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module shapes |
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use force_globals |
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use definitions |
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use atype_module |
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use vector_class |
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use simulation |
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use status |
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#ifdef IS_MPI |
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use mpiSimulation |
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#endif |
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implicit none |
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PRIVATE |
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INTEGER, PARAMETER:: CHEBYSHEV_TN = 1 |
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INTEGER, PARAMETER:: CHEBYSHEV_UN = 2 |
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INTEGER, PARAMETER:: LAGUERRE = 3 |
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INTEGER, PARAMETER:: HERMITE = 4 |
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logical, save :: haveShapeMap = .false. |
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public :: do_shape_pair |
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type :: ShapeList |
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integer :: nLMpairs = 0 |
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integer :: bigL = 0 |
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integer :: bigM = 0 |
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integer, allocatable, dimension(:) :: lValue |
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integer, allocatable, dimension(:) :: mValue |
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real(kind=dp), allocatable, dimension(:) :: contactFuncSinCoeff |
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real(kind=dp), allocatable, dimension(:) :: contactFuncCosCoeff |
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real(kind=dp), allocatable, dimension(:) :: rangeFuncSinCoeff |
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real(kind=dp), allocatable, dimension(:) :: rangeFuncCosCoeff |
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real(kind=dp), allocatable, dimension(:) :: strengthFuncSinCoeff |
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real(kind=dp), allocatable, dimension(:) :: strengthFuncCosCoeff |
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integer, allocatable, dimension(:) :: mValue |
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logical :: isLJ = .false. |
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real ( kind = dp ) :: epsilon = 0.0_dp |
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real ( kind = dp ) :: sigma = 0.0_dp |
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end type ShapeList |
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type(ShapeList), dimension(:),allocatable :: ShapeMap |
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contains |
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subroutine do_shape_pair(atom1, atom2, d, rij, r2, sw, vpair, fpair, & |
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pot, A, f, t, do_pot) |
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!! We assume that the rotation matrices have already been calculated |
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!! and placed in the A array. |
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r3 = r2*rij |
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r5 = r3*r2 |
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drdx = d(1) / rij |
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drdy = d(2) / rij |
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drdz = d(3) / rij |
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#ifdef IS_MPI |
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me1 = atid_Row(atom1) |
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me2 = atid_Col(atom2) |
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#else |
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me1 = atid(atom1) |
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me2 = atid(atom2) |
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#endif |
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if (ShapeMap(me1)%isLJ) then |
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sigma_i = ShapeMap(me1)%sigma |
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s_i = ShapeMap(me1)%sigma |
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eps_i = ShapeMap(me1)%epsilon |
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dsigmaidx = 0.0d0 |
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dsigmaidy = 0.0d0 |
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dsigmaidz = 0.0d0 |
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dsigmaidux = 0.0d0 |
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dsigmaiduy = 0.0d0 |
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dsigmaiduz = 0.0d0 |
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dsidx = 0.0d0 |
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dsidy = 0.0d0 |
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dsidz = 0.0d0 |
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dsidux = 0.0d0 |
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dsiduy = 0.0d0 |
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dsiduz = 0.0d0 |
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depsidx = 0.0d0 |
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depsidy = 0.0d0 |
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depsidz = 0.0d0 |
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depsidux = 0.0d0 |
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depsiduy = 0.0d0 |
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depsiduz = 0.0d0 |
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else |
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#ifdef IS_MPI |
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! rotate the inter-particle separation into the two different |
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! body-fixed coordinate systems: |
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xi = A_row(1,atom1)*d(1) + A_row(2,atom1)*d(2) + A_row(3,atom1)*d(3) |
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yi = A_row(4,atom1)*d(1) + A_row(5,atom1)*d(2) + A_row(6,atom1)*d(3) |
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zi = A_row(7,atom1)*d(1) + A_row(8,atom1)*d(2) + A_row(9,atom1)*d(3) |
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#else |
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! rotate the inter-particle separation into the two different |
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! body-fixed coordinate systems: |
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xi = a(1,atom1)*d(1) + a(2,atom1)*d(2) + a(3,atom1)*d(3) |
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yi = a(4,atom1)*d(1) + a(5,atom1)*d(2) + a(6,atom1)*d(3) |
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zi = a(7,atom1)*d(1) + a(8,atom1)*d(2) + a(9,atom1)*d(3) |
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#endif |
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xi2 = xi*xi |
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yi2 = yi*yi |
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zi2 = zi*zi |
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proji = sqrt(xi2 + yi2) |
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proji3 = proji*proji*proji |
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cti = zi / rij |
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dctidx = - zi * xi / r3 |
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dctidy = - zi * yi / r3 |
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dctidz = 1.0d0 / rij - zi2 / r3 |
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dctidux = yi / rij |
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dctiduy = -xi / rij |
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dctiduz = 0.0d0 |
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cpi = xi / proji |
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dcpidx = 1.0d0 / proji - xi2 / proji3 |
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dcpidy = - xi * yi / proji3 |
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dcpidz = 0.0d0 |
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dcpidux = xi * yi * zi / proji3 |
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dcpiduy = -zi * (1.0d0 / proji - xi2 / proji3) |
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dcpiduz = -yi * (1.0d0 / proji - xi2 / proji3) - (xi2 * yi / proji3) |
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spi = yi / proji |
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dspidx = - xi * yi / proji3 |
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dspidy = 1.0d0 / proji - yi2 / proji3 |
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dspidz = 0.0d0 |
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dspidux = -zi * (1.0d0 / proji - yi2 / proji3) |
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dspiduy = xi * yi * zi / proji3 |
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dspiduz = xi * (1.0d0 / proji - yi2 / proji3) + (xi * yi2 / proji3) |
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|
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call Associated_Legendre(cti, ShapeMap(me1)%bigL, & |
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ShapeMap(me1)%bigM, lmax, plm_i, dlm_i) |
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call Orthogonal_Polynomial(cpi, ShapeMap(me1)%bigM, CHEBYSHEV_TN, & |
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tm_i, dtm_i) |
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call Orthogonal_Polynomial(cpi, ShapeMap(me1)%bigM, CHEBYSHEV_UN, & |
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um_i, dum_i) |
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sigma_i = 0.0d0 |
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s_i = 0.0d0 |
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eps_i = 0.0d0 |
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dsigmaidx = 0.0d0 |
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dsigmaidy = 0.0d0 |
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dsigmaidz = 0.0d0 |
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dsigmaidux = 0.0d0 |
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dsigmaiduy = 0.0d0 |
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dsigmaiduz = 0.0d0 |
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dsidx = 0.0d0 |
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dsidy = 0.0d0 |
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dsidz = 0.0d0 |
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dsidux = 0.0d0 |
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dsiduy = 0.0d0 |
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dsiduz = 0.0d0 |
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depsidx = 0.0d0 |
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depsidy = 0.0d0 |
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depsidz = 0.0d0 |
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depsidux = 0.0d0 |
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depsiduy = 0.0d0 |
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depsiduz = 0.0d0 |
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do lm = 1, ShapeMap(me1)%nLMpairs |
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l = ShapeMap(me1)%lValue(lm) |
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m = ShapeMap(me1)%mValue(lm) |
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slm = ShapeMap(me1)%contactFuncSinCoeff(lm) |
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clm = ShapeMap(me1)%contactFuncCosCoeff(lm) |
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Phunc = (slm * spi * um_i(m-1) + clm * tm_i(m)) |
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dPhuncdX = (slm * (spi * dum_i(m-1) * dcpidx + dspidx * um_i(m-1)) & |
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+ clm * dtm_i(m) * dcpidx ) |
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dPhuncdY = (slm * (spi * dum_i(m-1) * dcpidy + dspidy * um_i(m-1)) & |
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+ clm * dtm_i(m) * dcpidy ) |
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dPhuncdZ = (slm * (spi * dum_i(m-1) * dcpidz + dspidz * um_i(m-1)) & |
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+ clm * dtm_i(m) * dcpidz ) |
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dPhuncdUx = (slm*(spi * dum_i(m-1) * dcpidux + dspidux * um_i(m-1)) & |
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+ clm * dtm_i(m) * dcpidux |
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dPhuncdUy = (slm*(spi * dum_i(m-1) * dcpiduy + dspiduy * um_i(m-1)) & |
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+ clm * dtm_i(m) * dcpiduy |
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dPhuncdUz = (slm*(spi * dum_i(m-1) * dcpiduz + dspiduz * um_i(m-1)) & |
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+ clm * dtm_i(m) * dcpiduz |
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sigma_i = sigma_i + plm_i(l,m)*Phunc |
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dsigmaidx = dsigmaidx + plm_i(l,m)*dPhuncdX + & |
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Phunc * dlm_i(l,m) * dctidx |
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dsigmaidy = dsigmaidy + plm_i(l,m)*dPhuncdY + & |
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Phunc * dlm_i(l,m) * dctidy |
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dsigmaidz = dsigmaidz + plm_i(l,m)*dPhuncdZ + & |
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Phunc * dlm_i(l,m) * dctidz |
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dsigmaidux = dsigmaidux + plm_i(l,m)* dPhuncdUx + & |
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Phunc * dlm_i(l,m) * dctidux |
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dsigmaiduy = dsigmaiduy + plm_i(l,m)* dPhuncdUy + & |
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Phunc * dlm_i(l,m) * dctiduy |
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dsigmaiduz = dsigmaiduz + plm_i(l,m)* dPhuncdUz + & |
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Phunc * dlm_i(l,m) * dctiduz |
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slm = ShapeMap(me1)%rangeFuncSinCoeff(lm) |
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clm = ShapeMap(me1)%rangeFuncCosCoeff(lm) |
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Phunc = (slm * spi * um_i(m-1) + clm * tm_i(m)) |
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dPhuncdX = (slm * (spi * dum_i(m-1) * dcpidx + dspidx * um_i(m-1)) & |
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+ clm * dtm_i(m) * dcpidx ) |
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dPhuncdY = (slm * (spi * dum_i(m-1) * dcpidy + dspidy * um_i(m-1)) & |
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+ clm * dtm_i(m) * dcpidy ) |
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dPhuncdZ = (slm * (spi * dum_i(m-1) * dcpidz + dspidz * um_i(m-1)) & |
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+ clm * dtm_i(m) * dcpidz ) |
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dPhuncdUx = (slm*(spi * dum_i(m-1) * dcpidux + dspidux * um_i(m-1)) & |
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+ clm * dtm_i(m) * dcpidux |
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dPhuncdUy = (slm*(spi * dum_i(m-1) * dcpiduy + dspiduy * um_i(m-1)) & |
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+ clm * dtm_i(m) * dcpiduy |
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dPhuncdUz = (slm*(spi * dum_i(m-1) * dcpiduz + dspiduz * um_i(m-1)) & |
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+ clm * dtm_i(m) * dcpiduz |
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s_i = s_i + plm_i(l,m)*Phunc |
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dsidx = dsidx + plm_i(l,m)*dPhuncdX + & |
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Phunc * dlm_i(l,m) * dctidx |
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dsidy = dsidy + plm_i(l,m)*dPhuncdY + & |
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Phunc * dlm_i(l,m) * dctidy |
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dsidz = dsidz + plm_i(l,m)*dPhuncdZ + & |
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Phunc * dlm_i(l,m) * dctidz |
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239 |
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dsidux = dsidux + plm_i(l,m)* dPhuncdUx + & |
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Phunc * dlm_i(l,m) * dctidux |
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dsiduy = dsiduy + plm_i(l,m)* dPhuncdUy + & |
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Phunc * dlm_i(l,m) * dctiduy |
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dsiduz = dsiduz + plm_i(l,m)* dPhuncdUz + & |
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Phunc * dlm_i(l,m) * dctiduz |
245 |
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246 |
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slm = ShapeMap(me1)%strengthFuncSinCoeff(lm) |
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clm = ShapeMap(me1)%strengthFuncCosCoeff(lm) |
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249 |
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Phunc = (slm * spi * um_i(m-1) + clm * tm_i(m)) |
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251 |
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dPhuncdX = (slm * (spi * dum_i(m-1) * dcpidx + dspidx * um_i(m-1)) & |
252 |
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+ clm * dtm_i(m) * dcpidx ) |
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dPhuncdY = (slm * (spi * dum_i(m-1) * dcpidy + dspidy * um_i(m-1)) & |
254 |
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+ clm * dtm_i(m) * dcpidy ) |
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dPhuncdZ = (slm * (spi * dum_i(m-1) * dcpidz + dspidz * um_i(m-1)) & |
256 |
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+ clm * dtm_i(m) * dcpidz ) |
257 |
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258 |
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dPhuncdUx = (slm*(spi * dum_i(m-1) * dcpidux + dspidux * um_i(m-1)) & |
259 |
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+ clm * dtm_i(m) * dcpidux |
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dPhuncdUy = (slm*(spi * dum_i(m-1) * dcpiduy + dspiduy * um_i(m-1)) & |
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+ clm * dtm_i(m) * dcpiduy |
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dPhuncdUz = (slm*(spi * dum_i(m-1) * dcpiduz + dspiduz * um_i(m-1)) & |
263 |
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+ clm * dtm_i(m) * dcpiduz |
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265 |
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eps_i = eps_i + plm_i(l,m)*Phunc |
266 |
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267 |
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depsidx = depsidx + plm_i(l,m)*dPhuncdX + & |
268 |
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Phunc * dlm_i(l,m) * dctidx |
269 |
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depsidy = depsidy + plm_i(l,m)*dPhuncdY + & |
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Phunc * dlm_i(l,m) * dctidy |
271 |
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depsidz = depsidz + plm_i(l,m)*dPhuncdZ + & |
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Phunc * dlm_i(l,m) * dctidz |
273 |
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274 |
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depsidux = depsidux + plm_i(l,m)* dPhuncdUx + & |
275 |
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Phunc * dlm_i(l,m) * dctidux |
276 |
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depsiduy = depsiduy + plm_i(l,m)* dPhuncdUy + & |
277 |
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Phunc * dlm_i(l,m) * dctiduy |
278 |
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depsiduz = depsiduz + plm_i(l,m)* dPhuncdUz + & |
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Phunc * dlm_i(l,m) * dctiduz |
280 |
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enddo |
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endif |
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! now do j: |
285 |
gezelter |
1314 |
|
286 |
gezelter |
1360 |
if (ShapeMap(me2)%isLJ) then |
287 |
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sigma_j = ShapeMap(me2)%sigma |
288 |
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s_j = ShapeMap(me2)%sigma |
289 |
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eps_j = ShapeMap(me2)%epsilon |
290 |
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dsigmajdx = 0.0d0 |
291 |
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dsigmajdy = 0.0d0 |
292 |
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dsigmajdz = 0.0d0 |
293 |
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dsigmajdux = 0.0d0 |
294 |
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dsigmajduy = 0.0d0 |
295 |
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dsigmajduz = 0.0d0 |
296 |
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dsjdx = 0.0d0 |
297 |
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dsjdy = 0.0d0 |
298 |
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dsjdz = 0.0d0 |
299 |
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dsjdux = 0.0d0 |
300 |
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dsjduy = 0.0d0 |
301 |
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dsjduz = 0.0d0 |
302 |
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depsjdx = 0.0d0 |
303 |
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depsjdy = 0.0d0 |
304 |
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depsjdz = 0.0d0 |
305 |
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depsjdux = 0.0d0 |
306 |
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depsjduy = 0.0d0 |
307 |
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depsjduz = 0.0d0 |
308 |
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else |
309 |
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310 |
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#ifdef IS_MPI |
311 |
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! rotate the inter-particle separation into the two different |
312 |
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! body-fixed coordinate systems: |
313 |
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! negative sign because this is the vector from j to i: |
314 |
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315 |
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xj = -(A_Col(1,atom2)*d(1) + A_Col(2,atom2)*d(2) + A_Col(3,atom2)*d(3)) |
316 |
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yj = -(A_Col(4,atom2)*d(1) + A_Col(5,atom2)*d(2) + A_Col(6,atom2)*d(3)) |
317 |
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zj = -(A_Col(7,atom2)*d(1) + A_Col(8,atom2)*d(2) + A_Col(9,atom2)*d(3)) |
318 |
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#else |
319 |
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! rotate the inter-particle separation into the two different |
320 |
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! body-fixed coordinate systems: |
321 |
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! negative sign because this is the vector from j to i: |
322 |
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323 |
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xj = -(a(1,atom2)*d(1) + a(2,atom2)*d(2) + a(3,atom2)*d(3)) |
324 |
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yj = -(a(4,atom2)*d(1) + a(5,atom2)*d(2) + a(6,atom2)*d(3)) |
325 |
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zj = -(a(7,atom2)*d(1) + a(8,atom2)*d(2) + a(9,atom2)*d(3)) |
326 |
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#endif |
327 |
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328 |
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xj2 = xj*xj |
329 |
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yj2 = yj*yj |
330 |
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zj2 = zj*zj |
331 |
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332 |
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projj = sqrt(xj2 + yj2) |
333 |
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projj3 = projj*projj*projj |
334 |
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335 |
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ctj = zj / rij |
336 |
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dctjdx = - zj * xj / r3 |
337 |
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dctjdy = - zj * yj / r3 |
338 |
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dctjdz = 1.0d0 / rij - zj2 / r3 |
339 |
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dctjdux = yj / rij |
340 |
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dctjduy = -xj / rij |
341 |
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dctjduz = 0.0d0 |
342 |
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343 |
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cpj = xj / projj |
344 |
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dcpjdx = 1.0d0 / projj - xj2 / projj3 |
345 |
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dcpjdy = - xj * yj / projj3 |
346 |
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dcpjdz = 0.0d0 |
347 |
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dcpjdux = xj * yj * zj / projj3 |
348 |
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dcpjduy = -zj * (1.0d0 / projj - xj2 / projj3) |
349 |
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dcpjduz = -yj * (1.0d0 / projj - xj2 / projj3) - (xj2 * yj / projj3) |
350 |
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351 |
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spj = yj / projj |
352 |
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dspjdx = - xj * yj / projj3 |
353 |
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dspjdy = 1.0d0 / projj - yj2 / projj3 |
354 |
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dspjdz = 0.0d0 |
355 |
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dspjdux = -zj * (1.0d0 / projj - yj2 / projj3) |
356 |
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dspjduy = xj * yj * zj / projj3 |
357 |
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dspjduz = xj * (1.0d0 / projj - yi2 / projj3) + (xj * yj2 / projj3) |
358 |
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359 |
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call Associated_Legendre(ctj, ShapeMap(me2)%bigL, & |
360 |
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ShapeMap(me2)%bigM, lmax, plm_j, dlm_j) |
361 |
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362 |
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call Orthogonal_Polynomial(cpj, ShapeMap(me2)%bigM, CHEBYSHEV_TN, & |
363 |
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tm_j, dtm_j) |
364 |
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call Orthogonal_Polynomial(cpj, ShapeMap(me2)%bigM, CHEBYSHEV_UN, & |
365 |
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um_j, dum_j) |
366 |
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367 |
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sigma_j = 0.0d0 |
368 |
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s_j = 0.0d0 |
369 |
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eps_j = 0.0d0 |
370 |
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dsigmajdx = 0.0d0 |
371 |
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dsigmajdy = 0.0d0 |
372 |
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dsigmajdz = 0.0d0 |
373 |
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dsigmajdux = 0.0d0 |
374 |
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dsigmajduy = 0.0d0 |
375 |
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dsigmajduz = 0.0d0 |
376 |
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dsjdx = 0.0d0 |
377 |
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dsjdy = 0.0d0 |
378 |
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dsjdz = 0.0d0 |
379 |
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dsjdux = 0.0d0 |
380 |
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dsjduy = 0.0d0 |
381 |
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dsjduz = 0.0d0 |
382 |
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depsjdx = 0.0d0 |
383 |
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depsjdy = 0.0d0 |
384 |
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depsjdz = 0.0d0 |
385 |
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depsjdux = 0.0d0 |
386 |
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depsjduy = 0.0d0 |
387 |
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depsjduz = 0.0d0 |
388 |
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389 |
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do lm = 1, ShapeMap(me2)%nLMpairs |
390 |
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391 |
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l = ShapeMap(me2)%lValue(lm) |
392 |
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m = ShapeMap(me2)%mValue(lm) |
393 |
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394 |
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slm = ShapeMap(me2)%contactFuncSinCoeff(lm) |
395 |
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clm = ShapeMap(me2)%contactFuncCosCoeff(lm) |
396 |
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397 |
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Phunc = (slm * spi * um_i(m-1) + clm * tm_i(m)) |
398 |
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399 |
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dPhuncdX = (slm * (spj * dum_j(m-1) * dcpjdx + dspjdx * um_j(m-1)) & |
400 |
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+ clm * dtm_j(m) * dcpjdx ) |
401 |
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dPhuncdY = (slm * (spj * dum_j(m-1) * dcpjdy + dspjdy * um_j(m-1)) & |
402 |
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+ clm * dtm_j(m) * dcpjdy ) |
403 |
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dPhuncdZ = (slm * (spj * dum_j(m-1) * dcpjdz + dspjdz * um_j(m-1)) & |
404 |
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+ clm * dtm_j(m) * dcpjdz ) |
405 |
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406 |
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dPhuncdUx = (slm*(spj * dum_j(m-1) * dcpjdux + dspjdux * um_j(m-1)) & |
407 |
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+ clm * dtm_j(m) * dcpjdux |
408 |
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dPhuncdUy = (slm*(spj * dum_j(m-1) * dcpjduy + dspjduy * um_j(m-1)) & |
409 |
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+ clm * dtm_j(m) * dcpjduy |
410 |
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dPhuncdUz = (slm*(spj * dum_j(m-1) * dcpjduz + dspjduz * um_j(m-1)) & |
411 |
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+ clm * dtm_j(m) * dcpjduz |
412 |
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413 |
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sigma_j = sigma_j + plm_j(l,m)*Phunc |
414 |
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415 |
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dsigmajdx = dsigmajdx + plm_j(l,m)*dPhuncdX + & |
416 |
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Phunc * dlm_j(l,m) * dctjdx |
417 |
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dsigmajdy = dsigmajdy + plm_j(l,m)*dPhuncdY + & |
418 |
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Phunc * dlm_j(l,m) * dctjdy |
419 |
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dsigmajdz = dsigmajdz + plm_j(l,m)*dPhuncdZ + & |
420 |
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Phunc * dlm_j(l,m) * dctjdz |
421 |
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422 |
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dsigmajdux = dsigmajdux + plm_j(l,m)* dPhuncdUx + & |
423 |
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Phunc * dlm_j(l,m) * dctjdux |
424 |
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dsigmajduy = dsigmajduy + plm_j(l,m)* dPhuncdUy + & |
425 |
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Phunc * dlm_j(l,m) * dctjduy |
426 |
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dsigmajduz = dsigmajduz + plm_j(l,m)* dPhuncdUz + & |
427 |
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Phunc * dlm_j(l,m) * dctjduz |
428 |
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429 |
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slm = ShapeMap(me2)%rangeFuncSinCoeff(lm) |
430 |
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clm = ShapeMap(me2)%rangeFuncCosCoeff(lm) |
431 |
gezelter |
1314 |
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432 |
gezelter |
1360 |
Phunc = (slm * spi * um_i(m-1) + clm * tm_i(m)) |
433 |
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434 |
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dPhuncdX = (slm * (spj * dum_j(m-1) * dcpjdx + dspjdx * um_j(m-1)) & |
435 |
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+ clm * dtm_j(m) * dcpjdx ) |
436 |
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dPhuncdY = (slm * (spj * dum_j(m-1) * dcpjdy + dspjdy * um_j(m-1)) & |
437 |
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+ clm * dtm_j(m) * dcpjdy ) |
438 |
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dPhuncdZ = (slm * (spj * dum_j(m-1) * dcpjdz + dspjdz * um_j(m-1)) & |
439 |
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+ clm * dtm_j(m) * dcpjdz ) |
440 |
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441 |
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dPhuncdUx = (slm*(spj * dum_j(m-1) * dcpjdux + dspjdux * um_j(m-1)) & |
442 |
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+ clm * dtm_j(m) * dcpjdux |
443 |
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dPhuncdUy = (slm*(spj * dum_j(m-1) * dcpjduy + dspjduy * um_j(m-1)) & |
444 |
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+ clm * dtm_j(m) * dcpjduy |
445 |
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dPhuncdUz = (slm*(spj * dum_j(m-1) * dcpjduz + dspjduz * um_j(m-1)) & |
446 |
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+ clm * dtm_j(m) * dcpjduz |
447 |
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448 |
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s_j = s_j + plm_j(l,m)*Phunc |
449 |
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450 |
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dsjdx = dsjdx + plm_j(l,m)*dPhuncdX + & |
451 |
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Phunc * dlm_j(l,m) * dctjdx |
452 |
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dsjdy = dsjdy + plm_j(l,m)*dPhuncdY + & |
453 |
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Phunc * dlm_j(l,m) * dctjdy |
454 |
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dsjdz = dsjdz + plm_j(l,m)*dPhuncdZ + & |
455 |
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Phunc * dlm_j(l,m) * dctjdz |
456 |
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457 |
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dsjdux = dsjdux + plm_j(l,m)* dPhuncdUx + & |
458 |
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Phunc * dlm_j(l,m) * dctjdux |
459 |
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dsjduy = dsjduy + plm_j(l,m)* dPhuncdUy + & |
460 |
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Phunc * dlm_j(l,m) * dctjduy |
461 |
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dsjduz = dsjduz + plm_j(l,m)* dPhuncdUz + & |
462 |
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Phunc * dlm_j(l,m) * dctjduz |
463 |
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464 |
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slm = ShapeMap(me2)%strengthFuncSinCoeff(lm) |
465 |
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clm = ShapeMap(me2)%strengthFuncCosCoeff(lm) |
466 |
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467 |
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Phunc = (slm * spi * um_i(m-1) + clm * tm_i(m)) |
468 |
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469 |
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dPhuncdX = (slm * (spj * dum_j(m-1) * dcpjdx + dspjdx * um_j(m-1)) & |
470 |
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+ clm * dtm_j(m) * dcpjdx ) |
471 |
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dPhuncdY = (slm * (spj * dum_j(m-1) * dcpjdy + dspjdy * um_j(m-1)) & |
472 |
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+ clm * dtm_j(m) * dcpjdy ) |
473 |
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dPhuncdZ = (slm * (spj * dum_j(m-1) * dcpjdz + dspjdz * um_j(m-1)) & |
474 |
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+ clm * dtm_j(m) * dcpjdz ) |
475 |
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476 |
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dPhuncdUx = (slm*(spj * dum_j(m-1) * dcpjdux + dspjdux * um_j(m-1)) & |
477 |
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+ clm * dtm_j(m) * dcpjdux |
478 |
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dPhuncdUy = (slm*(spj * dum_j(m-1) * dcpjduy + dspjduy * um_j(m-1)) & |
479 |
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+ clm * dtm_j(m) * dcpjduy |
480 |
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dPhuncdUz = (slm*(spj * dum_j(m-1) * dcpjduz + dspjduz * um_j(m-1)) & |
481 |
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+ clm * dtm_j(m) * dcpjduz |
482 |
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483 |
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eps_j = eps_j + plm_j(l,m)*Phunc |
484 |
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485 |
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depsjdx = depsjdx + plm_j(l,m)*dPhuncdX + & |
486 |
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Phunc * dlm_j(l,m) * dctjdx |
487 |
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depsjdy = depsjdy + plm_j(l,m)*dPhuncdY + & |
488 |
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Phunc * dlm_j(l,m) * dctjdy |
489 |
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depsjdz = depsjdz + plm_j(l,m)*dPhuncdZ + & |
490 |
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Phunc * dlm_j(l,m) * dctjdz |
491 |
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492 |
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depsjdux = depsjdux + plm_j(l,m)* dPhuncdUx + & |
493 |
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Phunc * dlm_j(l,m) * dctjdux |
494 |
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depsjduy = depsjduy + plm_j(l,m)* dPhuncdUy + & |
495 |
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Phunc * dlm_j(l,m) * dctjduy |
496 |
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depsjduz = depsjduz + plm_j(l,m)* dPhuncdUz + & |
497 |
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Phunc * dlm_j(l,m) * dctjduz |
498 |
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499 |
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enddo |
500 |
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endif |
501 |
gezelter |
1314 |
|
502 |
gezelter |
1360 |
! phew, now let's assemble the potential energy: |
503 |
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504 |
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505 |
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sigma = 0.5*(sigma_i + sigma_j) |
506 |
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507 |
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dsigmadxi = 0.5*dsigmaidx |
508 |
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dsigmadyi = 0.5*dsigmaidy |
509 |
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dsigmadzi = 0.5*dsigmaidz |
510 |
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dsigmaduxi = 0.5*dsigmaidux |
511 |
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dsigmaduyi = 0.5*dsigmaiduy |
512 |
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dsigmaduzi = 0.5*dsigmaiduz |
513 |
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514 |
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dsigmadxj = 0.5*dsigmajdx |
515 |
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dsigmadyj = 0.5*dsigmajdy |
516 |
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dsigmadzj = 0.5*dsigmajdz |
517 |
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dsigmaduxj = 0.5*dsigmajdux |
518 |
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dsigmaduyj = 0.5*dsigmajduy |
519 |
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dsigmaduzj = 0.5*dsigmajduz |
520 |
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521 |
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s = 0.5*(s_i + s_j) |
522 |
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523 |
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dsdxi = 0.5*dsidx |
524 |
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dsdyi = 0.5*dsidy |
525 |
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dsdzi = 0.5*dsidz |
526 |
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dsduxi = 0.5*dsidux |
527 |
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dsduyi = 0.5*dsiduy |
528 |
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dsduzi = 0.5*dsiduz |
529 |
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530 |
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dsdxj = 0.5*dsjdx |
531 |
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dsdyj = 0.5*dsjdy |
532 |
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dsdzj = 0.5*dsjdz |
533 |
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dsduxj = 0.5*dsjdux |
534 |
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dsduyj = 0.5*dsjduy |
535 |
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dsduzj = 0.5*dsjduz |
536 |
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537 |
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eps = sqrt(eps_i * eps_j) |
538 |
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539 |
|
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depsdxi = eps_j * depsidx / (2.0d0 * eps) |
540 |
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depsdyi = eps_j * depsidy / (2.0d0 * eps) |
541 |
|
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depsdzi = eps_j * depsidz / (2.0d0 * eps) |
542 |
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depsduxi = eps_j * depsidux / (2.0d0 * eps) |
543 |
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depsduyi = eps_j * depsiduy / (2.0d0 * eps) |
544 |
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depsduzi = eps_j * depsiduz / (2.0d0 * eps) |
545 |
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546 |
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depsdxj = eps_i * depsjdx / (2.0d0 * eps) |
547 |
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depsdyj = eps_i * depsjdy / (2.0d0 * eps) |
548 |
|
|
depsdzj = eps_i * depsjdz / (2.0d0 * eps) |
549 |
|
|
depsduxj = eps_i * depsjdux / (2.0d0 * eps) |
550 |
|
|
depsduyj = eps_i * depsjduy / (2.0d0 * eps) |
551 |
|
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depsduzj = eps_i * depsjduz / (2.0d0 * eps) |
552 |
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553 |
|
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rtdenom = r-sigma+s |
554 |
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rt = s / rtdenom |
555 |
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|
556 |
|
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drtdxi = (dsdxi + rt * (drdxi - dsigmadxi + dsdxi)) / rtdenom |
557 |
|
|
drtdyi = (dsdyi + rt * (drdyi - dsigmadyi + dsdyi)) / rtdenom |
558 |
|
|
drtdzi = (dsdzi + rt * (drdzi - dsigmadzi + dsdzi)) / rtdenom |
559 |
|
|
drtduxi = (dsduxi + rt * (drduxi - dsigmaduxi + dsduxi)) / rtdenom |
560 |
|
|
drtduyi = (dsduyi + rt * (drduyi - dsigmaduyi + dsduyi)) / rtdenom |
561 |
|
|
drtduzi = (dsduzi + rt * (drduzi - dsigmaduzi + dsduzi)) / rtdenom |
562 |
|
|
drtdxj = (dsdxj + rt * (drdxj - dsigmadxj + dsdxj)) / rtdenom |
563 |
|
|
drtdyj = (dsdyj + rt * (drdyj - dsigmadyj + dsdyj)) / rtdenom |
564 |
|
|
drtdzj = (dsdzj + rt * (drdzj - dsigmadzj + dsdzj)) / rtdenom |
565 |
|
|
drtduxj = (dsduxj + rt * (drduxj - dsigmaduxj + dsduxj)) / rtdenom |
566 |
|
|
drtduyj = (dsduyj + rt * (drduyj - dsigmaduyj + dsduyj)) / rtdenom |
567 |
|
|
drtduzj = (dsduzj + rt * (drduzj - dsigmaduzj + dsduzj)) / rtdenom |
568 |
|
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|
569 |
|
|
rt2 = rt*rt |
570 |
|
|
rt3 = rt2*rt |
571 |
|
|
rt5 = rt2*rt3 |
572 |
|
|
rt6 = rt3*rt3 |
573 |
|
|
rt11 = rt5*rt6 |
574 |
|
|
rt12 = rt6*rt6 |
575 |
|
|
rt126 = rt12 - rt6 |
576 |
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|
577 |
|
|
if (do_pot) then |
578 |
|
|
#ifdef IS_MPI |
579 |
|
|
pot_row(atom1) = pot_row(atom1) + 2.0d0*eps*rt126*sw |
580 |
|
|
pot_col(atom2) = pot_col(atom2) + 2.0d0*eps*rt126*sw |
581 |
|
|
#else |
582 |
|
|
pot = pot + 4.0d0*eps*rt126*sw |
583 |
|
|
endif |
584 |
|
|
|
585 |
|
|
dvdxi = 24.0d0*eps(2.0d0*rt11 - rt5)*drtdxi + 4.0d0*depsdxi*rt126 |
586 |
|
|
dvdyi = 24.0d0*eps(2.0d0*rt11 - rt5)*drtdyi + 4.0d0*depsdyi*rt126 |
587 |
|
|
dvdzi = 24.0d0*eps(2.0d0*rt11 - rt5)*drtdzi + 4.0d0*depsdzi*rt126 |
588 |
|
|
dvduxi = 24.0d0*eps(2.0d0*rt11 - rt5)*drtduxi + 4.0d0*depsduxi*rt126 |
589 |
|
|
dvduyi = 24.0d0*eps(2.0d0*rt11 - rt5)*drtduyi + 4.0d0*depsduyi*rt126 |
590 |
|
|
dvduzi = 24.0d0*eps(2.0d0*rt11 - rt5)*drtduzi + 4.0d0*depsduzi*rt126 |
591 |
|
|
|
592 |
|
|
dvdxj = 24.0d0*eps(2.0d0*rt11 - rt5)*drtdxj + 4.0d0*depsdxj*rt126 |
593 |
|
|
dvdyj = 24.0d0*eps(2.0d0*rt11 - rt5)*drtdyj + 4.0d0*depsdyj*rt126 |
594 |
|
|
dvdzj = 24.0d0*eps(2.0d0*rt11 - rt5)*drtdzj + 4.0d0*depsdzj*rt126 |
595 |
|
|
dvduxj = 24.0d0*eps(2.0d0*rt11 - rt5)*drtduxj + 4.0d0*depsduxj*rt126 |
596 |
|
|
dvduyj = 24.0d0*eps(2.0d0*rt11 - rt5)*drtduyj + 4.0d0*depsduyj*rt126 |
597 |
|
|
dvduzj = 24.0d0*eps(2.0d0*rt11 - rt5)*drtduzj + 4.0d0*depsduzj*rt126 |
598 |
|
|
|
599 |
|
|
! do the torques first since they are easy: |
600 |
|
|
! remember that these are still in the body fixed axes |
601 |
|
|
|
602 |
|
|
txi = dvduxi * sw |
603 |
|
|
tyi = dvduyi * sw |
604 |
|
|
tzi = dvduzi * sw |
605 |
|
|
|
606 |
|
|
txj = dvduxj * sw |
607 |
|
|
tyj = dvduyj * sw |
608 |
|
|
tzj = dvduzj * sw |
609 |
|
|
|
610 |
|
|
! go back to lab frame using transpose of rotation matrix: |
611 |
|
|
|
612 |
|
|
#ifdef IS_MPI |
613 |
|
|
t_Row(1,atom1) = t_Row(1,atom1) + a_Row(1,atom1)*txi + & |
614 |
|
|
a_Row(4,atom1)*tyi + a_Row(7,atom1)*tzi |
615 |
|
|
t_Row(2,atom1) = t_Row(2,atom1) + a_Row(2,atom1)*txi + & |
616 |
|
|
a_Row(5,atom1)*tyi + a_Row(8,atom1)*tzi |
617 |
|
|
t_Row(3,atom1) = t_Row(3,atom1) + a_Row(3,atom1)*txi + & |
618 |
|
|
a_Row(6,atom1)*tyi + a_Row(9,atom1)*tzi |
619 |
|
|
|
620 |
|
|
t_Col(1,atom2) = t_Col(1,atom2) + a_Col(1,atom2)*txj + & |
621 |
|
|
a_Col(4,atom2)*tyj + a_Col(7,atom2)*tzj |
622 |
|
|
t_Col(2,atom2) = t_Col(2,atom2) + a_Col(2,atom2)*txj + & |
623 |
|
|
a_Col(5,atom2)*tyj + a_Col(8,atom2)*tzj |
624 |
|
|
t_Col(3,atom2) = t_Col(3,atom2) + a_Col(3,atom2)*txj + & |
625 |
|
|
a_Col(6,atom2)*tyj + a_Col(9,atom2)*tzj |
626 |
|
|
#else |
627 |
|
|
t(1,atom1) = t(1,atom1) + a(1,atom1)*txi + a(4,atom1)*tyi + a(7,atom1)*tzi |
628 |
|
|
t(2,atom1) = t(2,atom1) + a(2,atom1)*txi + a(5,atom1)*tyi + a(8,atom1)*tzi |
629 |
|
|
t(3,atom1) = t(3,atom1) + a(3,atom1)*txi + a(6,atom1)*tyi + a(9,atom1)*tzi |
630 |
|
|
|
631 |
|
|
t(1,atom2) = t(1,atom2) + a(1,atom2)*txj + a(4,atom2)*tyj + a(7,atom2)*tzj |
632 |
|
|
t(2,atom2) = t(2,atom2) + a(2,atom2)*txj + a(5,atom2)*tyj + a(8,atom2)*tzj |
633 |
|
|
t(3,atom2) = t(3,atom2) + a(3,atom2)*txj + a(6,atom2)*tyj + a(9,atom2)*tzj |
634 |
|
|
#endif |
635 |
|
|
! Now, on to the forces: |
636 |
|
|
|
637 |
|
|
! first rotate the i terms back into the lab frame: |
638 |
|
|
|
639 |
|
|
fxi = dvdxi * sw |
640 |
|
|
fyi = dvdyi * sw |
641 |
|
|
fzi = dvdzi * sw |
642 |
|
|
|
643 |
|
|
fxj = dvdxj * sw |
644 |
|
|
fyj = dvdyj * sw |
645 |
|
|
fzj = dvdzj * sw |
646 |
|
|
|
647 |
|
|
#ifdef IS_MPI |
648 |
|
|
fxii = a_Row(1,atom1)*fxi + a_Row(4,atom1)*fyi + a_Row(7,atom1)*fzi |
649 |
|
|
fyii = a_Row(2,atom1)*fxi + a_Row(5,atom1)*fyi + a_Row(8,atom1)*fzi |
650 |
|
|
fzii = a_Row(3,atom1)*fxi + a_Row(6,atom1)*fyi + a_Row(9,atom1)*fzi |
651 |
|
|
|
652 |
|
|
fxjj = a_Col(1,atom2)*fxj + a_Col(4,atom2)*fyj + a_Col(7,atom2)*fzj |
653 |
|
|
fyjj = a_Col(2,atom2)*fxj + a_Col(5,atom2)*fyj + a_Col(8,atom2)*fzj |
654 |
|
|
fzjj = a_Col(3,atom2)*fxj + a_Col(6,atom2)*fyj + a_Col(9,atom2)*fzj |
655 |
|
|
#else |
656 |
|
|
fxii = a(1,atom1)*fxi + a(4,atom1)*fyi + a(7,atom1)*fzi |
657 |
|
|
fyii = a(2,atom1)*fxi + a(5,atom1)*fyi + a(8,atom1)*fzi |
658 |
|
|
fzii = a(3,atom1)*fxi + a(6,atom1)*fyi + a(9,atom1)*fzi |
659 |
|
|
|
660 |
|
|
fxjj = a(1,atom2)*fxj + a(4,atom2)*fyj + a(7,atom2)*fzj |
661 |
|
|
fyjj = a(2,atom2)*fxj + a(5,atom2)*fyj + a(8,atom2)*fzj |
662 |
|
|
fzjj = a(3,atom2)*fxj + a(6,atom2)*fyj + a(9,atom2)*fzj |
663 |
|
|
#endif |
664 |
|
|
|
665 |
|
|
fxij = -fxii |
666 |
|
|
fyij = -fyii |
667 |
|
|
fzij = -fzii |
668 |
|
|
|
669 |
|
|
fxji = -fxjj |
670 |
|
|
fyji = -fyjj |
671 |
|
|
fzji = -fzjj |
672 |
|
|
|
673 |
|
|
fxradial = fxii + fxji |
674 |
|
|
fyradial = fyii + fyji |
675 |
|
|
fzradial = fzii + fzji |
676 |
|
|
|
677 |
|
|
#ifdef IS_MPI |
678 |
|
|
f_Row(1,atom1) = f_Row(1,atom1) + fxradial |
679 |
|
|
f_Row(2,atom1) = f_Row(2,atom1) + fyradial |
680 |
|
|
f_Row(3,atom1) = f_Row(3,atom1) + fzradial |
681 |
|
|
|
682 |
|
|
f_Col(1,atom2) = f_Col(1,atom2) - fxradial |
683 |
|
|
f_Col(2,atom2) = f_Col(2,atom2) - fyradial |
684 |
|
|
f_Col(3,atom2) = f_Col(3,atom2) - fzradial |
685 |
|
|
#else |
686 |
|
|
f(1,atom1) = f(1,atom1) + fxradial |
687 |
|
|
f(2,atom1) = f(2,atom1) + fyradial |
688 |
|
|
f(3,atom1) = f(3,atom1) + fzradial |
689 |
|
|
|
690 |
|
|
f(1,atom2) = f(1,atom2) - fxradial |
691 |
|
|
f(2,atom2) = f(2,atom2) - fyradial |
692 |
|
|
f(3,atom2) = f(3,atom2) - fzradial |
693 |
|
|
#endif |
694 |
|
|
|
695 |
|
|
#ifdef IS_MPI |
696 |
|
|
id1 = AtomRowToGlobal(atom1) |
697 |
|
|
id2 = AtomColToGlobal(atom2) |
698 |
|
|
#else |
699 |
|
|
id1 = atom1 |
700 |
|
|
id2 = atom2 |
701 |
|
|
#endif |
702 |
|
|
|
703 |
|
|
if (molMembershipList(id1) .ne. molMembershipList(id2)) then |
704 |
|
|
|
705 |
|
|
fpair(1) = fpair(1) + fxradial |
706 |
|
|
fpair(2) = fpair(2) + fyradial |
707 |
|
|
fpair(3) = fpair(3) + fzradial |
708 |
|
|
|
709 |
|
|
endif |
710 |
|
|
|
711 |
|
|
end subroutine do_shape_pair |
712 |
|
|
|
713 |
|
|
SUBROUTINE Associated_Legendre(x, l, m, lmax, plm, dlm) |
714 |
|
|
|
715 |
|
|
! Purpose: Compute the associated Legendre functions |
716 |
|
|
! Plm(x) and their derivatives Plm'(x) |
717 |
|
|
! Input : x --- Argument of Plm(x) |
718 |
|
|
! l --- Order of Plm(x), l = 0,1,2,...,n |
719 |
|
|
! m --- Degree of Plm(x), m = 0,1,2,...,N |
720 |
|
|
! lmax --- Physical dimension of PLM and DLM |
721 |
|
|
! Output: PLM(l,m) --- Plm(x) |
722 |
|
|
! DLM(l,m) --- Plm'(x) |
723 |
|
|
! |
724 |
|
|
! adapted from the routines in |
725 |
|
|
! COMPUTATION OF SPECIAL FUNCTIONS by Shanjie Zhang and Jianming Jin |
726 |
|
|
! ISBN 0-471-11963-6 |
727 |
|
|
! |
728 |
|
|
! The original Fortran77 codes can be found here: |
729 |
|
|
! http://iris-lee3.ece.uiuc.edu/~jjin/routines/routines.html |
730 |
|
|
|
731 |
|
|
real (kind=8), intent(in) :: x |
732 |
|
|
integer, intent(in) :: l, m, lmax |
733 |
|
|
real (kind=8), dimension(0:lmax,0:m), intent(out) :: PLM, DLM |
734 |
|
|
integer :: i, j, ls |
735 |
|
|
real (kind=8) :: xq, xs |
736 |
|
|
|
737 |
|
|
! zero out both arrays: |
738 |
|
|
DO I = 0, m |
739 |
|
|
DO J = 0, l |
740 |
|
|
PLM(J,I) = 0.0D0 |
741 |
|
|
DLM(J,I) = 0.0D0 |
742 |
|
|
end DO |
743 |
|
|
end DO |
744 |
|
|
|
745 |
|
|
! start with 0,0: |
746 |
|
|
PLM(0,0) = 1.0D0 |
747 |
gezelter |
1314 |
|
748 |
gezelter |
1360 |
! x = +/- 1 functions are easy: |
749 |
|
|
IF (abs(X).EQ.1.0D0) THEN |
750 |
|
|
DO I = 1, m |
751 |
|
|
PLM(0, I) = X**I |
752 |
|
|
DLM(0, I) = 0.5D0*I*(I+1.0D0)*X**(I+1) |
753 |
|
|
end DO |
754 |
|
|
DO J = 1, m |
755 |
|
|
DO I = 1, l |
756 |
|
|
IF (I.EQ.1) THEN |
757 |
|
|
DLM(I, J) = 1.0D+300 |
758 |
|
|
ELSE IF (I.EQ.2) THEN |
759 |
|
|
DLM(I, J) = -0.25D0*(J+2)*(J+1)*J*(J-1)*X**(J+1) |
760 |
|
|
ENDIF |
761 |
|
|
end DO |
762 |
|
|
end DO |
763 |
|
|
RETURN |
764 |
|
|
ENDIF |
765 |
|
|
|
766 |
|
|
LS = 1 |
767 |
|
|
IF (abs(X).GT.1.0D0) LS = -1 |
768 |
|
|
XQ = sqrt(LS*(1.0D0-X*X)) |
769 |
|
|
XS = LS*(1.0D0-X*X) |
770 |
|
|
|
771 |
|
|
DO I = 1, l |
772 |
|
|
PLM(I, I) = -LS*(2.0D0*I-1.0D0)*XQ*PLM(I-1, I-1) |
773 |
|
|
enddo |
774 |
|
|
|
775 |
|
|
DO I = 0, l |
776 |
|
|
PLM(I, I+1)=(2.0D0*I+1.0D0)*X*PLM(I, I) |
777 |
|
|
enddo |
778 |
|
|
|
779 |
|
|
DO I = 0, l |
780 |
|
|
DO J = I+2, m |
781 |
|
|
PLM(I, J)=((2.0D0*J-1.0D0)*X*PLM(I,J-1) - & |
782 |
|
|
(I+J-1.0D0)*PLM(I,J-2))/(J-I) |
783 |
|
|
end DO |
784 |
|
|
end DO |
785 |
gezelter |
1314 |
|
786 |
gezelter |
1360 |
DLM(0, 0)=0.0D0 |
787 |
|
|
|
788 |
|
|
DO J = 1, m |
789 |
|
|
DLM(0, J)=LS*J*(PLM(0,J-1)-X*PLM(0,J))/XS |
790 |
|
|
end DO |
791 |
|
|
|
792 |
|
|
DO I = 1, l |
793 |
|
|
DO J = I, m |
794 |
|
|
DLM(I,J) = LS*I*X*PLM(I, J)/XS + (J+I)*(J-I+1.0D0)/XQ*PLM(I-1, J) |
795 |
|
|
end DO |
796 |
|
|
end DO |
797 |
|
|
|
798 |
|
|
RETURN |
799 |
|
|
END SUBROUTINE Associated_Legendre |
800 |
gezelter |
1314 |
|
801 |
|
|
|
802 |
gezelter |
1360 |
subroutine Orthogonal_Polynomial(x, m, function_type, pl, dpl) |
803 |
|
|
|
804 |
|
|
! Purpose: Compute orthogonal polynomials: Tn(x) or Un(x), |
805 |
|
|
! or Ln(x) or Hn(x), and their derivatives |
806 |
|
|
! Input : function_type --- Function code |
807 |
|
|
! =1 for Chebyshev polynomial Tn(x) |
808 |
|
|
! =2 for Chebyshev polynomial Un(x) |
809 |
|
|
! =3 for Laguerre polynomial Ln(x) |
810 |
|
|
! =4 for Hermite polynomial Hn(x) |
811 |
|
|
! n --- Order of orthogonal polynomials |
812 |
|
|
! x --- Argument of orthogonal polynomials |
813 |
|
|
! Output: PL(n) --- Tn(x) or Un(x) or Ln(x) or Hn(x) |
814 |
|
|
! DPL(n)--- Tn'(x) or Un'(x) or Ln'(x) or Hn'(x) |
815 |
|
|
! |
816 |
|
|
! adapted from the routines in |
817 |
|
|
! COMPUTATION OF SPECIAL FUNCTIONS by Shanjie Zhang and Jianming Jin |
818 |
|
|
! ISBN 0-471-11963-6 |
819 |
|
|
! |
820 |
|
|
! The original Fortran77 codes can be found here: |
821 |
|
|
! http://iris-lee3.ece.uiuc.edu/~jjin/routines/routines.html |
822 |
|
|
|
823 |
|
|
real(kind=8), intent(in) :: x |
824 |
|
|
integer, intent(in):: m |
825 |
|
|
integer, intent(in):: function_type |
826 |
|
|
real(kind=8), dimension(0:m), intent(inout) :: pl, dpl |
827 |
|
|
|
828 |
|
|
real(kind=8) :: a, b, c, y0, y1, dy0, dy1, yn, dyn |
829 |
|
|
integer :: k |
830 |
gezelter |
1317 |
|
831 |
gezelter |
1360 |
A = 2.0D0 |
832 |
|
|
B = 0.0D0 |
833 |
|
|
C = 1.0D0 |
834 |
|
|
Y0 = 1.0D0 |
835 |
|
|
Y1 = 2.0D0*X |
836 |
|
|
DY0 = 0.0D0 |
837 |
|
|
DY1 = 2.0D0 |
838 |
|
|
PL(0) = 1.0D0 |
839 |
|
|
PL(1) = 2.0D0*X |
840 |
|
|
DPL(0) = 0.0D0 |
841 |
|
|
DPL(1) = 2.0D0 |
842 |
|
|
IF (function_type.EQ.CHEBYSHEV_TN) THEN |
843 |
|
|
Y1 = X |
844 |
|
|
DY1 = 1.0D0 |
845 |
|
|
PL(1) = X |
846 |
|
|
DPL(1) = 1.0D0 |
847 |
|
|
ELSE IF (function_type.EQ.LAGUERRE) THEN |
848 |
|
|
Y1 = 1.0D0-X |
849 |
|
|
DY1 = -1.0D0 |
850 |
|
|
PL(1) = 1.0D0-X |
851 |
|
|
DPL(1) = -1.0D0 |
852 |
|
|
ENDIF |
853 |
|
|
DO K = 2, m |
854 |
|
|
IF (function_type.EQ.LAGUERRE) THEN |
855 |
|
|
A = -1.0D0/K |
856 |
|
|
B = 2.0D0+A |
857 |
|
|
C = 1.0D0+A |
858 |
|
|
ELSE IF (function_type.EQ.HERMITE) THEN |
859 |
|
|
C = 2.0D0*(K-1.0D0) |
860 |
|
|
ENDIF |
861 |
|
|
YN = (A*X+B)*Y1-C*Y0 |
862 |
|
|
DYN = A*Y1+(A*X+B)*DY1-C*DY0 |
863 |
|
|
PL(K) = YN |
864 |
|
|
DPL(K) = DYN |
865 |
|
|
Y0 = Y1 |
866 |
|
|
Y1 = YN |
867 |
|
|
DY0 = DY1 |
868 |
|
|
DY1 = DYN |
869 |
|
|
end DO |
870 |
|
|
RETURN |
871 |
|
|
|
872 |
|
|
end subroutine Orthogonal_Polynomial |
873 |
|
|
|
874 |
gezelter |
1317 |
end module shapes |