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gyacomo/src/calculus_mod.F90
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calculus_mod.F90
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MODULE calculus
! Routine to evaluate gradients, interpolation schemes and integrals
USE basic
USE prec_const
USE grid
USE utility
IMPLICIT NONE
REAL(dp), dimension(-2:2) :: dz_usu = &
(/ onetwelfth, -twothird, &
0._dp, &
twothird, -onetwelfth /) ! fd4 centered stencil
REAL(dp), dimension(-2:1) :: dz_o2e = &
(/ onetwentyfourth,-nineeighths, nineeighths,-onetwentyfourth /) ! fd4 odd to even stencil
REAL(dp), dimension(-1:2) :: dz_e2o = &
(/ onetwentyfourth,-nineeighths, nineeighths,-onetwentyfourth /) ! fd4 odd to even stencil
REAL(dp), dimension(-2:2) :: dz2_usu = &
(/-1.0_dp/12.0_dp, 4.0_dp/3.0_dp, -5.0_dp/2.0_dp, 4.0_dp/3.0_dp, -1.0_dp/12.0_dp /)! 2th derivative, 4th order (for parallel hypdiff)
REAL(dp), dimension(-2:2) :: dz4_usu = &
(/ 1._dp, -4._dp, 6._dp, -4._dp, 1._dp /)* 0.0625 ! 4th derivative, 2nd order (for parallel hypdiff)
PUBLIC :: simpson_rule_z, interp_z, grad_z, grad_z4
CONTAINS
SUBROUTINE grad_z(target,f,ddzf)
implicit none
! Compute the periodic boundary condition 4 points centered finite differences
! formula among staggered grid or not.
! not staggered : the derivative results must be on the same grid as the field
! staggered : the derivative is computed from a grid to the other
INTEGER, INTENT(IN) :: target
COMPLEX(dp),dimension(izgs:izge), intent(in) :: f
COMPLEX(dp),dimension( izs:ize ), intent(out) :: ddzf
IF(Nz .GT. 3) THEN ! Cannot apply four points stencil on less than four points grid
IF(SG) THEN
IF(TARGET .EQ. 0) THEN
CALL grad_z_o2e(f,ddzf)
ELSE
CALL grad_z_e2o(f,ddzf)
ENDIF
ELSE ! No staggered grid -> usual centered finite differences
DO iz = izs,ize
ddzf(iz) = dz_usu(-2)*f(iz-2) + dz_usu(-1)*f(iz-1) &
+dz_usu( 1)*f(iz+1) + dz_usu( 2)*f(iz+2)
ENDDO
ddzf(:) = ddzf(:) * inv_deltaz
ENDIF
ELSE
ddzf = 0._dp
ENDIF
CONTAINS
SUBROUTINE grad_z_o2e(fo,ddzfe) ! Paruta 2018 eq (27)
! gives the gradient of a field from the odd grid to the even one
implicit none
COMPLEX(dp),dimension(izgs:izge), intent(in) :: fo
COMPLEX(dp),dimension( izs:ize ), intent(out) :: ddzfe !
DO iz = izs,ize
ddzfe(iz) = dz_o2e(-2)*fo(iz-2) + dz_o2e(-1)*fo(iz-1) &
+dz_o2e( 0)*fo(iz ) + dz_o2e( 1)*fo(iz+1)
ENDDO
ddzfe(:) = ddzfe(:) * inv_deltaz
END SUBROUTINE grad_z_o2e
SUBROUTINE grad_z_e2o(fe,ddzfo) ! n2v for Paruta 2018 eq (28)
! gives the gradient of a field from the even grid to the odd one
implicit none
COMPLEX(dp),dimension(izgs:izge), intent(in) :: fe
COMPLEX(dp),dimension( izs:ize ), intent(out) :: ddzfo
DO iz = izs,ize
ddzfo(iz) = dz_e2o(-1)*fe(iz-1) + dz_e2o(0)*fe(iz ) &
+dz_e2o( 1)*fe(iz+1) + dz_e2o(2)*fe(iz+2)
ENDDO
ddzfo(:) = ddzfo(:) * inv_deltaz
END SUBROUTINE grad_z_e2o
END SUBROUTINE grad_z
SUBROUTINE grad_z2(f,ddz2f)
implicit none
! Compute the second order fourth derivative for periodic boundary condition
COMPLEX(dp),dimension(izgs:izge), intent(in) :: f
COMPLEX(dp),dimension( izs:ize ), intent(out) :: ddz2f
IF(Nz .GT. 3) THEN ! Cannot apply four points stencil on less than four points grid
DO iz = izs,ize
ddz2f(iz) = dz2_usu(-2)*f(iz-2) + dz2_usu(-1)*f(iz-1) &
+dz2_usu( 0)*f(iz )&
+dz2_usu( 1)*f(iz+1) + dz2_usu( 2)*f(iz+2)
ENDDO
ELSE
ddz2f = 0._dp
ENDIF
ddz2f = ddz2f * inv_deltaz**2
END SUBROUTINE grad_z2
SUBROUTINE grad_z4(f,ddz4f)
implicit none
! Compute the second order fourth derivative for periodic boundary condition
COMPLEX(dp),dimension(izgs:izge), intent(in) :: f
COMPLEX(dp),dimension( izs:ize ), intent(out) :: ddz4f
IF(Nz .GT. 3) THEN ! Cannot apply four points stencil on less than four points grid
DO iz = izs,ize
ddz4f(iz) = dz4_usu(-2)*f(iz-2) + dz4_usu(-1)*f(iz-1) &
+dz4_usu( 1)*f(iz+1) + dz4_usu( 2)*f(iz+2)
ENDDO
ELSE
ddz4f = 0._dp
ENDIF
ddz4f = ddz4f * inv_deltaz**4
END SUBROUTINE grad_z4
SUBROUTINE interp_z(target,f_in,f_out)
! Function meant to interpolate one field defined on a even/odd z into
! the other odd/even z grid.
! If Staggered Grid flag (SG) is false, returns identity
implicit none
INTEGER, intent(in) :: target ! target grid : 0 for even grid, 1 for odd
COMPLEX(dp),dimension(izgs:izge), intent(in) :: f_in
COMPLEX(dp),dimension( izs:ize ), intent(out) :: f_out !
IF(SG) THEN
IF(target .EQ. 0) THEN
CALL interp_o2e_z(f_in,f_out)
ELSE
CALL interp_e2o_z(f_in,f_out)
ENDIF
ELSE ! No staggered grid -> identity
f_out(izs:ize) = f_in(izs:ize)
ENDIF
CONTAINS
SUBROUTINE interp_o2e_z(fo,fe)
! gives the value of a field from the odd grid to the even one
implicit none
COMPLEX(dp),dimension(izgs:izge), intent(in) :: fo
COMPLEX(dp),dimension( izs:ize ), intent(out) :: fe !
! 4th order interp
DO iz = izs,ize
fe(iz) = onesixteenth * (-fo(iz-2) + 9._dp*(fo(iz-1) + fo(iz)) - fo(iz+1))
ENDDO
END SUBROUTINE interp_o2e_z
SUBROUTINE interp_e2o_z(fe,fo)
! gives the value of a field from the even grid to the odd one
implicit none
COMPLEX(dp),dimension(izgs:izge), intent(in) :: fe
COMPLEX(dp),dimension( izs:ize ), intent(out) :: fo
! 4th order interp
DO iz = izs,ize
fo(iz) = onesixteenth * (-fe(iz-1) + 9._dp*(fe(iz) + fe(iz+1)) - fe(iz+2))
ENDDO
END SUBROUTINE interp_e2o_z
END SUBROUTINE interp_z
SUBROUTINE simpson_rule_z(f,intf)
! integrate f(z) over z using the simpon's rule. Assume periodic boundary conditions (f(ize+1) = f(izs))
!from molix BJ Frei
implicit none
complex(dp),dimension(izs:ize), intent(in) :: f
COMPLEX(dp), intent(out) :: intf
COMPLEX(dp) :: buffer, local_int
INTEGER :: root, i_
IF(Nz .EQ. 1) THEN !2D zpinch simulations
intf = f(izs)
ELSE !3D fluxtube
IF(mod(Nz,2) .ne. 0 ) THEN
ERROR STOP 'Simpson rule: Nz must be an even number !!!!'
ENDIF
! Buil local sum using the weights of composite Simpson's rule
local_int = 0._dp
DO iz = izs,ize
local_int = local_int + zweights_SR(iz)*f(iz)
ENDDO
buffer = local_int
root = 0
!Gather manually among the rank_z=0 processes and perform the sum
intf = 0._dp
IF (num_procs_z .GT. 1) THEN
!! Everyone sends its local_sum to root = 0
IF (rank_z .NE. root) THEN
CALL MPI_SEND(buffer, 1 , MPI_DOUBLE_COMPLEX, root, 5678, comm_z, ierr)
ELSE
! Recieve from all the other processes
DO i_ = 0,num_procs_z-1
IF (i_ .NE. rank_z) &
CALL MPI_RECV(buffer, 1 , MPI_DOUBLE_COMPLEX, i_, 5678, comm_z, MPI_STATUS_IGNORE, ierr)
intf = intf + buffer
ENDDO
ENDIF
CALL manual_0D_bcast(intf)
ELSE
intf = local_int
ENDIF
intf = onethird*deltaz*intf
ENDIF
END SUBROUTINE simpson_rule_z
END MODULE calculus
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