sll_m_time_composition.F90

Go to the documentation of this file.

! Define coefficients for composition methods of symmetric and first order methods
!
!
 
module sll_m_time_composition
 
!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
#include "sll_memory.h"
#include "sll_working_precision.h"
 
   implicit none
 
   public :: &
      sll_t_comp_coeff_sym_sym
 
   private
!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 
   type sll_t_comp_coeff_sym_sym
      sll_int32 :: order
      sll_real64, dimension(:), allocatable :: gamma  !coefficients, already symmetric
      sll_int32 :: stages
   contains
      procedure, pass(this) :: init => time_composition_sym_sym
!     procedure, pass(this) :: coeff => comp_coeff_
   end type sll_t_comp_coeff_sym_sym
 
contains
 
! function time_composition_sym_sym_stages( order)
! end function time_composition_sym_sym_stages
 
   subroutine time_composition_sym_sym(this, order, stages)
      sll_int32, intent(in) :: order, stages
      class(sll_t_comp_coeff_sym_sym), intent(inout) :: this
      sll_int32 :: idx
 
      this%order = order
      this%stages = stages
 
      allocate (this%gamma(1:stages))
      SELECT CASE (order)
      CASE (1)
         this%gamma = 1.0_f64/stages
 
         !########################################
      CASE (2)
         SELECT CASE (stages)
         CASE (3)
            this%gamma(1) = 1.3512071919596576340476878089715_f64
            this%gamma(2) = -1.7024143839193152680953756179429_f64
         END SELECT
 
         !########################################
      CASE (6)
         SELECT CASE (stages)
         CASE (7)
            this%gamma(1) = 0.78451361047755726381949763_f64
            this%gamma(2) = 0.23557321335935813368479318_f64
            this%gamma(3) = -1.17767998417887100694641568_f64
            this%gamma(4) = -1.31518632068391121888424973_f64
         CASE (9)
            this%gamma(1) = 0.39216144400731413927925056_f64
            this%gamma(2) = 0.33259913678935943859974864_f64
            this%gamma(3) = -0.70624617255763935980996482_f64
            this%gamma(4) = 0.08221359629355080023149045_f64
            this%gamma(5) = 0.79854399093482996339895035_f64
         END SELECT
 
         !###################################################
      CASE (8)
         SELECT CASE (stages)
         CASE (15)
            this%gamma(1) = 0.74167036435061295344822780_f64
            this%gamma(2) = -0.40910082580003159399730010_f64
            this%gamma(3) = 0.19075471029623837995387626_f64
            this%gamma(4) = -0.57386247111608226665638773_f64
            this%gamma(5) = 0.29906418130365592384446354_f64
            this%gamma(6) = 0.33462491824529818378495798_f64
            this%gamma(7) = 0.31529309239676659663205666_f64
            this%gamma(8) = -0.79688793935291635401978884_f64
         CASE (17)
            this%gamma(1) = 0.13020248308889008087881763_f64
            this%gamma(2) = 0.56116298177510838456196441_f64
            this%gamma(3) = -0.38947496264484728640807860_f64
            this%gamma(4) = 0.15884190655515560089621075_f64
            this%gamma(5) = -0.39590389413323757733623154_f64
            this%gamma(6) = 0.18453964097831570709183254_f64
            this%gamma(7) = 0.25837438768632204729397911_f64
            this%gamma(8) = 0.29501172360931029887096624_f64
            this%gamma(9) = -0.60550853383003451169892108_f64
         END SELECT
         !###################################################
      CASE (10)
         SELECT CASE (stages)
         CASE (35)
            this%gamma(1) = 0.07879572252168641926390768_f64
            this%gamma(2) = 0.31309610341510852776481247_f64
            this%gamma(3) = 0.02791838323507806610952027_f64
            this%gamma(4) = -0.22959284159390709415121340_f64
            this%gamma(5) = 0.13096206107716486317465686_f64
            this%gamma(6) = -0.26973340565451071434460973_f64
            this%gamma(7) = 0.07497334315589143566613711_f64
            this%gamma(8) = 0.11199342399981020488957508_f64
            this%gamma(9) = 0.36613344954622675119314812_f64
            this%gamma(10) = -0.39910563013603589787862981_f64
            this%gamma(11) = 0.10308739852747107731580277_f64
            this%gamma(12) = 0.41143087395589023782070412_f64
            this%gamma(13) = -0.00486636058313526176219566_f64
            this%gamma(14) = -0.39203335370863990644808194_f64
            this%gamma(15) = 0.05194250296244964703718290_f64
            this%gamma(16) = 0.05066509075992449633587434_f64
            this%gamma(17) = 0.04967437063972987905456880_f64
            this%gamma(18) = 0.04931773575959453791768001_f64
         END SELECT
      END SELECT
 
!symmetry
      do idx = 1, stages/2  !fortran intrinsic ceiling
         this%gamma(stages - (idx - 1)) = this%gamma(idx)
      end do
 
   end subroutine time_composition_sym_sym
 
end module sll_m_time_composition