VYukawaFilm.f90 42.5 KB
 Miriam Hinzen committed Oct 01, 2018 1 2 ``````module m_VYukawaFilm `````` Miriam Hinzen committed May 02, 2019 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 `````` ! Computation of the film-case Yukawa potential for the preconditioning of the ! residual charge density in 5 steps: ! 1. pseudo-charge density generation ! 2. vacuum potential generation ! 3. interstitial potential generation ! 4. muffin-tin potential generation ! 5. modification for charge neutrality ! The Yukawa potential is the solution to the modified Helmholtz equation ! ( Delta - lambda^2 ) V_lambda = -4 pi ( rho_out - rho_in ) ! subject to some conditions. ! The general scheme (steps 1 to 4) is the same as for the Poisson equation -- ! we use Green function methods for the z-dependent vacuum and interstitial ! potentials as well as for the muffin-tin potential and apply Weinert's ! method. ! You can choose between two variants: ! 1. variant: ! zero Dirichlet boundary conditions at +/- infinity; ! multiplication with a decaying exponential in vacuum; ! modification in the film for charge neutrality (step 5) ! 2. variant: ! zero Dirichlet boundary conditions near the film boundary in vacuum (D/2+2R); ! modification in the film for charge neutrality (step 5) ! In both cases charge neutrality is broken. ! To restore charge neutrality, we need the integral over the potential to be ! zero. ! In step 5 we therefore solve the modified Helmholtz equation again with ! constant right-hand side, for an additive correction to the potential. ! The constant is chosen such that the integral over the final potential is ! zero. contains subroutine VYukawaFilm( stars, vacuum, cell, sym, input, mpi, atoms, sphhar, oneD, noco, den, & `````` Miriam Hinzen committed Oct 01, 2018 39 40 41 42 43 `````` VYukawa ) use m_constants use m_types use m_psqpw `````` Miriam Hinzen committed Oct 01, 2018 44 `````` use m_vmts `````` Miriam Hinzen committed Oct 01, 2018 45 46 47 48 49 50 51 52 53 54 55 `````` implicit none type(t_stars), intent(in) :: stars type(t_vacuum), intent(in) :: vacuum type(t_cell), intent(in) :: cell type(t_sym), intent(in) :: sym type(t_input), intent(in) :: input type(t_mpi), intent(in) :: mpi type(t_atoms), intent(in) :: atoms type(t_sphhar), intent(in) :: sphhar type(t_oneD), intent(in) :: oneD `````` Miriam Hinzen committed Apr 05, 2019 56 57 `````` type(t_noco), intent(in) :: noco type(t_potden), intent(inout) :: den `````` Miriam Hinzen committed Oct 01, 2018 58 59 60 61 `````` type(t_potden), intent(inout) :: VYukawa complex :: psq(stars%ng3) `````` Miriam Hinzen committed May 02, 2019 62 63 64 `````` complex :: alphm(stars%ng2,2) real :: dh_prec real :: coshdh(stars%ng2) `````` Miriam Hinzen committed Oct 01, 2018 65 `````` `````` Miriam Hinzen committed May 02, 2019 66 `````` `````` Miriam Hinzen committed Oct 01, 2018 67 68 `````` ! PSEUDO-CHARGE DENSITY `````` Miriam Hinzen committed May 02, 2019 69 `````` call psqpw( mpi, atoms, sphhar, stars, vacuum, cell, input, sym, oneD, & `````` Miriam Hinzen committed Apr 05, 2019 70 71 `````` den%pw(:,1), den%mt(:,:,:,1), den%vacz(:,:,1), .false., VYukawa%potdenType, & psq ) `````` Miriam Hinzen committed Oct 01, 2018 72 73 `````` `````` Miriam Hinzen committed May 02, 2019 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 `````` ChooseVariant: if ( .true. ) then ! VACUUM POTENTIAL call VYukawaFilmVacuumVariant1( & stars, vacuum, cell, sym, input, atoms%rmt(1), & psq, den%vacxy(:,:,:,1), den%vacz(:,:,1), & VYukawa%vacxy, VYukawa%vacz, alphm ) ! INTERSTITIAL POTENTIAL call VYukawaFilmInterstitialVariant1( & stars, vacuum, cell, sym, input, & psq, VYukawa%vacxy, VYukawa%vacz, alphm, & VYukawa%pw(:,1) ) else ChooseVariant ! VACUUM POTENTIAL call VYukawaFilmVacuumVariant2( & stars, vacuum, cell, sym, input, 2*atoms%rmt(1), & psq, den%vacxy(:,:,:,1), den%vacz(:,:,1), & VYukawa%vacxy, VYukawa%vacz, alphm, dh_prec, coshdh ) ! INTERSTITIAL POTENTIAL call VYukawaFilmInterstitialVariant2( & stars, vacuum, cell, sym, input, & psq, VYukawa%vacxy, VYukawa%vacz, alphm, dh_prec, coshdh, & VYukawa%pw(:,1) ) `````` Miriam Hinzen committed Oct 01, 2018 107 `````` `````` Miriam Hinzen committed May 02, 2019 108 `````` end if ChooseVariant `````` Miriam Hinzen committed Oct 01, 2018 109 110 111 112 `````` ! MUFFIN-TIN POTENTIAL `````` Miriam Hinzen committed Apr 05, 2019 113 114 115 `````` call Vmts( input, mpi, stars, sphhar, atoms, sym, cell, oneD, & VYukawa%pw(:,1), den%mt(:,0:,:,1), VYukawa%potdenType, & VYukawa%mt(:,0:,:,1) ) `````` Miriam Hinzen committed Oct 01, 2018 116 `````` `````` Miriam Hinzen committed Apr 05, 2019 117 118 `````` ! MODIFICATION FOR CHARGE NEUTRALITY `````` Miriam Hinzen committed Oct 01, 2018 119 `````` `````` Miriam Hinzen committed May 02, 2019 120 121 `````` call VYukawaModify( stars, vacuum, cell, sym, input, mpi, atoms, sphhar, oneD, noco, & den, & `````` Miriam Hinzen committed Apr 05, 2019 122 `````` VYukawa ) `````` Miriam Hinzen committed Oct 01, 2018 123 124 `````` `````` Miriam Hinzen committed Apr 05, 2019 125 `````` end subroutine VYukawaFilm `````` Miriam Hinzen committed Oct 01, 2018 126 127 `````` `````` Miriam Hinzen committed Oct 01, 2018 128 `````` `````` Miriam Hinzen committed May 02, 2019 129 130 131 132 `````` subroutine VYukawaFilmVacuumVariant1( & stars, vacuum, cell, sym, input, rmt, & psq, rhtxy, rht, & VVxy, VVz, alphm ) `````` Miriam Hinzen committed Oct 01, 2018 133 `````` `````` Miriam Hinzen committed May 02, 2019 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 `````` ! 1. part: Compute the contribution from the interstitial charge density to the vacuum potential as a function of q_xy and z (analytic expression for integral) ! 2. part: Compute the contribution from the vacuum charge density to the vacuum potential as a function of q_xy and z by numerical integration use m_ExpSave use m_constants use m_types use m_intgr, only: intgz1Reverse use m_qsf implicit none type(t_stars), intent(in) :: stars type(t_vacuum), intent(in) :: vacuum type(t_cell), intent(in) :: cell type(t_sym), intent(in) :: sym type(t_input), intent(in) :: input real, intent(in) :: rmt complex, intent(in) :: psq(stars%ng3) complex, intent(in) :: rhtxy(vacuum%nmzxyd,stars%ng2-1,2) real, intent(in) :: rht(vacuum%nmzd,2) complex, intent(out) :: VVxy(vacuum%nmzxyd,2:stars%ng2,2) ! this is the qxy /= 0 part of the vacuum potential real, intent(out) :: VVz(vacuum%nmzd,2) ! this is the qxy = 0 part of the vacuum potential complex, intent(out) :: alphm(stars%ng2,2) ! these are the integrals in upper and lower vacuum, now including the first star---integral for star ig2 is in alphm(ig2,ivac) complex :: sum_qz(2,stars%ng2) complex :: c_ph(-stars%mx3:stars%mx3,stars%ng2) complex :: signIqz real :: g_damped(stars%ng2), qz, sign, vcons(stars%ng2) real :: exp_m(vacuum%nmzd,stars%ng2), exp_p(vacuum%nmzd,stars%ng2) real :: expDhg(stars%ng2), expDg(stars%ng2) real :: z(vacuum%nmzd) integer :: iz, irec2, irec3, ivac, iqz complex :: fa(vacuum%nmzxyd,2:stars%ng2), fb(vacuum%nmzxyd,2:stars%ng2) complex :: alpha(vacuum%nmzxyd,2:stars%ng2,2), beta(vacuum%nmzxyd,2:stars%ng2,2), gamma(vacuum%nmzxyd,2:stars%ng2) real :: ga(vacuum%nmzd), gb(vacuum%nmzd) real :: delta(vacuum%nmzd,2), epsilon(vacuum%nmzd,2), zeta(vacuum%nmzd) ! DEFINITIONS / ALLOCATIONS / INITIALISATIONS do iz = 1, vacuum%nmz z(iz) = ( iz - 1 ) * vacuum%delz end do do irec2 = 1, stars%ng2 g_damped(irec2) = sqrt( stars%sk2(irec2) ** 2 + input%preconditioning_param ** 2 ) vcons(irec2) = tpi_const / g_damped(irec2) do iz = 1, vacuum%nmz exp_m(iz,irec2) = exp_save( - g_damped(irec2) * z(iz) ) exp_p(iz,irec2) = exp_save( g_damped(irec2) * z(iz) ) end do expDhg(irec2) = exp_save( - cell%z1 * g_damped(irec2) ) expDg(irec2) = exp_save( -2 * cell%z1 * g_damped(irec2) ) end do sum_qz = (0.,0.) VVxy = (0.,0.) VVz = 0. ! CONTRIBUTION FROM THE INTERSTITIAL CHARGE DENSITY do irec2 = 1, stars%ng2 do ivac = 1, vacuum%nvac sign = 3. - 2. * ivac do iqz = -stars%mx3, stars%mx3 irec3 = stars%ig(stars%kv2(1,irec2),stars%kv2(2,irec2),iqz) ! use only stars within the g_max sphere -> stars outside the sphere have per definition index ig3n = 0 if ( irec3 /= 0 ) then c_ph(iqz,irec2) = stars%rgphs(stars%kv2(1,irec2),stars%kv2(2,irec2),iqz) qz = iqz * cell%bmat(3,3) signIqz = sign * ImagUnit * qz sum_qz(ivac,irec2) = sum_qz(ivac,irec2) + c_ph(iqz,irec2) * psq(irec3) * ( exp( signIqz * cell%z1 ) - exp( - signIqz * cell%z1 ) * expDg(irec2) ) / ( signIqz + g_damped(irec2) ) endif enddo if( irec2 /= 1 ) then VVxy(1:vacuum%nmzxy,irec2,ivac) = vcons(irec2) * sum_qz(ivac,irec2) * exp_m(1:vacuum%nmzxy,irec2) else VVz(1:vacuum%nmz,ivac) = vcons(1) * sum_qz(ivac,1) * exp_m(1:vacuum%nmz,1) end if enddo enddo ! CONTRIBUTION FROM THE VACUUM CHARGE DENSITY ! shifting z: do irec2 = 1, stars%ng2 exp_m(1:vacuum%nmz,irec2) = exp_m(1:vacuum%nmz,irec2) * expDhg(irec2) exp_p(1:vacuum%nmz,irec2) = exp_p(1:vacuum%nmz,irec2) / expDhg(irec2) end do ! case irec2 > 1: do irec2 = 2, stars%ng2 do ivac = 1, vacuum%nvac ! integrands: fa(1:vacuum%nmzxy,irec2) = rhtxy(1:vacuum%nmzxy,irec2-1,ivac) * exp_m(1:vacuum%nmzxy,irec2) fb(1:vacuum%nmzxy,irec2) = rhtxy(1:vacuum%nmzxy,irec2-1,ivac) * exp_p(1:vacuum%nmzxy,irec2) ! integrals: ! alpha(z,q_xy,ivac) = int_z^infty rho(z',q_xy,ivac) exp(-sqrt(q_xy**2+prec_param**2)*z') dz' ! beta (z,q_xy,ivac) = int_{D/2}^z rho(z',q_xy,ivac) exp(+sqrt(q_xy**2+prec_param**2)*z') dz' ! where for z < 0 the lower vacuum charge density (ivac=2) is defined by rho(q_xy,z,ivac=2) := rho(q_xy,-z,ivac=2) call intgz1Reverse( fa(:,irec2), vacuum%delz, vacuum%nmzxy, alpha(:,irec2,ivac), .true. ) call qsfComplex( vacuum%delz, fb(:,irec2), beta(:,irec2,ivac), vacuum%nmzxy, 1 ) ! alphm(q_xy,ivac) = alpha(D/2,q_xy,ivac) --- these integrals are also needed for the interstitial potential alphm(irec2,ivac) = alpha(1,irec2,ivac) end do if ( vacuum%nvac == 1 ) then if ( sym%invs ) then alphm(irec2,2) = conjg( alphm(irec2,1) ) else alphm(irec2,2) = alphm(irec2,1) end if end if do ivac = 1, vacuum%nvac gamma(1:vacuum%nmzxy,irec2) = exp_m(1:vacuum%nmzxy,irec2) * ( alphm(irec2,mod(ivac,2)+1) + beta(1:vacuum%nmzxy,irec2,ivac) ) & + exp_p(1:vacuum%nmzxy,irec2) * alpha(1:vacuum%nmzxy,irec2,ivac) ! mod(ivac,2)+1 outputs the other ivac value where ( 2. * gamma(:,irec2) == gamma(:,irec2) ) gamma(:,irec2) = cmplx( 0., 0. ) VVxy(1:vacuum%nmzxy,irec2,ivac) = VVxy(1:vacuum%nmzxy,irec2,ivac) + vcons(irec2) * gamma(1:vacuum%nmzxy,irec2) end do end do ! case irec2 = 1: do ivac = 1, vacuum%nvac ga(1:vacuum%nmz) = rht(1:vacuum%nmz,ivac) * exp_m(1:vacuum%nmz,1) gb(1:vacuum%nmz) = rht(1:vacuum%nmz,ivac) * exp_p(1:vacuum%nmz,1) call intgz1Reverse( ga(:), vacuum%delz, vacuum%nmz, delta(:,ivac), .true. ) ! integrals call qsf( vacuum%delz, gb(:), epsilon(:,ivac), vacuum%nmz, 1 ) alphm(1,ivac) = delta(1,ivac) end do if ( vacuum%nvac == 1 ) alphm(1,2) = alphm(1,1) do ivac = 1, vacuum%nvac zeta(1:vacuum%nmz) = exp_m(1:vacuum%nmz,1) * ( alphm(1,mod(ivac,2)+1) + epsilon(1:vacuum%nmz,ivac) ) & + exp_p(1:vacuum%nmz,1) * delta(1:vacuum%nmz,ivac) where ( 2. * zeta == zeta ) zeta = 0. VVz(1:vacuum%nmz,ivac) = VVz(1:vacuum%nmz,ivac) + vcons(1) * zeta(1:vacuum%nmz) end do ! damping in vacuum: do ivac = 1, vacuum%nvac VVz(1:vacuum%nmz,ivac) = VVz(1:vacuum%nmz,ivac) * exp( -0.1 / rmt * z(1:vacuum%nmz) ) do irec2 = 2, stars%ng2 VVxy(1:vacuum%nmzxy,irec2,ivac) = VVxy(1:vacuum%nmzxy,irec2,ivac) * exp( -0.1 / rmt * z(1:vacuum%nmzxy) ) end do end do end subroutine VYukawaFilmVacuumVariant1 subroutine VYukawaFilmInterstitialVariant1( & stars, vacuum, cell, sym, input, & psq, VVxy, VVz, alphm, & VIq ) ! main parts: ! 1. part: Compute the contribution from the interstitial charge density to the interstitial potential as a function of q_xy and z (analytic expression for integral) ! 2. part: Add the contribution from the vacuum charge density to the interstitial potential, which had already been computed earlier for the vacuum potential ! 4. part: Compute the coefficients V^I(q_xy,q_z) from the function V^I(q_xy,z) by a 1D Fourier transform: ! V^I(q_xy,z) = sum_{q_z} V^I(q_xy,q_z) * exp( ImagUnit * q_z * z ) ! In order to be able to match the interstitial and vacuum potentials smoothly at the interface, the Fourier transform is done ! in a slightly larger region. -> 3. part ! 3. part: Interpolate the vacuum potential in a small region surrounding the slab `````` Miriam Hinzen committed Oct 01, 2018 297 298 299 300 301 302 303 `````` use m_ExpSave use m_constants use m_types use m_cfft implicit none `````` Miriam Hinzen committed May 02, 2019 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 `````` type(t_stars), intent(in) :: stars type(t_vacuum), intent(in) :: vacuum type(t_cell), intent(in) :: cell type(t_sym), intent(in) :: sym type(t_input), intent(in) :: input complex, intent(in) :: psq(stars%ng3) complex, intent(in) :: VVxy(vacuum%nmzxyd,2:stars%ng2,2) real, intent(in) :: VVz(vacuum%nmzd,2) complex, intent(in) :: alphm(stars%ng2,2) complex, intent(out) :: VIq(stars%ng3) real :: partitioning, rz, qz, q integer :: irec2, irec3, iz, jz, ivac, iqz, nfft, nzmax, nzmin, nzdh, nLower, nUpper, jvac complex, allocatable :: VIz(:,:), eta(:,:) complex :: VIqz(-stars%mx3:stars%mx3,stars%ng2), c_ph(-stars%mx3:stars%mx3,stars%ng2) complex :: vcons1(stars%ng3) real :: VIzReal(3*stars%mx3,stars%ng2), VIzImag(3*stars%mx3,stars%ng2) real, allocatable :: exp_m(:,:), exp_p(:,:) real, allocatable :: z(:) real :: g_damped(stars%ng2), vcons2(stars%ng2), expDhg(stars%ng2) `````` Miriam Hinzen committed Oct 17, 2018 325 326 327 328 `````` ! DEFINITIONS / ALLOCATIONS / INITIALISATIONS `````` Miriam Hinzen committed May 02, 2019 329 330 `````` ! grid points z_i: nfft = 3 * stars%mx3 ! number of grid points for Fourier transform `````` Miriam Hinzen committed Oct 17, 2018 331 `````` partitioning = 1. / real( nfft ) `````` Miriam Hinzen committed May 02, 2019 332 333 334 `````` nzmax = nfft / 2 ! index of maximal z below D~/2 nzmin = nzmax - nfft + 1 ! index of minimal z above -D~/2 nzdh = ceiling( cell%z1 / cell%amat(3,3) * nfft ) - 1 ! index of maximal z below D/2 `````` Miriam Hinzen committed Oct 17, 2018 335 `````` allocate( z(nzmin:nzmax) ) `````` Miriam Hinzen committed May 02, 2019 336 `````` ! definition of z_i: ! indexing: z_0 = 0; positive indices for z > 0; negative indices for z < 0 `````` Miriam Hinzen committed Oct 17, 2018 337 338 `````` do iz = nzmin, nzmax z(iz) = cell%amat(3,3) * iz * partitioning `````` Miriam Hinzen committed Oct 01, 2018 339 `````` end do `````` Miriam Hinzen committed Oct 17, 2018 340 `````` ! other variables: `````` Miriam Hinzen committed May 02, 2019 341 342 `````` allocate( VIz(nzmin:nzmax,stars%ng2), eta(nzmin:nzmax,stars%ng2) ) allocate( exp_m(nzmin:nzmax,stars%ng2), exp_p(nzmin:nzmax,stars%ng2) ) `````` Miriam Hinzen committed Oct 01, 2018 343 344 `````` do irec2 = 1, stars%ng2 g_damped(irec2) = sqrt( stars%sk2(irec2) ** 2 + input%preconditioning_param ** 2 ) `````` Miriam Hinzen committed May 02, 2019 345 346 347 348 349 350 `````` vcons2(irec2) = -1. / ( 2. * g_damped(irec2) ) do iz = nzmin, nzmax exp_m(iz,irec2) = exp_save( - g_damped(irec2) * z(iz) ) exp_p(iz,irec2) = exp_save( g_damped(irec2) * z(iz) ) end do expDhg(irec2) = exp_save( - cell%z1 * g_damped(irec2) ) `````` Miriam Hinzen committed Oct 01, 2018 351 352 353 354 355 356 357 358 359 `````` end do do irec3 = 1, stars%ng3 vcons1(irec3) = fpi_const * psq(irec3) / ( stars%sk3(irec3) ** 2 + input%preconditioning_param ** 2 ) end do VIz = (0.,0.) VIq = (0.,0.) ! CONTRIBUTION FROM THE INTERSTITIAL CHARGE DENSITY `````` Miriam Hinzen committed May 02, 2019 360 `````` `````` Miriam Hinzen committed Oct 01, 2018 361 `````` ! compute V^I(q_xy,z) as a function of q_xy and z `````` Miriam Hinzen committed Oct 17, 2018 362 `````` do irec2 = 1, stars%ng2 `````` Miriam Hinzen committed May 02, 2019 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 `````` do iz = -nzdh, nzdh do iqz = -stars%mx3, stars%mx3 irec3 = stars%ig(stars%kv2(1,irec2),stars%kv2(2,irec2),iqz) if ( irec3 /= 0 ) then ! use only stars within the g_max sphere c_ph(iqz,irec2) = stars%rgphs(stars%kv2(1,irec2),stars%kv2(2,irec2),iqz) qz = iqz * cell%bmat(3,3) VIz(iz,irec2) = VIz(iz,irec2) & + vcons1(irec3) * c_ph(iqz,irec2) * & ( exp( ImagUnit * qz * z(iz) ) & + vcons2(irec2) * expDhg(irec2) * & ( ( g_damped(irec2) + ImagUnit * qz ) * exp_p(iz,irec2) * exp( ImagUnit * qz * cell%z1 ) & + ( g_damped(irec2) - ImagUnit * qz ) * exp_m(iz,irec2) * exp( - ImagUnit * qz * cell%z1 ) ) ) end if enddo end do ! irec2 loop continues ! CONTRIBUTION FROM THE VACUUM CHARGE DENSITY ! irec2 loop continues eta(-nzdh:nzdh,irec2) = exp_m(-nzdh:nzdh,irec2) * alphm(irec2,2) + exp_p(-nzdh:nzdh,irec2) * alphm(irec2,1) where ( 2.0 * eta(:,irec2) == eta(:,irec2) ) eta(:,irec2) = cmplx( 0.0, 0.0 ) VIz(-nzdh:nzdh,irec2) = VIz(-nzdh:nzdh,irec2) + tpi_const / g_damped(irec2) * eta(-nzdh:nzdh,irec2) ! irec2 loop continues ! INTERPOLATION IN VACUUM REGION ! use Lagrange polynomials of order 3 to interpolate the vacuum potential outside I ! q, q-1 and q-2 (scaled with +/-1 or +/-0.5) are the factors of the Lagrange basis polynomials ! irec2 loop continues do ivac = 1, 2 select case( ivac ) case( 1 ) nUpper = nzmax; nLower = nzdh + 1; jvac = 1 case( 2 ) nLower = nzmin; nUpper = -nzdh - 1; jvac = 2; if ( sym%invs .or. sym%zrfs ) jvac = 1 end select do iz = nLower, nUpper rz = ( abs( z(iz) ) - cell%z1 ) / vacuum%delz + 1.0 jz = rz ! index of maximal vacuum grid point below z_i q = rz - jz ! factor in Lagrange basis polynomials if ( irec2 == 1 ) then VIz(iz,irec2) = 0.5 * ( q - 1. ) * ( q - 2. ) * VVz(jz, jvac) & - q * ( q - 2. ) * VVz(jz+1,jvac) & + 0.5 * q * ( q - 1. ) * VVz(jz+2,jvac) else if ( jz + 2 <= vacuum%nmzxy ) then VIz(iz,irec2) = 0.5 * ( q - 1. ) * ( q - 2. ) * VVxy(jz, irec2,jvac) & - q * ( q - 2. ) * VVxy(jz+1,irec2,jvac) & + 0.5 * q * ( q - 1. ) * VVxy(jz+2,irec2,jvac) if ( ( sym%invs .and. .not. sym%zrfs ) .and. ivac == 2 ) VIz(iz,irec2) = conjg( VIz(iz,irec2) ) end if end do end do end do ! irec2 ! 1D FOURIER TRANSFORM TO FIND THE COEFFICIENTS V^I(q_xy,q_z) ! change the indexing for the subroutine cfft, and split real and imaginary parts VIzReal(1:nzmax+1,:) = real( VIz(0:nzmax,:) ); VIzReal(nzmax+2:nfft,:) = real( VIz(nzmin:-1,:) ) VIzImag(1:nzmax+1,:) = aimag( VIz(0:nzmax,:) ); VIzImag(nzmax+2:nfft,:) = aimag( VIz(nzmin:-1,:) ) ! V^I(q_xy,z) = sum_{q_z} V^I(q_xy,q_z) * exp( ImagUnit * q_z * z ) do irec2 = 1, stars%ng2 call cfft( VIzReal(:,irec2), VIzImag(:,irec2), nfft, nfft, nfft, -1 ) ! irec2 loop continues ! reorder VIqz(0,irec2) = cmplx( VIzReal(1,irec2), VIzImag(1,irec2) ) do iqz = 1, stars%mx3 VIqz( iqz,irec2) = cmplx( VIzReal(iqz+1, irec2), VIzImag(iqz+1, irec2) ) VIqz(-iqz,irec2) = cmplx( VIzReal(nfft+1-iqz,irec2), VIzImag(nfft+1-iqz,irec2) ) end do ! add the computed components to V^I(q_xy,q_z): do iqz= -stars%mx3, stars%mx3 irec3 = stars%ig(stars%kv2(1,irec2),stars%kv2(2,irec2),iqz) if ( irec3 /= 0 ) VIq(irec3) = VIq(irec3) + VIqz(iqz,irec2) * partitioning / ( stars%nstr(irec3) / stars%nstr2(irec2) ) end do end do end subroutine VYukawaFilmInterstitialVariant1 subroutine VYukawaFilmVacuumVariant2( & stars, vacuum, cell, sym, input, rmt, & psq, rhtxy, rht, & VVxy, VVz, alphm, dh_prec, coshdh ) ! 1. part: Compute the contribution from the interstitial charge density to the vacuum potential as a function of q_xy and z (analytic expression for integral) ! 2. part: Compute the contribution from the vacuum charge density to the vacuum potential as a function of q_xy and z by numerical integration use m_ExpSave use m_constants use m_types use m_intgr, only: intgz1Reverse use m_qsf implicit none type(t_stars), intent(in) :: stars type(t_vacuum), intent(in) :: vacuum type(t_cell), intent(in) :: cell type(t_sym), intent(in) :: sym type(t_input), intent(in) :: input real, intent(in) :: rmt complex, intent(in) :: psq(stars%ng3) complex, intent(in) :: rhtxy(vacuum%nmzxyd,stars%ng2-1,2) real, intent(in) :: rht(vacuum%nmzd,2) complex, intent(out) :: VVxy(vacuum%nmzxyd,2:stars%ng2,2) ! this is the qxy /= 0 part of the vacuum potential real, intent(out) :: VVz(vacuum%nmzd,2) ! this is the qxy = 0 part of the vacuum potential complex, intent(out) :: alphm(stars%ng2,2) ! these are the integrals in upper and lower vacuum, now including the first star---integral for star ig2 is in alphm(ig2,ivac) real, intent(out) :: dh_prec real, intent(out) :: coshdh(stars%ng2) integer :: iz, irec2, irec3, ivac, iqz, nzdhprec, sign real :: dh, qz, qxy_numerics real, allocatable :: z(:) complex, dimension(stars%ng2) :: sum_qz complex, dimension(stars%ng3) :: vcons3 real, dimension(stars%ng2) :: g_damped, vcons2 complex, dimension(-stars%mx3:stars%mx3,stars%ng2) :: c_ph, quotq real, allocatable :: quotz(:,:), sinhz(:,:) real, dimension(-1:1,stars%ng2) :: quotvardh complex, dimension(-stars%mx3:stars%mx3) :: expdhqz complex, allocatable :: fa(:,:), fb(:,:) complex, allocatable :: alpha(:,:,:), beta(:,:,:), gamma(:,:) real, allocatable :: ga(:), gb(:) real, allocatable :: delta(:,:), epsilon(:,:), zeta(:) ! DEFINITIONS / ALLOCATIONS / INITIALISATIONS dh = cell%z1 ! half the thickness of the film nzdhprec = ceiling( rmt / vacuum%delz ) ! index of dh_prec, see below dh_prec = dh + ( nzdhprec - 1 ) * vacuum%delz ! dh_prec is about dh + R; preconditioning boundary qxy_numerics = sqrt( ( 100 / dh_prec ) ** 2 - input%preconditioning_param ** 2 ) allocate( z(nzdhprec) ) allocate( quotz(-nzdhprec:nzdhprec,stars%ng2) ) allocate( sinhz(nzdhprec,stars%ng2) ) do iz = 1, nzdhprec ! new boundary z(iz) = ( iz - 1 ) * vacuum%delz + dh end do do irec2 = 1, stars%ng2 g_damped(irec2) = sqrt( stars%sk2(irec2) ** 2 + input%preconditioning_param ** 2 ) vcons2(irec2) = fpi_const / g_damped(irec2) coshdh(irec2) = cosh( g_damped(irec2) * ( dh_prec - dh ) ) `````` Miriam Hinzen committed Apr 05, 2019 514 `````` if( stars%sk2(irec2) < qxy_numerics ) then ! numerics ok `````` Miriam Hinzen committed May 02, 2019 515 516 517 518 519 `````` do iz = 1, nzdhprec quotz( iz,irec2) = ( cosh( g_damped(irec2) * z(iz) ) / cosh( g_damped(irec2) * dh_prec ) & + sinh( g_damped(irec2) * z(iz) ) / sinh( g_damped(irec2) * dh_prec ) ) / 2 quotz(-iz,irec2) = ( cosh( g_damped(irec2) * z(iz) ) / cosh( g_damped(irec2) * dh_prec ) & - sinh( g_damped(irec2) * z(iz) ) / sinh( g_damped(irec2) * dh_prec ) ) / 2 `````` Miriam Hinzen committed Oct 17, 2018 520 `````` end do `````` Miriam Hinzen committed May 02, 2019 521 522 523 524 `````` quotvardh( 1,irec2) = ( cosh( g_damped(irec2) * dh ) / sinh( g_damped(irec2) * dh_prec ) & + sinh( g_damped(irec2) * dh ) / cosh( g_damped(irec2) * dh_prec ) ) / 2 quotvardh(-1,irec2) = ( cosh( g_damped(irec2) * dh ) / sinh( g_damped(irec2) * dh_prec ) & - sinh( g_damped(irec2) * dh ) / cosh( g_damped(irec2) * dh_prec ) ) / 2 `````` Miriam Hinzen committed Apr 05, 2019 525 `````` else ! numerical treatment necessary `````` Miriam Hinzen committed May 02, 2019 526 527 528 `````` do iz = 1, nzdhprec quotz( iz,irec2) = exp_save( g_damped(irec2) * ( z(iz) - dh_prec ) ) quotz(-iz,irec2) = exp_save( g_damped(irec2) * ( -z(iz) - dh_prec ) ) `````` Miriam Hinzen committed Apr 05, 2019 529 `````` end do `````` Miriam Hinzen committed May 02, 2019 530 531 `````` quotvardh( 1,irec2) = quotz( 1,irec2) quotvardh(-1,irec2) = quotz(-1,irec2) `````` Miriam Hinzen committed Apr 05, 2019 532 `````` end if `````` Miriam Hinzen committed May 02, 2019 533 534 535 536 537 538 539 540 541 542 543 544 `````` do iz = 1, nzdhprec sinhz(iz,irec2) = sinh( g_damped(irec2) * ( dh_prec - z(iz) ) ) end do do iqz = -stars%mx3, stars%mx3 quotq(iqz,irec2) = ImagUnit * iqz * cell%bmat(3,3) / g_damped(irec2) end do end do sum_qz = (0.,0.) VVxy = (0.,0.) VVz = 0. do irec3 = 1, stars%ng3 vcons3(irec3) = fpi_const * psq(irec3) / ( stars%sk3(irec3) ** 2 + input%preconditioning_param ** 2 ) `````` Miriam Hinzen committed Apr 05, 2019 545 `````` end do `````` Miriam Hinzen committed May 02, 2019 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751 752 753 754 755 756 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784 785 786 787 788 789 790 791 792 793 `````` do iqz = -stars%mx3, stars%mx3 expdhqz(iqz) = exp( ImagUnit * iqz * cell%bmat(3,3) * dh ) end do ! CONTRIBUTION FROM THE INTERSTITIAL CHARGE DENSITY do ivac = 1, vacuum%nvac sign = 3 - 2 * ivac do irec2 = 1, stars%ng2 do iqz = -stars%mx3, stars%mx3 irec3 = stars%ig(stars%kv2(1,irec2),stars%kv2(2,irec2),iqz) ! use only stars within the g_max sphere -> stars outside the sphere have per definition index ig3n = 0 if ( irec3 /= 0 ) then c_ph(iqz,irec2) = stars%rgphs(stars%kv2(1,irec2),stars%kv2(2,irec2),iqz) sum_qz(irec2) = sum_qz(irec2) + & c_ph(iqz,irec2) * vcons3(irec3) * & ( ( quotvardh( 1,irec2) - sign * quotq(iqz,irec2) * quotz( 1,irec2) ) * expdhqz( sign*iqz) & - ( quotvardh(-1,irec2) - sign * quotq(iqz,irec2) * quotz(-1,irec2) ) * expdhqz(-sign*iqz) ) endif enddo if( irec2 /= 1 ) then VVxy(1:nzdhprec,irec2,ivac) = sum_qz(irec2) * sign * sinhz(1:nzdhprec,irec2) else VVz( 1:nzdhprec, ivac) = sum_qz(1) * sign * sinhz(1:nzdhprec,1) end if enddo enddo ! CONTRIBUTION FROM THE VACUUM CHARGE DENSITY allocate( fa(nzdhprec,2:stars%ng2), fb(nzdhprec,2:stars%ng2) ) allocate( alpha(nzdhprec,2:stars%ng2,2), beta(nzdhprec,2:stars%ng2,2), gamma(nzdhprec,2:stars%ng2) ) ! case irec2 > 1: do irec2 = 2, stars%ng2 do ivac = 1, vacuum%nvac ! integrands: fa(1:nzdhprec,irec2) = rhtxy(1:nzdhprec,irec2-1,ivac) * sinhz(1:nzdhprec,irec2) fb(1:nzdhprec,irec2) = rhtxy(1:nzdhprec,irec2-1,ivac) * quotz(1:nzdhprec,irec2) ! integrals: ! alpha(z,q_xy,ivac) = int_z^infty rho(z',q_xy,ivac) sinhz dz' ! beta (z,q_xy,ivac) = int_{D/2}^z rho(z',q_xy,ivac) quotz dz' ! where for z < 0 the lower vacuum charge density (ivac=2) is defined by rho(q_xy,z,ivac=2) := rho(q_xy,-z,ivac=2) call intgz1Reverse( fa(:,irec2), vacuum%delz, nzdhprec, alpha(:,irec2,ivac), .false. ) call qsfComplex( vacuum%delz, fb(:,irec2), beta(:,irec2,ivac), nzdhprec, 1 ) ! alphm(q_xy,ivac) = alpha(D/2,q_xy,ivac) --- these integrals are also needed for the interstitial potential alphm(irec2,ivac) = alpha(1,irec2,ivac) end do if ( vacuum%nvac == 1 ) then if ( sym%invs ) then alphm(irec2,2) = conjg( alphm(irec2,1) ) else alphm(irec2,2) = alphm(irec2,1) end if end if do ivac = 1, vacuum%nvac gamma(1:nzdhprec,irec2) = quotz(-1:-nzdhprec:-1,irec2) * alphm(irec2,mod(ivac,2)+1) & + quotz(1:nzdhprec,irec2) * alpha(1:nzdhprec,irec2,ivac) & + sinhz(1:nzdhprec,irec2) * beta(1:nzdhprec,irec2,ivac) VVxy(1:nzdhprec,irec2,ivac) = VVxy(1:nzdhprec,irec2,ivac) + vcons2(irec2) * gamma(1:nzdhprec,irec2) end do end do allocate( ga(nzdhprec), gb(nzdhprec) ) allocate( delta(nzdhprec,2), epsilon(nzdhprec,2), zeta(nzdhprec) ) ! case irec2 = 1: do ivac = 1, vacuum%nvac ga(1:nzdhprec) = rht(1:nzdhprec,ivac) * sinhz(1:nzdhprec,1) gb(1:nzdhprec) = rht(1:nzdhprec,ivac) * quotz(1:nzdhprec,1) call intgz1Reverse( ga(:), vacuum%delz, nzdhprec, delta(:,ivac), .false. ) call qsf( vacuum%delz, gb(:), epsilon(:,ivac), nzdhprec, 1 ) alphm(1,ivac) = delta(1,ivac) end do if ( vacuum%nvac == 1 ) alphm(1,2) = alphm(1,1) do ivac = 1, vacuum%nvac zeta(1:nzdhprec) = quotz(-1:-nzdhprec:-1,1) * alphm(1,mod(ivac,2)+1) & + quotz(1:nzdhprec,1) * delta(1:nzdhprec,ivac) & + sinhz(1:nzdhprec,1) * epsilon(1:nzdhprec,ivac) VVz(1:nzdhprec,ivac) = VVz(1:nzdhprec,ivac) + vcons2(1) * zeta(1:nzdhprec) end do end subroutine VYukawaFilmVacuumVariant2 subroutine VYukawaFilmInterstitialVariant2( & stars, vacuum, cell, sym, input, & psq, VVxy, VVz, alphm, dh_prec, coshdh, & VIq ) ! main parts: ! 1. part: Compute the contribution from the interstitial charge density to the interstitial potential as a function of q_xy and z (analytic expression for integral) ! 2. part: Add the contribution from the vacuum charge density to the interstitial potential, which had already been computed earlier for the vacuum potential ! 4. part: Compute the coefficients V^I(q_xy,q_z) from the function V^I(q_xy,z) by a 1D Fourier transform: ! V^I(q_xy,z) = sum_{q_z} V^I(q_xy,q_z) * exp( ImagUnit * q_z * z ) ! In order to be able to match the interstitial and vacuum potentials smoothly at the interface, the Fourier transform is done ! in a slightly larger region. -> 3. part ! 3. part: Interpolate the vacuum potential in a small region surrounding the slab use m_ExpSave use m_constants use m_types use m_cfft implicit none type(t_stars), intent(in) :: stars type(t_vacuum), intent(in) :: vacuum type(t_cell), intent(in) :: cell type(t_sym), intent(in) :: sym type(t_input), intent(in) :: input complex, intent(in) :: psq(stars%ng3) complex, intent(in) :: VVxy(vacuum%nmzxyd,2:stars%ng2,2) real, intent(in) :: VVz(vacuum%nmzd,2) complex, intent(in) :: alphm(stars%ng2,2) real, intent(in) :: dh_prec real, intent(in) :: coshdh(stars%ng2) complex, intent(out) :: VIq(stars%ng3) real :: partitioning, rz, qz, q, qxy_numerics integer :: irec2, irec3, iz, jz, ivac, iqz, jvac integer :: nfft, nzmax, nzmin, nzdh, nLower, nUpper complex, allocatable :: VIz(:,:), eta(:,:) complex, allocatable :: expzqz(:,:) complex, dimension(-stars%mx3:stars%mx3,stars%ng2) :: VIqz, c_ph complex, dimension(-stars%mx3:stars%mx3,stars%ng2) :: qquot, qquottrigp, qquottrigm complex, dimension(stars%ng3) :: vcons3 real, dimension(3*stars%mx3,stars%ng2) :: VIzReal, VIzImag real, allocatable :: quotz(:,:), sinhz(:,:) real, allocatable :: z(:) real, dimension(stars%ng2) :: g_damped, vcons2 ! DEFINITIONS / ALLOCATIONS / INITIALISATIONS ! grid points z_i: qxy_numerics = sqrt( ( 100 / dh_prec ) ** 2 - input%preconditioning_param ** 2 ) nfft = 3 * stars%mx3 ! number of grid points for Fourier transform partitioning = 1. / real( nfft ) nzmax = nfft / 2 ! index of maximal z below D~/2 nzmin = nzmax - nfft + 1 ! index of minimal z above -D~/2 nzdh = ceiling( cell%z1 / cell%amat(3,3) * nfft ) - 1 ! index of maximal z below D/2 allocate( z(nzmin:nzmax) ) ! definition of z_i: ! indexing: z_0 = 0; positive indices for z > 0; negative indices for z < 0 do iz = nzmin, nzmax z(iz) = cell%amat(3,3) * iz * partitioning end do ! other variables: allocate( VIz(nzmin:nzmax,stars%ng2) ) allocate( eta(-nzdh:nzdh,stars%ng2) ) allocate( sinhz(-nzdh:nzdh,stars%ng2) ) allocate( quotz(-nzdh:nzdh,stars%ng2) ) allocate( expzqz(-nzdh:nzdh,-stars%mx3:stars%mx3) ) do irec2 = 1, stars%ng2 g_damped(irec2) = sqrt( stars%sk2(irec2) ** 2 + input%preconditioning_param ** 2 ) vcons2(irec2) = fpi_const / g_damped(irec2) if( stars%sk2(irec2) < qxy_numerics ) then ! numerics ok do iz = -nzdh, nzdh quotz( iz,irec2) = ( cosh( g_damped(irec2) * z(iz) ) / cosh( g_damped(irec2) * dh_prec ) & + sinh( g_damped(irec2) * z(iz) ) / sinh( g_damped(irec2) * dh_prec ) ) / 2 end do else ! numerical treatment necessary do iz = -nzdh, nzdh quotz( iz,irec2) = exp_save( g_damped(irec2) * ( z(iz) - dh_prec ) ) end do end if do iz = -nzdh, nzdh sinhz(iz,irec2) = sinh( g_damped(irec2) * ( dh_prec - z(iz) ) ) do iqz = -stars%mx3, stars%mx3 expzqz(iz,iqz) = exp( ImagUnit * iqz * cell%bmat(3,3) * z(iz) ) end do end do do iqz = -stars%mx3, stars%mx3 qquot(iqz,irec2) = ImagUnit * iqz * cell%bmat(3,3) / g_damped(irec2) qquottrigp(iqz,irec2) = coshdh(irec2) + sinhz(nzdh,irec2) * qquot(iqz,irec2) qquottrigm(iqz,irec2) = coshdh(irec2) - sinhz(nzdh,irec2) * qquot(iqz,irec2) end do end do do irec3 = 1, stars%ng3 vcons3(irec3) = fpi_const * psq(irec3) / ( stars%sk3(irec3) ** 2 + input%preconditioning_param ** 2 ) end do VIz = (0.,0.) VIq = (0.,0.) ! CONTRIBUTION FROM THE INTERSTITIAL CHARGE DENSITY ! compute V^I(q_xy,z) as a function of q_xy and z do irec2 = 1, stars%ng2 do iz = -nzdh, nzdh do iqz = -stars%mx3, stars%mx3 irec3 = stars%ig(stars%kv2(1,irec2),stars%kv2(2,irec2),iqz) if ( irec3 /= 0 ) then ! use only stars within the g_max sphere c_ph(iqz,irec2) = stars%rgphs(stars%kv2(1,irec2),stars%kv2(2,irec2),iqz) qz = iqz * cell%bmat(3,3) VIz(iz,irec2) = VIz(iz,irec2) & + vcons3(irec3) * c_ph(iqz,irec2) * & ( expzqz(iz,iqz) & - qquottrigp(iqz,irec2) * expzqz( nzdh,iqz) * quotz( iz,irec2) & - qquottrigm(iqz,irec2) * expzqz(-nzdh,iqz) * quotz(-iz,irec2) ) end if enddo end do ! irec2 loop continues ! CONTRIBUTION FROM THE VACUUM CHARGE DENSITY ! irec2 loop continues eta(-nzdh:nzdh,irec2) = quotz(nzdh:-nzdh:-1,irec2) * alphm(irec2,2) & + quotz(-nzdh:nzdh, irec2) * alphm(irec2,1) VIz(-nzdh:nzdh,irec2) = VIz(-nzdh:nzdh,irec2) + vcons2(irec2) * eta(-nzdh:nzdh,irec2) ! irec2 loop continues ! INTERPOLATION IN VACUUM REGION ! use Lagrange polynomials of order 3 to interpolate the vacuum potential outside I ! q, q-1 and q-2 (scaled with +/-1 or +/-0.5) are the factors of the Lagrange basis polynomials ! irec2 loop continues do ivac = 1, 2 select case( ivac ) case( 1 ) nUpper = nzmax; nLower = nzdh + 1; jvac = 1 case( 2 ) nLower = nzmin; nUpper = -nzdh - 1; jvac = 2; if ( sym%invs .or. sym%zrfs ) jvac = 1 end select do iz = nLower, nUpper rz = ( abs( z(iz) ) - cell%z1 ) / vacuum%delz + 1.0 jz = rz ! index of maximal vacuum grid point below z_i q = rz - jz ! factor in Lagrange basis polynomials if ( irec2 == 1 ) then VIz(iz,irec2) = 0.5 * ( q - 1. ) * ( q - 2. ) * VVz(jz, jvac) & - q * ( q - 2. ) * VVz(jz+1,jvac) & + 0.5 * q * ( q - 1. ) * VVz(jz+2,jvac) else if ( jz + 2 <= vacuum%nmzxy ) then VIz(iz,irec2) = 0.5 * ( q - 1. ) * ( q - 2. ) * VVxy(jz, irec2,jvac) & - q * ( q - 2. ) * VVxy(jz+1,irec2,jvac) & + 0.5 * q * ( q - 1. ) * VVxy(jz+2,irec2,jvac) if ( ( sym%invs .and. .not. sym%zrfs ) .and. ivac == 2 ) VIz(iz,irec2) = conjg( VIz(iz,irec2) ) end if end do end do end do ! irec2 `````` Miriam Hinzen committed Oct 17, 2018 794 `````` `````` Miriam Hinzen committed Oct 01, 2018 795 `````` `````` Miriam Hinzen committed Oct 17, 2018 796 `````` ! 1D FOURIER TRANSFORM TO FIND THE COEFFICIENTS V^I(q_xy,q_z) `````` Miriam Hinzen committed Oct 01, 2018 797 `````` `````` Miriam Hinzen committed Oct 17, 2018 798 799 800 801 802 803 804 805 `````` ! change the indexing for the subroutine cfft, and split real and imaginary parts VIzReal(1:nzmax+1,:) = real( VIz(0:nzmax,:) ); VIzReal(nzmax+2:nfft,:) = real( VIz(nzmin:-1,:) ) VIzImag(1:nzmax+1,:) = aimag( VIz(0:nzmax,:) ); VIzImag(nzmax+2:nfft,:) = aimag( VIz(nzmin:-1,:) ) ! V^I(q_xy,z) = sum_{q_z} V^I(q_xy,q_z) * exp( ImagUnit * q_z * z ) do irec2 = 1, stars%ng2 call cfft( VIzReal(:,irec2), VIzImag(:,irec2), nfft, nfft, nfft, -1 ) ! irec2 loop continues `````` Miriam Hinzen committed Oct 01, 2018 806 `````` `````` Miriam Hinzen committed Oct 17, 2018 807 `````` ! reorder `````` Miriam Hinzen committed Oct 01, 2018 808 `````` VIqz(0,irec2) = cmplx( VIzReal(1,irec2), VIzImag(1,irec2) ) `````` Miriam Hinzen committed Oct 17, 2018 809 810 811 `````` do iqz = 1, stars%mx3 VIqz( iqz,irec2) = cmplx( VIzReal(iqz+1, irec2), VIzImag(iqz+1, irec2) ) VIqz(-iqz,irec2) = cmplx( VIzReal(nfft+1-iqz,irec2), VIzImag(nfft+1-iqz,irec2) ) `````` Miriam Hinzen committed Oct 01, 2018 812 `````` end do `````` Miriam Hinzen committed Oct 17, 2018 813 814 815 816 817 `````` ! add the computed components to V^I(q_xy,q_z): do iqz= -stars%mx3, stars%mx3 irec3 = stars%ig(stars%kv2(1,irec2),stars%kv2(2,irec2),iqz) if ( irec3 /= 0 ) VIq(irec3) = VIq(irec3) + VIqz(iqz,irec2) * partitioning / ( stars%nstr(irec3) / stars%nstr2(irec2) ) `````` Miriam Hinzen committed Oct 01, 2018 818 819 820 `````` end do end do `````` Miriam Hinzen committed Apr 05, 2019 821 `````` `````` Miriam Hinzen committed May 02, 2019 822 `````` end subroutine VYukawaFilmInterstitialVariant2 `````` Miriam Hinzen committed Oct 01, 2018 823 824 825 `````` `````` Miriam Hinzen committed May 02, 2019 826 `````` subroutine VYukawaModify( stars, vacuum, cell, sym, input, mpi, atoms, sphhar, oneD, noco, den, & `````` Miriam Hinzen committed Apr 05, 2019 827 828 829 830 831 832 833 `````` VYukawa ) ! This subroutine adds a potential to the previously computed Yukawa ! potential to ensure charge neutrality. ! The added potential itself is a solution to the modified Helmholtz ! equation with constant right-hand side, where the constant is chosen such ! that charge neutrality is obtained. `````` Miriam Hinzen committed May 02, 2019 834 835 836 `````` ! The charge is distributed only over the film region, and we therefore ! solve the differential equation subject to a boundary condition on the ! film surface, in contrast to the basic Yukawa potential above. `````` Miriam Hinzen committed Apr 05, 2019 837 838 839 840 841 842 843 844 845 846 847 848 849 850 851 852 853 854 855 856 857 858 859 860 861 862 863 864 865 866 867 868 869 870 871 872 873 874 875 876 877 878 879 880 881 882 883 884 885 886 887 888 889 890 891 892 893 894 895 896 897 898 899 `````` use m_constants use m_types use m_vmts use m_constants use m_cdntot use m_cfft implicit none type(t_stars), intent(in) :: stars type(t_vacuum), intent(in) :: vacuum type(t_cell), intent(in) :: cell type(t_sym), intent(in) :: sym type(t_input), intent(in) :: input type(t_mpi), intent(in) :: mpi type(t_atoms), intent(in) :: atoms type(t_sphhar), intent(in) :: sphhar type(t_oneD), intent(in) :: oneD type(t_noco), intent(in) :: noco type(t_potden), intent(inout) :: den type(t_potden), intent(inout) :: VYukawa integer :: n, lh, irec3, iz, iqz, nfft, nzmax, nzmin, nzdh real :: q0, qhat, qbar, ldh, partitioning, dh real :: q(input%jspins), qis(input%jspins), qmt(atoms%ntype,input%jspins),qvac(2,input%jspins), qtot, qistot complex :: psq(stars%ng3) type(t_potden) :: VYukawaModification real, allocatable :: z(:) real :: VIzReal(3*stars%mx3), VIzImag(3*stars%mx3) complex, allocatable :: VIz(:) complex :: VIqz(-stars%mx3:stars%mx3) ! DEFINITIONS / ALLOCATIONS / INITIALISATIONS ! constants: dh = cell%z1 ! half the width of the film ! indexing of grid points z_i: nfft = 3 * stars%mx3 ! number of grid points for Fourier transform partitioning = 1. / real( nfft ) nzmax = nfft / 2 ! index of maximal z below D~/2 nzmin = nzmax - nfft + 1 ! index of minimal z above -D~/2 nzdh = ceiling( dh / cell%amat(3,3) * nfft ) - 1 ! index of maximal z below D/2 allocate( z(nzmin:nzmax) ) ! definition of grid points z_i: ! indexing: z_0 = 0; positive indices for z > 0; negative indices for z < 0 do iz = nzmin, nzmax z(iz) = cell%amat(3,3) * iz * partitioning end do ! INTEGRATION OF THE PREVIOUSLY COMPUTED YUKAWA POTENTIAL ! initialise VYukawaModification with in-going VYukawa and prepare for integration call VYukawaModification%init( stars, atoms, sphhar, vacuum, noco, input%jspins, 4 ) call VYukawaModification%copyPotDen( VYukawa ) do n = 1, atoms%ntype do lh = 0, sphhar%nlhd VYukawaModification%mt(1:atoms%jri(n),lh,n,1) = VYukawaModification%mt(1:atoms%jri(n),lh,n,1) * atoms%rmsh(1:atoms%jri(n),n) ** 2 end do end do ! integrate the potential over the film region `````` Matthias Redies committed Apr 11, 2019 900 `````` call integrate_cdn( stars, atoms, sym, vacuum, input, cell, oneD, VYukawaModification, q, qis, qmt, qvac, qtot, qistot ) `````` Miriam Hinzen committed Apr 05, 2019 901 `````` q0 = qtot / cell%area `````` Miriam Hinzen committed May 02, 2019 902 `````` ldh = input%preconditioning_param * dh `````` Miriam Hinzen committed Apr 05, 2019 903 904 905 906 907 908 909 910 911 912 913 914 915 916 917 918 919 920 921 922 923 924 925 926 927 928 929 930 931 932 933 934 935 936 937 938 939 940 941 942 943 944 945 946 947 948 949 950 951 952 953 954 955 956 957 958 959 960 961 962 963 964 965 966 967 `````` qhat = ( q0 / ( 2 * dh ) ) / ( sinh(ldh) / ( ldh * cosh( ldh ) ) - 1 ) qbar = input%preconditioning_param ** 2 / fpi_const * qhat ! SET UP CONSTANT CHARGE DENSITY ! instead of den%pw(1,1) = qbar we directly set the pseudo charge density den%mt = 0; den%pw = 0; den%vacxy = 0; den%vacz = 0 do n = 1, atoms%ntype den%mt(1:atoms%jri(n),0,n,1) = sfp_const * qbar * atoms%rmsh(1:atoms%jri(n),n) ** 2 end do psq = cmplx(0.0,0.0); psq(1) = qbar ! CALCULATE THE INTERSTITIAL POTENTIAL AS A FUNCTION OF z ! initialise and calculate out-going modification potential; reuse VYukawaModification VYukawaModification%mt = 0; VYukawaModification%pw = 0; VYukawaModification%vacxy = 0; VYukawaModification%vacz = 0 allocate( VIz(nzmin:nzmax) ) VIz = (0.,0.) do iz = -nzdh+1, nzdh-1 VIz(iz) = qhat * ( 1 - cosh( input%preconditioning_param * z(iz) ) / cosh( ldh ) ) end do ! 1D FOURIER TRANSFORM TO FIND THE 3D-FOURIER COEFFICIENTS ! change the indexing for the subroutine cfft, and split real and imaginary parts VIzReal(1:nzmax+1) = real( VIz(0:nzmax) ); VIzReal(nzmax+2:nfft) = real( VIz(nzmin:-1) ) VIzImag(1:nzmax+1) = aimag( VIz(0:nzmax) ); VIzImag(nzmax+2:nfft) = aimag( VIz(nzmin:-1) ) call cfft( VIzReal(:), VIzImag(:), nfft, nfft, nfft, -1 ) ! reorder VIqz = 0 VIqz(0) = cmplx( VIzReal(1), VIzImag(1) ) do iqz = 1, stars%mx3 VIqz( iqz) = cmplx( VIzReal(iqz+1 ), VIzImag(iqz+1 ) ) VIqz(-iqz) = cmplx( VIzReal(nfft+1-iqz), VIzImag(nfft+1-iqz) ) end do ! add the computed components do iqz= -stars%mx3, stars%mx3 irec3 = stars%ig(stars%kv2(1,1),stars%kv2(2,1),iqz) if ( irec3 /= 0 ) VYukawaModification%pw(irec3,1) = VYukawaModification%pw(irec3,1) + VIqz(iqz) * partitioning / ( stars%nstr(irec3) / stars%nstr2(1) ) end do ! MUFFIN-TIN POTENTIAL call Vmts( input, mpi, stars, sphhar, atoms, sym, cell, oneD, & VYukawaModification%pw(:,1), den%mt(:,0:,:,1), VYukawaModification%potdenType, & VYukawaModification%mt(:,0:,:,1) ) ! APPLYING THE MODIFICATION TO THE YUKAWA POTENTIAL call VYukawa%AddPotDen( VYukawa, VYukawaModification ) end subroutine VYukawaModify `````` Miriam Hinzen committed Oct 01, 2018 968 ``end module m_VYukawaFilm``