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**s/r prever - prepares projection matrix for the vertical
* exclusively for pseudo-staggered model
* NK-th mode = computational mode
*
#include "model_macros_f.h"
*
subroutine prever( F_eval_8, F_evec_8, F_wk1_8, F_wk2_8, 1,1
& F_z_8, F_hz_8, F_nk, KDIM )
#include "impnone.cdk"
*
integer F_nk, KDIM
real*8 F_eval_8(*), F_evec_8(KDIM,*), F_wk1_8(KDIM,*), F_wk2_8(*),
% F_z_8(KDIM), F_hz_8(KDIM)
*
*author jean cote - 1990
*
*revision
* v2_00 - Desgagne M. - initial MPI version (from prever v1_03)
* v2_30 - Edouard S. - replace Schm_elast_L by Schm_cptop_L
*
*arguments
* Name I/O Description
*----------------------------------------------------------------
* F_eval_8 O - eigenvalues
* F_evec_8 O - eigenvector matrix
* F_wk1_8 - work field
* F_wk2_8 - work field
* F_z_8 I - vertical levels
* F_hz_8 I - distance between vertical levels
* F_nk I - number of vertical levels
*
*implicits
#include "dcst.cdk"
#include "schm.cdk"
#include "cstv.cdk"
*
integer i, j
real*8 pds, pdt, pdsc, pdordr
*
**
*
pdt = 0.25
pdordr = -1.0
*
do 20 j=1,F_nk
*
do i=1,j-2
F_evec_8(i,j) = 0.0
F_wk1_8(i,j) = 0.0
end do
*
i = j - 1
if ( i.gt.0 ) then
pds = (F_z_8(i+1) + F_z_8(i))/2.
pds = pds*pds
F_evec_8(i,j) = - pds/F_hz_8(i)
F_wk1_8(i,j) = pdt * F_hz_8(i)
endif
*
i = j
if ( i-1.gt.0 .and. i.lt.F_nk ) then
pds = (F_z_8(i+1) + F_z_8(i))/2.
pdsc= (F_z_8(i) + F_z_8(i-1))/2.
pds = pds*pds
pdsc= pdsc*pdsc
F_evec_8(i,j) = ( pdsc/F_hz_8(i-1) + pds/F_hz_8(i) )
F_wk1_8(i,j) = pdt * ( F_hz_8(i-1) + F_hz_8(i) )
else if ( i.eq.1 ) then
pds = (F_z_8(i+1) + F_z_8(i))/2.
pds = pds*pds
F_evec_8(i,j) = pds/F_hz_8(i)
F_wk1_8(i,j) = pdt * F_hz_8(i)
else if ( i.eq.F_nk ) then
pds = (F_z_8(i) + F_z_8(i-1))/2.
pds = pds*pds
F_evec_8(i,j) = pds/F_hz_8(i-1)
F_wk1_8(i,j) = pdt * F_hz_8(i-1)
endif
20 continue
* Apply vertical boundary conditions
* ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
F_evec_8(F_nk,F_nk) = F_evec_8(F_nk,F_nk) + Dcst_cappa_8*F_z_8(F_nk)
if (.not. Schm_cptop_L) then
F_evec_8(1,1) = F_evec_8(1,1) - Dcst_cappa_8*F_z_8(1)
elseif (.not. Schm_hydro_L) then
pdsc = Schm_nonhy_8 * Dcst_rgasd_8*Cstv_tstr_8
% /(Dcst_grav_8 *Cstv_tau_8 )**2
F_evec_8(1,1) = F_evec_8(1,1) + pdsc*F_z_8(1)
endif
*
* since A and B are singular, the singularity is lifted by
* transforming the original problem into:
*
* BX = 1/(lambda + s) * (A + sB)X
*
pds = 0.0
do i=1,F_nk-1
pdsc = (F_z_8(i+1) + F_z_8(i))/2.
pds = pds + F_hz_8(i)/pdsc
end do
*
pds = ( float(2*F_nk-2)/pds ) ** 2
*
do j=1,F_nk
do i=1,j
F_evec_8(i,j) = F_evec_8(i,j) + pds * F_wk1_8(i,j)
end do
end do
call geneigl( F_eval_8, F_wk1_8, F_evec_8, F_wk2_8, pdordr,
% 1, F_nk, KDIM, 3*F_nk-1)
*
* recover the eigenvalues lambda(i) from r(i) = 1/(lambda(i) + s)
* and normalize the eigenvectors
*
do j=1,F_nk
if ( j.eq.F_nk ) then
pdt = 1.0
F_eval_8(j) = -1.0e38
else
pdt = 1.0/sqrt( F_eval_8(j) )
F_eval_8(j) = (pds - 1.0/F_eval_8(j))
endif
do i=1,F_nk
F_evec_8(i,j) = pdt * F_wk1_8(i,j)
end do
end do
*
return
end