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gyacomo/src/time_integration_mod.F90
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time_integration_mod.F90
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MODULE time_integration
USE prec_const
IMPLICIT NONE
PRIVATE
INTEGER, PUBLIC, PROTECTED :: ntimelevel=4 ! Total number of time levels required by the numerical scheme
INTEGER, PUBLIC, PROTECTED :: updatetlevel ! Current time level to be updated
real(dp),PUBLIC,PROTECTED,DIMENSION(:,:),ALLOCATABLE :: A_E,A_I
real(dp),PUBLIC,PROTECTED,DIMENSION(:),ALLOCATABLE :: b_E,b_Es,b_I
real(dp),PUBLIC,PROTECTED,DIMENSION(:),ALLOCATABLE :: c_E,c_I !Coeff for Expl/Implic time integration in case of time dependent RHS (i.e. dy/dt = f(y,t)) see Baptiste Frei CSE Rapport 06/17
character(len=10),PUBLIC,PROTECTED :: numerical_scheme='RK4'
PUBLIC :: set_updatetlevel, time_integration_readinputs, time_integration_outputinputs
CONTAINS
SUBROUTINE set_updatetlevel(new_updatetlevel)
INTEGER, INTENT(in) :: new_updatetlevel
updatetlevel = new_updatetlevel
END SUBROUTINE set_updatetlevel
SUBROUTINE time_integration_readinputs
! Read the input parameters
USE prec_const
USE basic, ONLY : lu_in
IMPLICIT NONE
NAMELIST /TIME_INTEGRATION_PAR/ numerical_scheme
READ(lu_in,time_integration_par)
CALL set_numerical_scheme
END SUBROUTINE time_integration_readinputs
SUBROUTINE time_integration_outputinputs(fidres, str)
! Write the input parameters to the results_xx.h5 file
USE prec_const
USE futils, ONLY: attach
IMPLICIT NONE
INTEGER, INTENT(in) :: fidres
CHARACTER(len=256), INTENT(in) :: str
CALL attach(fidres, TRIM(str), "numerical_scheme", numerical_scheme)
END SUBROUTINE time_integration_outputinputs
SUBROUTINE set_numerical_scheme
! Initialize Butcher coefficient of numerical_scheme
use basic
IMPLICIT NONE
SELECT CASE (numerical_scheme)
CASE ('RK4')
CALL RK4
CASE ('SSPx_RK3')
CALL SSPx_RK3
CASE ('SSPx_RK2')
CALL SSPx_RK2
CASE ('DOPRI5')
CALL DOPRI5
CASE DEFAULT
IF (my_id .EQ. 0) WRITE(*,*) 'Cannot initialize time integration scheme. Name invalid.'
END SELECT
IF (my_id .EQ. 0) WRITE(*,*) " Time integration with ", numerical_scheme
END SUBROUTINE set_numerical_scheme
SUBROUTINE RK4
! Butcher coeff for RK4 (default)
USE basic
USE prec_const
IMPLICIT NONE
INTEGER,PARAMETER :: nbstep = 4
CALL allocate_array_dp1(c_E,1,nbstep)
CALL allocate_array_dp1(b_E,1,nbstep)
CALL allocate_array_dp2(A_E,1,nbstep,1,nbstep)
ntimelevel = 4
c_E(1) = 0.0_dp
c_E(2) = 1.0_dp/2.0_dp
c_E(3) = 1.0_dp/2.0_dp
c_E(4) = 1.0_dp
b_E(1) = 1.0_dp/6.0_dp
b_E(2) = 1.0_dp/3.0_dp
b_E(3) = 1.0_dp/3.0_dp
b_E(4) = 1.0_dp/6.0_dp
A_E(2,1) = 1.0_dp/2.0_dp
A_E(3,2) = 1.0_dp/2.0_dp
A_E(4,3) = 1.0_dp
END SUBROUTINE RK4
SUBROUTINE SSPx_RK3
! Butcher coeff for modified strong stability preserving RK3
! used in GX (Hammett 2022, Mandell et al. 2022)
USE basic
USE prec_const
IMPLICIT NONE
INTEGER,PARAMETER :: nbstep = 3
REAL(dp) :: a1, a2, a3, w1, w2, w3
a1 = (1._dp/6._dp)**(1._dp/3._dp)! (1/6)^(1/3)
! a1 = 0.5503212081491044571635029569733887910843_dp ! (1/6)^(1/3)
a2 = a1
a3 = a1
w1 = 0.5_dp*(-1._dp + SQRT( 9._dp - 2._dp * 6._dp**(2._dp/3._dp))) ! (-1 + sqrt(9-2*6^(2/3)))/2
! w1 = 0.2739744023885328783052273138309828937054_dp ! (sqrt(9-2*6^(2/3))-1)/2
w2 = 0.5_dp*(-1._dp + 6._dp**(2._dp/3._dp) - SQRT(9._dp - 2._dp * 6._dp**(2._dp/3._dp))) ! (6^(2/3)-1-sqrt(9-2*6^(2/3)))/2
! w2 = 0.3769892220587804931852815570891834795475_dp ! (6^(2/3)-1-sqrt(9-2*6^(2/3)))/2
w3 = 1._dp/a1 - w2 * (1._dp + w1)
! w3 = 1.3368459739528868457369981115334667265415_dp
CALL allocate_array_dp1(c_E,1,nbstep)
CALL allocate_array_dp1(b_E,1,nbstep)
CALL allocate_array_dp2(A_E,1,nbstep,1,nbstep)
ntimelevel = 3
c_E(1) = 0.0_dp
c_E(2) = 1.0_dp/2.0_dp
c_E(3) = 1.0_dp/2.0_dp
b_E(1) = a1 * (w1*w2 + w3)
b_E(2) = a2 * w2
b_E(3) = a3
A_E(2,1) = a1
A_E(3,1) = a1 * w1
A_E(3,2) = a2
END SUBROUTINE SSPx_RK3
SUBROUTINE SSPx_RK2
! Butcher coeff for modified strong stability preserving RK2
! used in GX (Hammett 2022, Mandell et al. 2022)
USE basic
USE prec_const
IMPLICIT NONE
INTEGER,PARAMETER :: nbstep = 2
REAL(dp) :: alpha, beta
alpha = 1._dp/SQRT(2._dp)
beta = SQRT(2._dp) - 1._dp
CALL allocate_array_dp1(c_E,1,nbstep)
CALL allocate_array_dp1(b_E,1,nbstep)
CALL allocate_array_dp2(A_E,1,nbstep,1,nbstep)
ntimelevel = 2
c_E(1) = 0.0_dp
c_E(2) = 1.0_dp/2.0_dp
b_E(1) = alpha*beta/2._dp
b_E(2) = alpha/2._dp
A_E(2,1) = alpha
END SUBROUTINE SSPx_RK2
SUBROUTINE DOPRI5
! Butcher coeff for DOPRI5 --> Stiffness detection
! DOPRI5 used for stiffness detection.
! 5 order method/7 stages
USE basic
IMPLICIT NONE
INTEGER,PARAMETER :: nbstep =7
CALL allocate_array_dp1(c_E,1,nbstep)
CALL allocate_array_dp1(b_E,1,nbstep)
CALL allocate_array_dp2(A_E,1,nbstep,1,nbstep)
ntimelevel = 7
!
c_E(1) = 0._dp
c_E(2) = 1.0_dp/5.0_dp
c_E(3) = 3.0_dp /10.0_dp
c_E(4) = 4.0_dp/5.0_dp
c_E(5) = 8.0_dp/9.0_dp
c_E(6) = 1.0_dp
c_E(7) = 1.0_dp
!
A_E(2,1) = 1.0_dp/5.0_dp
A_E(3,1) = 3.0_dp/40.0_dp
A_E(3,2) = 9.0_dp/40.0_dp
A_E(4,1) = 44.0_dp/45.0_dp
A_E(4,2) = -56.0_dp/15.0_dp
A_E(4,3) = 32.0_dp/9.0_dp
A_E(5,1 ) = 19372.0_dp/6561.0_dp
A_E(5,2) = -25360.0_dp/2187.0_dp
A_E(5,3) = 64448.0_dp/6561.0_dp
A_E(5,4) = -212.0_dp/729.0_dp
A_E(6,1) = 9017.0_dp/3168.0_dp
A_E(6,2)= -355.0_dp/33.0_dp
A_E(6,3) = 46732.0_dp/5247.0_dp
A_E(6,4) = 49.0_dp/176.0_dp
A_E(6,5) = -5103.0_dp/18656.0_dp
A_E(7,1) = 35.0_dp/384.0_dp
A_E(7,3) = 500.0_dp/1113.0_dp
A_E(7,4) = 125.0_dp/192.0_dp
A_E(7,5) = -2187.0_dp/6784.0_dp
A_E(7,6) = 11.0_dp/84.0_dp
!
b_E(1) = 35.0_dp/384.0_dp
b_E(2) = 0._dp
b_E(3) = 500.0_dp/1113.0_dp
b_E(4) = 125.0_dp/192.0_dp
b_E(5) = -2187.0_dp/6784.0_dp
b_E(6) = 11.0_dp/84.0_dp
b_E(7) = 0._dp
!
END SUBROUTINE DOPRI5
SUBROUTINE DOPRI5_ADAPT
! Butcher coeff for DOPRI5 --> Stiffness detection
! DOPRI5 used for stiffness detection.
! 5 order method/7 stages
USE basic
IMPLICIT NONE
INTEGER,PARAMETER :: nbstep =7
CALL allocate_array_dp1(c_E,1,nbstep)
CALL allocate_array_dp1(b_E,1,nbstep)
CALL allocate_array_dp1(b_Es,1,nbstep)
CALL allocate_array_dp2(A_E,1,nbstep,1,nbstep)
ntimelevel = 7
!
c_E(1) = 0._dp
c_E(2) = 1.0_dp/5.0_dp
c_E(3) = 3.0_dp /10.0_dp
c_E(4) = 4.0_dp/5.0_dp
c_E(5) = 8.0_dp/9.0_dp
c_E(6) = 1.0_dp
c_E(7) = 1.0_dp
!
A_E(2,1) = 1.0_dp/5.0_dp
A_E(3,1) = 3.0_dp/40.0_dp
A_E(3,2) = 9.0_dp/40.0_dp
A_E(4,1) = 44.0_dp/45.0_dp
A_E(4,2) = -56.0_dp/15.0_dp
A_E(4,3) = 32.0_dp/9.0_dp
A_E(5,1 ) = 19372.0_dp/6561.0_dp
A_E(5,2) = -25360.0_dp/2187.0_dp
A_E(5,3) = 64448.0_dp/6561.0_dp
A_E(5,4) = -212.0_dp/729.0_dp
A_E(6,1) = 9017.0_dp/3168.0_dp
A_E(6,2)= -355.0_dp/33.0_dp
A_E(6,3) = 46732.0_dp/5247.0_dp
A_E(6,4) = 49.0_dp/176.0_dp
A_E(6,5) = -5103.0_dp/18656.0_dp
A_E(7,1) = 35.0_dp/384.0_dp
A_E(7,3) = 500.0_dp/1113.0_dp
A_E(7,4) = 125.0_dp/192.0_dp
A_E(7,5) = -2187.0_dp/6784.0_dp
A_E(7,6) = 11.0_dp/84.0_dp
!
b_E(1) = 35.0_dp/384.0_dp
b_E(2) = 0._dp
b_E(3) = 500.0_dp/1113.0_dp
b_E(4) = 125.0_dp/192.0_dp
b_E(5) = -2187.0_dp/6784.0_dp
b_E(6) = 11.0_dp/84.0_dp
b_E(7) = 0._dp
!
b_Es(1) = 5179.0_dp/57600.0_dp
b_Es(2) = 0._dp
b_Es(3) = 7571.0_dp/16695.0_dp
b_Es(4) = 393.0_dp/640.0_dp
b_Es(5) = -92097.0_dp/339200.0_dp
b_Es(6) = 187.0_dp/2100.0_dp
b_Es(7) = 1._dp/40._dp
!
END SUBROUTINE DOPRI5_ADAPT
END MODULE time_integration
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