%eam_rvals(eam_n_r),stat=alloc_stat) |
| 406 |
if (alloc_stat /= 0 ) then |
| 407 |
if (present(stat)) stat = -1 |
| 408 |
return |
| 409 |
end if |
| 410 |
allocate(thisEAMType%eam_rhovals(eam_n_rho),stat=alloc_stat) |
| 411 |
if (alloc_stat /= 0 ) then |
| 412 |
if (present(stat)) stat = -1 |
| 413 |
return |
| 414 |
end if |
| 415 |
allocate(thisEAMType%eam_F_rho(eam_n_rho),stat=alloc_stat) |
| 416 |
if (alloc_stat /= 0 ) then |
| 417 |
if (present(stat)) stat = -1 |
| 418 |
return |
| 419 |
end if |
| 420 |
allocate(thisEAMType%eam_Z_r(eam_n_r),stat=alloc_stat) |
| 421 |
if (alloc_stat /= 0 ) then |
| 422 |
if (present(stat)) stat = -1 |
| 423 |
return |
| 424 |
end if |
| 425 |
allocate(thisEAMType%eam_rho_r(eam_n_r),stat=alloc_stat) |
| 426 |
if (alloc_stat /= 0 ) then |
| 427 |
if (present(stat)) stat = -1 |
| 428 |
return |
| 429 |
end if |
| 430 |
allocate(thisEAMType%eam_phi_r(eam_n_r),stat=alloc_stat) |
| 431 |
if (alloc_stat /= 0 ) then |
| 432 |
if (present(stat)) stat = -1 |
| 433 |
return |
| 434 |
end if |
| 435 |
allocate(thisEAMType%eam_F_rho_pp(eam_n_rho),stat=alloc_stat) |
| 436 |
if (alloc_stat /= 0 ) then |
| 437 |
if (present(stat)) stat = -1 |
| 438 |
return |
| 439 |
end if |
| 440 |
allocate(thisEAMType%eam_Z_r_pp(eam_n_r),stat=alloc_stat) |
| 441 |
if (alloc_stat /= 0 ) then |
| 442 |
if (present(stat)) stat = -1 |
| 443 |
return |
| 444 |
end if |
| 445 |
allocate(thisEAMType%eam_rho_r_pp(eam_n_r),stat=alloc_stat) |
| 446 |
if (alloc_stat /= 0 ) then |
| 447 |
if (present(stat)) stat = -1 |
| 448 |
return |
| 449 |
end if |
| 450 |
allocate(thisEAMType%eam_phi_r_pp(eam_n_r),stat=alloc_stat) |
| 451 |
if (alloc_stat /= 0 ) then |
| 452 |
if (present(stat)) stat = -1 |
| 453 |
return |
| 454 |
end if |
| 455 |
|
| 456 |
|
| 457 |
end subroutine allocate_EAMType |
| 458 |
|
| 459 |
|
| 460 |
subroutine deallocate_EAMType(thisEAMType) |
| 461 |
type (EAMtype), pointer :: thisEAMType |
| 462 |
|
| 463 |
! free Arrays in reverse order of allocation... |
| 464 |
deallocate(thisEAMType%eam_phi_r_pp) |
| 465 |
deallocate(thisEAMType%eam_rho_r_pp) |
| 466 |
deallocate(thisEAMType%eam_Z_r_pp) |
| 467 |
deallocate(thisEAMType%eam_F_rho_pp) |
| 468 |
deallocate(thisEAMType%eam_phi_r) |
| 469 |
deallocate(thisEAMType%eam_rho_r) |
| 470 |
deallocate(thisEAMType%eam_Z_r) |
| 471 |
deallocate(thisEAMType%eam_F_rho) |
| 472 |
deallocate(thisEAMType%eam_rhovals) |
| 473 |
deallocate(thisEAMType%eam_rvals) |
| 474 |
|
| 475 |
end subroutine deallocate_EAMType |
| 476 |
|
| 477 |
!! Calculates rho_r |
| 478 |
subroutine calc_eam_prepair_rho(atom1,atom2,d,r,rijsq) |
| 479 |
integer :: atom1,atom2 |
| 480 |
real(kind = dp), dimension(3) :: d |
| 481 |
real(kind = dp), intent(inout) :: r |
| 482 |
real(kind = dp), intent(inout) :: rijsq |
| 483 |
! value of electron density rho do to atom i at atom j |
| 484 |
real(kind = dp) :: rho_i_at_j |
| 485 |
! value of electron density rho do to atom j at atom i |
| 486 |
real(kind = dp) :: rho_j_at_i |
| 487 |
|
| 488 |
! we don't use the derivatives, dummy variables |
| 489 |
real( kind = dp) :: drho,d2rho |
| 490 |
integer :: eam_err |
| 491 |
|
| 492 |
integer :: myid_atom1 |
| 493 |
integer :: myid_atom2 |
| 494 |
|
| 495 |
! check to see if we need to be cleaned at the start of a force loop |
| 496 |
|
| 497 |
|
| 498 |
|
| 499 |
|
| 500 |
#ifdef IS_MPI |
| 501 |
myid_atom1 = atid_Row(atom1) |
| 502 |
myid_atom2 = atid_Col(atom2) |
| 503 |
#else |
| 504 |
myid_atom1 = atid(atom1) |
| 505 |
myid_atom2 = atid(atom2) |
| 506 |
#endif |
| 507 |
|
| 508 |
if (r.lt.EAMList%EAMParams(myid_atom1)%eam_rcut) then |
| 509 |
|
| 510 |
|
| 511 |
|
| 512 |
call eam_splint(EAMList%EAMParams(myid_atom1)%eam_nr, & |
| 513 |
EAMList%EAMParams(myid_atom1)%eam_rvals, & |
| 514 |
EAMList%EAMParams(myid_atom1)%eam_rho_r, & |
| 515 |
EAMList%EAMParams(myid_atom1)%eam_rho_r_pp, & |
| 516 |
r, rho_i_at_j,drho,d2rho) |
| 517 |
|
| 518 |
|
| 519 |
|
| 520 |
#ifdef IS_MPI |
| 521 |
rho_col(atom2) = rho_col(atom2) + rho_i_at_j |
| 522 |
#else |
| 523 |
rho(atom2) = rho(atom2) + rho_i_at_j |
| 524 |
#endif |
| 525 |
! write(*,*) atom1,atom2,r,rho_i_at_j |
| 526 |
endif |
| 527 |
|
| 528 |
if (r.lt.EAMList%EAMParams(myid_atom2)%eam_rcut) then |
| 529 |
call eam_splint(EAMList%EAMParams(myid_atom2)%eam_nr, & |
| 530 |
EAMList%EAMParams(myid_atom2)%eam_rvals, & |
| 531 |
EAMList%EAMParams(myid_atom2)%eam_rho_r, & |
| 532 |
EAMList%EAMParams(myid_atom2)%eam_rho_r_pp, & |
| 533 |
r, rho_j_at_i,drho,d2rho) |
| 534 |
|
| 535 |
|
| 536 |
|
| 537 |
|
| 538 |
#ifdef IS_MPI |
| 539 |
rho_row(atom1) = rho_row(atom1) + rho_j_at_i |
| 540 |
#else |
| 541 |
rho(atom1) = rho(atom1) + rho_j_at_i |
| 542 |
#endif |
| 543 |
endif |
| 544 |
|
| 545 |
|
| 546 |
|
| 547 |
|
| 548 |
|
| 549 |
|
| 550 |
end subroutine calc_eam_prepair_rho |
| 551 |
|
| 552 |
|
| 553 |
|
| 554 |
|
| 555 |
!! Calculate the functional F(rho) for all local atoms |
| 556 |
subroutine calc_eam_preforce_Frho(nlocal,pot) |
| 557 |
integer :: nlocal |
| 558 |
real(kind=dp) :: pot |
| 559 |
integer :: i,j |
| 560 |
integer :: atom |
| 561 |
real(kind=dp) :: U,U1,U2 |
| 562 |
integer :: atype1 |
| 563 |
integer :: me |
| 564 |
integer :: n_rho_points |
| 565 |
|
| 566 |
|
| 567 |
cleanme = .true. |
| 568 |
!! Scatter the electron density from pre-pair calculation back to local atoms |
| 569 |
#ifdef IS_MPI |
| 570 |
call scatter(rho_row,rho,plan_row,eam_err) |
| 571 |
if (eam_err /= 0 ) then |
| 572 |
write(errMsg,*) " Error scattering rho_row into rho" |
| 573 |
call handleError(RoutineName,errMesg) |
| 574 |
endif |
| 575 |
call scatter(rho_col,rho_tmp,plan_col,eam_err) |
| 576 |
if (eam_err /= 0 ) then |
| 577 |
write(errMsg,*) " Error scattering rho_col into rho" |
| 578 |
call handleError(RoutineName,errMesg) |
| 579 |
endif |
| 580 |
|
| 581 |
rho(1:nlocal) = rho(1:nlocal) + rho_tmp(1:nlocal) |
| 582 |
#endif |
| 583 |
|
| 584 |
|
| 585 |
|
| 586 |
!! Calculate F(rho) and derivative |
| 587 |
do atom = 1, nlocal |
| 588 |
me = atid(atom) |
| 589 |
n_rho_points = EAMList%EAMParams(me)%eam_nrho |
| 590 |
! Check to see that the density is not greater than the larges rho we have calculated |
| 591 |
if (rho(atom) < EAMList%EAMParams(me)%eam_rhovals(n_rho_points)) then |
| 592 |
call eam_splint(n_rho_points, & |
| 593 |
EAMList%EAMParams(me)%eam_rhovals, & |
| 594 |
EAMList%EAMParams(me)%eam_f_rho, & |
| 595 |
EAMList%EAMParams(me)%eam_f_rho_pp, & |
| 596 |
rho(atom), & ! Actual Rho |
| 597 |
u, u1, u2) |
| 598 |
else |
| 599 |
! Calculate F(rho with the largest available rho value |
| 600 |
call eam_splint(n_rho_points, & |
| 601 |
EAMList%EAMParams(me)%eam_rhovals, & |
| 602 |
EAMList%EAMParams(me)%eam_f_rho, & |
| 603 |
EAMList%EAMParams(me)%eam_f_rho_pp, & |
| 604 |
EAMList%EAMParams(me)%eam_rhovals(n_rho_points), & ! Largest rho |
| 605 |
u,u1,u2) |
| 606 |
end if |
| 607 |
|
| 608 |
|
| 609 |
frho(atom) = u |
| 610 |
dfrhodrho(atom) = u1 |
| 611 |
d2frhodrhodrho(atom) = u2 |
| 612 |
pot = pot + u |
| 613 |
|
| 614 |
enddo |
| 615 |
|
| 616 |
|
| 617 |
|
| 618 |
#ifdef IS_MPI |
| 619 |
!! communicate f(rho) and derivatives back into row and column arrays |
| 620 |
call gather(frho,frho_row,plan_row, eam_err) |
| 621 |
if (eam_err /= 0) then |
| 622 |
call handleError("cal_eam_forces()","MPI gather frho_row failure") |
| 623 |
endif |
| 624 |
call gather(dfrhodrho,dfrhodrho_row,plan_row, eam_err) |
| 625 |
if (eam_err /= 0) then |
| 626 |
call handleError("cal_eam_forces()","MPI gather dfrhodrho_row failure") |
| 627 |
endif |
| 628 |
call gather(frho,frho_col,plan_col, eam_err) |
| 629 |
if (eam_err /= 0) then |
| 630 |
call handleError("cal_eam_forces()","MPI gather frho_col failure") |
| 631 |
endif |
| 632 |
call gather(dfrhodrho,dfrhodrho_col,plan_col, eam_err) |
| 633 |
if (eam_err /= 0) then |
| 634 |
call handleError("cal_eam_forces()","MPI gather dfrhodrho_col failure") |
| 635 |
endif |
| 636 |
|
| 637 |
|
| 638 |
|
| 639 |
|
| 640 |
|
| 641 |
if (nmflag) then |
| 642 |
call gather(d2frhodrhodrho,d2frhodrhodrho_row,plan_row) |
| 643 |
call gather(d2frhodrhodrho,d2frhodrhodrho_col,plan_col) |
| 644 |
endif |
| 645 |
#endif |
| 646 |
|
| 647 |
|
| 648 |
end subroutine calc_eam_preforce_Frho |
| 649 |
|
| 650 |
|
| 651 |
|
| 652 |
|
| 653 |
!! Does EAM pairwise Force calculation. |
| 654 |
subroutine do_eam_pair(atom1,atom2,d,rij,r2,pot,f,do_pot,do_stress) |
| 655 |
!Arguments |
| 656 |
integer, intent(in) :: atom1, atom2 |
| 657 |
real( kind = dp ), intent(in) :: rij, r2 |
| 658 |
real( kind = dp ) :: pot |
| 659 |
real( kind = dp ), dimension(3,nLocal) :: f |
| 660 |
real( kind = dp ), intent(in), dimension(3) :: d |
| 661 |
logical, intent(in) :: do_pot, do_stress |
| 662 |
|
| 663 |
real( kind = dp ) :: drdx,drdy,drdz |
| 664 |
real( kind = dp ) :: d2 |
| 665 |
real( kind = dp ) :: phab,pha,dvpdr,d2vpdrdr |
| 666 |
real( kind = dp ) :: rha,drha,d2rha, dpha |
| 667 |
real( kind = dp ) :: rhb,drhb,d2rhb, dphb |
| 668 |
real( kind = dp ) :: dudr |
| 669 |
real( kind = dp ) :: rci,rcj |
| 670 |
real( kind = dp ) :: drhoidr,drhojdr |
| 671 |
real( kind = dp ) :: d2rhoidrdr |
| 672 |
real( kind = dp ) :: d2rhojdrdr |
| 673 |
real( kind = dp ) :: Fx,Fy,Fz |
| 674 |
real( kind = dp ) :: r,d2pha,phb,d2phb |
| 675 |
|
| 676 |
integer :: id1,id2 |
| 677 |
integer :: mytype_atom1 |
| 678 |
integer :: mytype_atom2 |
| 679 |
|
| 680 |
!Local Variables |
| 681 |
|
| 682 |
! write(*,*) "Frho: ", Frho(atom1) |
| 683 |
|
| 684 |
phab = 0.0E0_DP |
| 685 |
dvpdr = 0.0E0_DP |
| 686 |
d2vpdrdr = 0.0E0_DP |
| 687 |
|
| 688 |
if (rij .lt. EAM_rcut) then |
| 689 |
#ifdef IS_MPI |
| 690 |
!!!!! FIX ME |
| 691 |
mytype_atom1 = atid_row(atom1) |
| 692 |
#else |
| 693 |
mytype_atom1 = atid(atom1) |
| 694 |
#endif |
| 695 |
|
| 696 |
drdx = d(1)/rij |
| 697 |
drdy = d(2)/rij |
| 698 |
drdz = d(3)/rij |
| 699 |
|
| 700 |
|
| 701 |
call eam_splint(EAMList%EAMParams(mytype_atom1)%eam_nr, & |
| 702 |
EAMList%EAMParams(mytype_atom1)%eam_rvals, & |
| 703 |
EAMList%EAMParams(mytype_atom1)%eam_rho_r, & |
| 704 |
EAMList%EAMParams(mytype_atom1)%eam_rho_r_pp, & |
| 705 |
rij, rha,drha,d2rha) |
| 706 |
|
| 707 |
!! Calculate Phi(r) for atom1. |
| 708 |
call eam_splint(EAMList%EAMParams(mytype_atom1)%eam_nr, & |
| 709 |
EAMList%EAMParams(mytype_atom1)%eam_rvals, & |
| 710 |
EAMList%EAMParams(mytype_atom1)%eam_phi_r, & |
| 711 |
EAMList%EAMParams(mytype_atom1)%eam_phi_r_pp, & |
| 712 |
rij, pha,dpha,d2pha) |
| 713 |
|
| 714 |
|
| 715 |
! get cutoff for atom 1 |
| 716 |
rci = EAMList%EAMParams(mytype_atom1)%eam_rcut |
| 717 |
#ifdef IS_MPI |
| 718 |
mytype_atom2 = atid_col(atom2) |
| 719 |
#else |
| 720 |
mytype_atom2 = atid(atom2) |
| 721 |
#endif |
| 722 |
|
| 723 |
! Calculate rho,drho and d2rho for atom1 |
| 724 |
call eam_splint(EAMList%EAMParams(mytype_atom2)%eam_nr, & |
| 725 |
EAMList%EAMParams(mytype_atom2)%eam_rvals, & |
| 726 |
EAMList%EAMParams(mytype_atom2)%eam_rho_r, & |
| 727 |
EAMList%EAMParams(mytype_atom2)%eam_rho_r_pp, & |
| 728 |
rij, rhb,drhb,d2rhb) |
| 729 |
|
| 730 |
!! Calculate Phi(r) for atom2. |
| 731 |
call eam_splint(EAMList%EAMParams(mytype_atom2)%eam_nr, & |
| 732 |
EAMList%EAMParams(mytype_atom2)%eam_rvals, & |
| 733 |
EAMList%EAMParams(mytype_atom2)%eam_phi_r, & |
| 734 |
EAMList%EAMParams(mytype_atom2)%eam_phi_r_pp, & |
| 735 |
rij, phb,dphb,d2phb) |
| 736 |
|
| 737 |
|
| 738 |
! get type specific cutoff for atom 2 |
| 739 |
rcj = EAMList%EAMParams(mytype_atom1)%eam_rcut |
| 740 |
|
| 741 |
|
| 742 |
|
| 743 |
if (rij.lt.rci) then |
| 744 |
phab = phab + 0.5E0_DP*(rhb/rha)*pha |
| 745 |
dvpdr = dvpdr + 0.5E0_DP*((rhb/rha)*dpha + & |
| 746 |
pha*((drhb/rha) - (rhb*drha/rha/rha))) |
| 747 |
d2vpdrdr = d2vpdrdr + 0.5E0_DP*((rhb/rha)*d2pha + & |
| 748 |
2.0E0_DP*dpha*((drhb/rha) - (rhb*drha/rha/rha)) + & |
| 749 |
pha*((d2rhb/rha) - 2.0E0_DP*(drhb*drha/rha/rha) + & |
| 750 |
(2.0E0_DP*rhb*drha*drha/rha/rha/rha) - (rhb*d2rha/rha/rha))) |
| 751 |
endif |
| 752 |
|
| 753 |
|
| 754 |
if (rij.lt.rcj) then |
| 755 |
phab = phab + 0.5E0_DP*(rha/rhb)*phb |
| 756 |
dvpdr = dvpdr + 0.5E0_DP*((rha/rhb)*dphb + & |
| 757 |
phb*((drha/rhb) - (rha*drhb/rhb/rhb))) |
| 758 |
d2vpdrdr = d2vpdrdr + 0.5E0_DP*((rha/rhb)*d2phb + & |
| 759 |
2.0E0_DP*dphb*((drha/rhb) - (rha*drhb/rhb/rhb)) + & |
| 760 |
phb*((d2rha/rhb) - 2.0E0_DP*(drha*drhb/rhb/rhb) + & |
| 761 |
(2.0E0_DP*rha*drhb*drhb/rhb/rhb/rhb) - (rha*d2rhb/rhb/rhb))) |
| 762 |
endif |
| 763 |
|
| 764 |
drhoidr = drha |
| 765 |
drhojdr = drhb |
| 766 |
|
| 767 |
d2rhoidrdr = d2rha |
| 768 |
d2rhojdrdr = d2rhb |
| 769 |
|
| 770 |
|
| 771 |
#ifdef IS_MPI |
| 772 |
dudr = drhojdr*dfrhodrho_row(atom1)+drhoidr*dfrhodrho_col(atom2) & |
| 773 |
+ dvpdr |
| 774 |
|
| 775 |
#else |
| 776 |
dudr = drhojdr*dfrhodrho(atom1)+drhoidr*dfrhodrho(atom2) & |
| 777 |
+ dvpdr |
| 778 |
! write(*,*) "Atom1,Atom2, dfrhodrho(atom1) dfrhodrho(atom2): ", atom1,atom2,dfrhodrho(atom1),dfrhodrho(atom2) |
| 779 |
#endif |
| 780 |
|
| 781 |
fx = dudr * drdx |
| 782 |
fy = dudr * drdy |
| 783 |
fz = dudr * drdz |
| 784 |
|
| 785 |
|
| 786 |
#ifdef IS_MPI |
| 787 |
if (do_pot) then |
| 788 |
pot_Row(atom1) = pot_Row(atom1) + phab*0.5 |
| 789 |
pot_Col(atom2) = pot_Col(atom2) + phab*0.5 |
| 790 |
end if |
| 791 |
|
| 792 |
f_Row(1,atom1) = f_Row(1,atom1) + fx |
| 793 |
f_Row(2,atom1) = f_Row(2,atom1) + fy |
| 794 |
f_Row(3,atom1) = f_Row(3,atom1) + fz |
| 795 |
|
| 796 |
f_Col(1,atom2) = f_Col(1,atom2) - fx |
| 797 |
f_Col(2,atom2) = f_Col(2,atom2) - fy |
| 798 |
f_Col(3,atom2) = f_Col(3,atom2) - fz |
| 799 |
#else |
| 800 |
|
| 801 |
if(do_pot) then |
| 802 |
pot = pot + phab |
| 803 |
end if |
| 804 |
|
| 805 |
f(1,atom1) = f(1,atom1) + fx |
| 806 |
f(2,atom1) = f(2,atom1) + fy |
| 807 |
f(3,atom1) = f(3,atom1) + fz |
| 808 |
|
| 809 |
f(1,atom2) = f(1,atom2) - fx |
| 810 |
f(2,atom2) = f(2,atom2) - fy |
| 811 |
f(3,atom2) = f(3,atom2) - fz |
| 812 |
#endif |
| 813 |
|
| 814 |
if (nmflag) then |
| 815 |
|
| 816 |
drhoidr = drha |
| 817 |
drhojdr = drhb |
| 818 |
d2rhoidrdr = d2rha |
| 819 |
d2rhojdrdr = d2rhb |
| 820 |
|
| 821 |
#ifdef IS_MPI |
| 822 |
d2 = d2vpdrdr + & |
| 823 |
d2rhoidrdr*dfrhodrho_col(atom2) + & |
| 824 |
d2rhojdrdr*dfrhodrho_row(atom1) + & |
| 825 |
drhoidr*drhoidr*d2frhodrhodrho_col(atom2) + & |
| 826 |
drhojdr*drhojdr*d2frhodrhodrho_row(atom1) |
| 827 |
|
| 828 |
#else |
| 829 |
|
| 830 |
d2 = d2vpdrdr + & |
| 831 |
d2rhoidrdr*dfrhodrho(atom2) + & |
| 832 |
d2rhojdrdr*dfrhodrho(atom1) + & |
| 833 |
drhoidr*drhoidr*d2frhodrhodrho(atom2) + & |
| 834 |
drhojdr*drhojdr*d2frhodrhodrho(atom1) |
| 835 |
#endif |
| 836 |
end if |
| 837 |
|
| 838 |
|
| 839 |
|
| 840 |
|
| 841 |
if (do_stress) then |
| 842 |
|
| 843 |
#ifdef IS_MPI |
| 844 |
id1 = tagRow(atom1) |
| 845 |
id2 = tagColumn(atom2) |
| 846 |
#else |
| 847 |
id1 = atom1 |
| 848 |
id2 = atom2 |
| 849 |
#endif |
| 850 |
|
| 851 |
if (molMembershipList(id1) .ne. molMembershipList(id2)) then |
| 852 |
|
| 853 |
tau_Temp(1) = tau_Temp(1) - d(1) * fx |
| 854 |
tau_Temp(2) = tau_Temp(2) - d(1) * fy |
| 855 |
tau_Temp(3) = tau_Temp(3) - d(1) * fz |
| 856 |
tau_Temp(4) = tau_Temp(4) - d(2) * fx |
| 857 |
tau_Temp(5) = tau_Temp(5) - d(2) * fy |
| 858 |
tau_Temp(6) = tau_Temp(6) - d(2) * fz |
| 859 |
tau_Temp(7) = tau_Temp(7) - d(3) * fx |
| 860 |
tau_Temp(8) = tau_Temp(8) - d(3) * fy |
| 861 |
tau_Temp(9) = tau_Temp(9) - d(3) * fz |
| 862 |
|
| 863 |
virial_Temp = virial_Temp + & |
| 864 |
(tau_Temp(1) + tau_Temp(5) + tau_Temp(9)) |
| 865 |
|
| 866 |
endif |
| 867 |
endif |
| 868 |
endif |
| 869 |
|
| 870 |
|
| 871 |
end subroutine do_eam_pair |
| 872 |
|
| 873 |
|
| 874 |
subroutine eam_splint(nx, xa, ya, yppa, x, y, dy, d2y) |
| 875 |
|
| 876 |
integer :: atype, nx, j |
| 877 |
real( kind = DP ), dimension(:) :: xa |
| 878 |
real( kind = DP ), dimension(:) :: ya |
| 879 |
real( kind = DP ), dimension(:) :: yppa |
| 880 |
real( kind = DP ) :: x, y |
| 881 |
real( kind = DP ) :: dy, d2y |
| 882 |
real( kind = DP ) :: del, h, a, b, c, d |
| 883 |
integer :: pp_arraySize |
| 884 |
|
| 885 |
|
| 886 |
! this spline code assumes that the x points are equally spaced |
| 887 |
! do not attempt to use this code if they are not. |
| 888 |
|
| 889 |
|
| 890 |
! find the closest point with a value below our own: |
| 891 |
j = FLOOR(real((nx-1),kind=dp) * (x - xa(1)) / (xa(nx) - xa(1))) + 1 |
| 892 |
|
| 893 |
! check to make sure we're inside the spline range: |
| 894 |
if ((j.gt.nx).or.(j.lt.1)) then |
| 895 |
write(errMSG,*) "EAM_splint: x is outside bounds of spline" |
| 896 |
call handleError(routineName,errMSG) |
| 897 |
endif |
| 898 |
! check to make sure we haven't screwed up the calculation of j: |
| 899 |
if ((x.lt.xa(j)).or.(x.gt.xa(j+1))) then |
| 900 |
if (j.ne.nx) then |
| 901 |
write(errMSG,*) "EAM_splint:",x," x is outside bounding range" |
| 902 |
call handleError(routineName,errMSG) |
| 903 |
endif |
| 904 |
endif |
| 905 |
|
| 906 |
del = xa(j+1) - x |
| 907 |
h = xa(j+1) - xa(j) |
| 908 |
|
| 909 |
a = del / h |
| 910 |
b = 1.0E0_DP - a |
| 911 |
c = a*(a*a - 1.0E0_DP)*h*h/6.0E0_DP |
| 912 |
d = b*(b*b - 1.0E0_DP)*h*h/6.0E0_DP |
| 913 |
|
| 914 |
y = a*ya(j) + b*ya(j+1) + c*yppa(j) + d*yppa(j+1) |
| 915 |
|
| 916 |
dy = (ya(j+1)-ya(j))/h & |
| 917 |
- (3.0E0_DP*a*a - 1.0E0_DP)*h*yppa(j)/6.0E0_DP & |
| 918 |
+ (3.0E0_DP*b*b - 1.0E0_DP)*h*yppa(j+1)/6.0E0_DP |
| 919 |
|
| 920 |
|
| 921 |
d2y = a*yppa(j) + b*yppa(j+1) |
| 922 |
|
| 923 |
|
| 924 |
end subroutine eam_splint |
| 925 |
|
| 926 |
|
| 927 |
subroutine eam_spline(nx, xa, ya, yppa, yp1, ypn, boundary) |
| 928 |
|
| 929 |
|
| 930 |
! yp1 and ypn are the first derivatives of y at the two endpoints |
| 931 |
! if boundary is 'L' the lower derivative is used |
| 932 |
! if boundary is 'U' the upper derivative is used |
| 933 |
! if boundary is 'B' then both derivatives are used |
| 934 |
! if boundary is anything else, then both derivatives are assumed to be 0 |
| 935 |
|
| 936 |
integer :: nx, i, k, max_array_size |
| 937 |
|
| 938 |
real( kind = DP ), dimension(:) :: xa |
| 939 |
real( kind = DP ), dimension(:) :: ya |
| 940 |
real( kind = DP ), dimension(:) :: yppa |
| 941 |
real( kind = DP ), dimension(size(xa)) :: u |
| 942 |
real( kind = DP ) :: yp1,ypn,un,qn,sig,p |
| 943 |
character(len=*) :: boundary |
| 944 |
|
| 945 |
! make sure the sizes match |
| 946 |
if ((nx /= size(xa)) .or. (nx /= size(ya))) then |
| 947 |
call handleWarning("EAM_SPLINE","Array size mismatch") |
| 948 |
end if |
| 949 |
|
| 950 |
if ((boundary.eq.'l').or.(boundary.eq.'L').or. & |
| 951 |
(boundary.eq.'b').or.(boundary.eq.'B')) then |
| 952 |
yppa(1) = -0.5E0_DP |
| 953 |
u(1) = (3.0E0_DP/(xa(2)-xa(1)))*((ya(2)-& |
| 954 |
ya(1))/(xa(2)-xa(1))-yp1) |
| 955 |
else |
| 956 |
yppa(1) = 0.0E0_DP |
| 957 |
u(1) = 0.0E0_DP |
| 958 |
endif |
| 959 |
|
| 960 |
do i = 2, nx - 1 |
| 961 |
sig = (xa(i) - xa(i-1)) / (xa(i+1) - xa(i-1)) |
| 962 |
p = sig * yppa(i-1) + 2.0E0_DP |
| 963 |
yppa(i) = (sig - 1.0E0_DP) / p |
| 964 |
u(i) = (6.0E0_DP*((ya(i+1)-ya(i))/(xa(i+1)-xa(i)) - & |
| 965 |
(ya(i)-ya(i-1))/(xa(i)-xa(i-1)))/ & |
| 966 |
(xa(i+1)-xa(i-1)) - sig * u(i-1))/p |
| 967 |
enddo |
| 968 |
|
| 969 |
if ((boundary.eq.'u').or.(boundary.eq.'U').or. & |
| 970 |
(boundary.eq.'b').or.(boundary.eq.'B')) then |
| 971 |
qn = 0.5E0_DP |
| 972 |
un = (3.0E0_DP/(xa(nx)-xa(nx-1)))* & |
| 973 |
(ypn-(ya(nx)-ya(nx-1))/(xa(nx)-xa(nx-1))) |
| 974 |
else |
| 975 |
qn = 0.0E0_DP |
| 976 |
un = 0.0E0_DP |
| 977 |
endif |
| 978 |
|
| 979 |
yppa(nx)=(un-qn*u(nx-1))/(qn*yppa(nx-1)+1.0E0_DP) |
| 980 |
|
| 981 |
do k = nx-1, 1, -1 |
| 982 |
yppa(k)=yppa(k)*yppa(k+1)+u(k) |
| 983 |
enddo |
| 984 |
|
| 985 |
end subroutine eam_spline |
| 986 |
|
| 987 |
|
| 988 |
|
| 989 |
|
| 990 |
end module eam |
