Returns an rk_scheme instance describing the scheme represented by the passed variant type.
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| type(rk_scheme_id_type), | intent(in) | :: | variant |
type(rk_scheme_type) function get_rk_scheme(variant) result(scheme)
use mp, only: mp_abort, proc0
implicit none
type(rk_scheme_id_type), intent(in) :: variant
integer :: validity
scheme%name = variant%name
select case(variant%id)
case(rk_dopri%id)
scheme%number_of_stages = 7
scheme%order = 5
allocate(scheme%lower_order_coeffs, source = &
[5179/57600.0, 0.0,7571/16695.0, 393/640.0, -92097/339200.0, 187/2100.0, 1/40.0])
scheme%high_order_coeffs = [35/384.0, 0.0, 500/1113.0, 125/192.0, -2187/6784.0, 11/84.0, 0.0]
scheme%time_points = [0.0, 1/5.0, 3/10.0, 4/5.0, 8/9.0, 1.0, 1.0]
scheme%follow_high_order = .true.
allocate(scheme%coeffs(scheme%number_of_stages - 1, scheme%number_of_stages))
scheme%coeffs = 0.0
scheme%coeffs(:1, 2) = [1/5.0]
scheme%coeffs(:2, 3) = [3/40.0, 9/40.0]
scheme%coeffs(:3, 4) = [44/45.0, -56/15.0, 32/9.0]
scheme%coeffs(:4, 5) = [19372/6561.0, -25360/2187.0, 64448/6561.0, -212/729.0]
scheme%coeffs(:5, 6) = [9017/3168.0, -355/33.0, 46732/5247.0, 49/176.0, -5103/18656.0]
scheme%coeffs(:6, 7) = [35/384.0, 0.0, 500/1113.0, 125/192.0, -2187/6784.0, 11/84.0]
case(rk_f45%id)
scheme%number_of_stages = 6
scheme%order = 5
allocate(scheme%lower_order_coeffs, source = &
[25/216.0, 0.0, 1408/2565.0, 2197/4104.0, -1/5.0, 0.0])
scheme%high_order_coeffs = [16/135.0, 0.0, 6656/12825.0, 28561/56430.0, -9/50.0, 2/55.0]
scheme%time_points = [0.0, 1/4.0, 3/8.0, 12/13.0, 1.0, 1/2.0]
scheme%follow_high_order = .true.
allocate(scheme%coeffs(scheme%number_of_stages - 1, scheme%number_of_stages))
scheme%coeffs = 0.0
scheme%coeffs(:1, 2) = [1/4.0]
scheme%coeffs(:2, 3) = [3/32.0, 9/32.0]
scheme%coeffs(:3, 4) = [1932/2197.0, -7200/2197.0, 7296/2197.0]
scheme%coeffs(:4, 5) = [439/216.0, -8.0, 3680/513.0, -845/4104.0]
scheme%coeffs(:5, 6) = [-8/27.0, 2.0, -3544/2565.0, 1859/4104.0, -11/40.0]
case(rk_cashkarp%id)
scheme%number_of_stages = 6
scheme%order = 5
allocate(scheme%lower_order_coeffs, source = &
[2825/27648.0, 0.0, 18575/48384.0, 13525/55296.0, 277/14336.0, 1/4.0])
scheme%high_order_coeffs = [37/378.0, 0.0, 250/621.0, 125/594.0, 0.0, 512/1771.0]
scheme%time_points = [0.0, 1/5.0, 3/10.0, 3/5.0, 1.0, 7/8.0]
scheme%follow_high_order = .true.
allocate(scheme%coeffs(scheme%number_of_stages - 1, scheme%number_of_stages))
scheme%coeffs = 0.0
scheme%coeffs(:1, 2) = [1/5.0]
scheme%coeffs(:2, 3) = [3/40.0, 9/40.0]
scheme%coeffs(:3, 4) = [3/10.0, -9/10.0, 6/5.0]
scheme%coeffs(:4, 5) = [-11/54.0, 5/2.0, -70/27.0, 35/27.0]
scheme%coeffs(:5, 6) = [1631/55296.0, 175/512.0, 575/13824.0, 44275/110592.0, 253/4096.0]
case(rk_heun%id)
scheme%number_of_stages = 2
scheme%order = 2
allocate(scheme%lower_order_coeffs, source = &
[1.0, 0.0])
scheme%high_order_coeffs = [1/2.0, 1/2.0]
scheme%time_points = [0.0, 1.0]
scheme%follow_high_order = .true.
allocate(scheme%coeffs(scheme%number_of_stages - 1, scheme%number_of_stages))
scheme%coeffs = 0.0
scheme%coeffs(:1, 2) = [1.0]
case(rk_ralston%id)
scheme%number_of_stages = 2
scheme%order = 2
allocate(scheme%lower_order_coeffs, source = &
[1.0, 0.0])
scheme%high_order_coeffs = [1/4.0, 3/4.0]
scheme%time_points = [0.0, 2/3.0]
scheme%follow_high_order = .true.
allocate(scheme%coeffs(scheme%number_of_stages - 1, scheme%number_of_stages))
scheme%coeffs = 0.0
scheme%coeffs(:1, 2) = [2/3.0]
case(rk_midpoint%id)
scheme%number_of_stages = 2
scheme%order = 2
allocate(scheme%lower_order_coeffs, source = &
[1.0, 0.0])
scheme%high_order_coeffs = [0.0, 1.0]
scheme%time_points = [0.0, 1/2.0]
scheme%follow_high_order = .true.
allocate(scheme%coeffs(scheme%number_of_stages - 1, scheme%number_of_stages))
scheme%coeffs = 0.0
scheme%coeffs(:1, 2) = [1/2.0]
case(rk_bs23%id)
scheme%number_of_stages = 4
scheme%order = 3
allocate(scheme%lower_order_coeffs, source = &
[7/24.0, 1/4.0, 1/3.0, 1/8.0])
scheme%high_order_coeffs = [2/9.0, 1/3.0, 4/9.0, 0.0]
scheme%time_points = [0.0, 1/2.0, 3/4.0, 1.0]
scheme%follow_high_order = .true.
allocate(scheme%coeffs(scheme%number_of_stages - 1, scheme%number_of_stages))
scheme%coeffs = 0.0
scheme%coeffs(:1, 2) = [1/2.0]
scheme%coeffs(:2, 3) = [0.0, 3/4.0]
scheme%coeffs(:3, 4) = [2/9.0, 1/3.0, 4/9.0]
case(rk_bs45%id)
scheme%number_of_stages = 8
scheme%order = 5
allocate(scheme%lower_order_coeffs, source = &
[6059/80640.0, 0.0, 8559189/30983680.0, 26411/124800.0, &
-927/89600.0, 443/1197.0, 7267/94080.0, 0.0])
scheme%high_order_coeffs = [587/8064.0, 0.0, 4440339/15491840.0, 24353/124800.0, &
387/44800.0, 2152/5985.0, 7267/94080.0, 0.0]
scheme%time_points = [0.0, 1/6.0, 2/9.0, 3/7.0, 2/3.0, 3/4.0, 1.0, 1.0]
scheme%follow_high_order = .true.
allocate(scheme%coeffs(scheme%number_of_stages - 1, scheme%number_of_stages))
scheme%coeffs = 0.0
scheme%coeffs(:1, 2) = [1/6.0]
scheme%coeffs(:2, 3) = [2/27.0, 4/27.0]
scheme%coeffs(:3, 4) = [183/1372.0, -162/343.0, 1053/1372.0]
scheme%coeffs(:4, 5) = [68/297.0, -4/11.0, 42/143.0, 1960/3861.0]
scheme%coeffs(:5, 6) = [597/22528.0, 81/352.0, 63099/585728.0, 58653/366080.0, &
4617/20480.0]
scheme%coeffs(:6, 7) = [174197/959244.0, -30942/79937.0, 8152137/19744439.0, &
666106/1039181.0, -29421/29068.0, 482048/414219.0]
scheme%coeffs(:7, 8) = [587/8064.0, 0.0, 4440339/15491840.0, 24353/124800.0, &
387/44800.0, 2152/5985.0, 7267/94080.0]
case(rk_euler%id)
scheme%number_of_stages = 1
scheme%order = 1
allocate(scheme%lower_order_coeffs, source = &
[1.0])
scheme%high_order_coeffs = [1.0]
scheme%time_points = [0.0]
scheme%follow_high_order = .true.
allocate(scheme%coeffs(scheme%number_of_stages - 1, scheme%number_of_stages))
scheme%coeffs = 0.0
case default
call mp_abort("Invalid RK scheme passed to get_rk_scheme", .true.)
end select
validity = scheme%validate()
if (proc0 .and. (validity /= 0)) then
print*,'The RK scheme failed validity check with error code:',validity,'and scheme',scheme%name
call mp_abort("RK scheme failed validity check", .true.)
end if
end function get_rk_scheme