| [3] | 1 | MODULE solpcg |
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| 2 | !!====================================================================== |
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| 3 | !! *** MODULE solfet |
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| 4 | !! Ocean solver : preconditionned conjugate gradient solver |
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| 5 | !!===================================================================== |
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| 6 | |
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| 7 | !!---------------------------------------------------------------------- |
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| 8 | !! sol_pcg : preconditionned conjugate gradient solver |
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| 9 | !!---------------------------------------------------------------------- |
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| 10 | !! * Modules used |
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| 11 | USE oce ! ocean dynamics and tracers variables |
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| 12 | USE dom_oce ! ocean space and time domain variables |
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| 13 | USE sol_oce ! ocean solver variables |
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| 14 | USE lib_mpp ! distributed memory computing |
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| 15 | USE lbclnk ! ocean lateral boundary conditions (or mpp link) |
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| [16] | 16 | USE in_out_manager ! I/O manager |
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| [3] | 17 | |
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| 18 | IMPLICIT NONE |
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| 19 | PRIVATE |
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| 20 | |
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| 21 | !! * Routine accessibility |
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| 22 | PUBLIC sol_pcg ! ??? |
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| 23 | |
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| 24 | !! * Substitutions |
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| 25 | # include "vectopt_loop_substitute.h90" |
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| 26 | !!---------------------------------------------------------------------- |
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| [247] | 27 | !!---------------------------------------------------------------------- |
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| 28 | !! OPA 9.0 , LOCEAN-IPSL (2005) |
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| [719] | 29 | !! $Header$ |
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| [247] | 30 | !! This software is governed by the CeCILL licence see modipsl/doc/NEMO_CeCILL.txt |
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| 31 | !!---------------------------------------------------------------------- |
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| [3] | 32 | CONTAINS |
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| 33 | |
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| 34 | SUBROUTINE sol_pcg( kindic ) |
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| 35 | !!---------------------------------------------------------------------- |
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| 36 | !! *** ROUTINE sol_pcg *** |
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| 37 | !! |
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| 38 | !! ** Purpose : Solve the ellipic equation for the barotropic stream |
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| [16] | 39 | !! function system (lk_dynspg_rl=T) or the transport divergence |
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| [359] | 40 | !! system (lk_dynspg_flt=T) using a diagonal preconditionned |
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| [3] | 41 | !! conjugate gradient method. |
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| 42 | !! In the former case, the barotropic stream function trend has a |
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| 43 | !! zero boundary condition along all coastlines (i.e. continent |
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| 44 | !! as well as islands) while in the latter the boundary condition |
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| 45 | !! specification is not required. |
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| 46 | !! |
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| 47 | !! ** Method : Diagonal preconditionned conjugate gradient method. |
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| 48 | !! the algorithm is multitasked. (case of 5 points matrix) |
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| 49 | !! define pa = q^-1 * a |
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| 50 | !! pgcb = q^-1 * gcb |
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| 51 | !! < . ; . >_q = ( . )^t q ( . ) |
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| 52 | !! where q is the preconditioning matrix = diagonal matrix of the |
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| 53 | !! diagonal elements of a |
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| 54 | !! Initialization: |
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| 55 | !! x(o) = gcx |
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| 56 | !! r(o) = d(o) = pgcb - pa.x(o) |
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| 57 | !! rr(o)= < r(o) , r(o) >_q |
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| 58 | !! Iteration n : |
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| 59 | !! z(n) = pa.d(n) |
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| 60 | !! alp(n) = rr(n) / < z(n) , d(n) >_q |
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| 61 | !! x(n+1) = x(n) + alp(n) d(n) |
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| 62 | !! r(n+1) = r(n) - alp(n) z(n) |
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| 63 | !! rr(n+1)= < r(n+1) , r(n+1) >_q |
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| 64 | !! bet(n) = rr(n+1) / rr(n) |
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| 65 | !! r(n+1) = r(n+1) + bet(n+1) d(n) |
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| 66 | !! Convergence test : |
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| 67 | !! rr(n+1) / < gcb , gcb >_q =< epsr |
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| 68 | !! |
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| 69 | !! ** Action : - niter : solver number of iteration done |
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| 70 | !! - res : solver residu reached |
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| 71 | !! - gcx() : solution of the elliptic system |
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| 72 | !! |
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| 73 | !! References : |
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| 74 | !! Madec et al. 1988, Ocean Modelling, issue 78, 1-6. |
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| 75 | !! |
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| 76 | !! History : |
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| 77 | !! ! 90-10 (G. Madec) Original code |
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| 78 | !! ! 91-11 (G. Madec) |
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| 79 | !! ! 93-04 (M. Guyon) loops and suppress pointers |
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| 80 | !! ! 95-09 (M. Imbard, J. Escobar) mpp exchange |
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| 81 | !! ! 96-05 (G. Madec) merge sor and pcg formulations |
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| 82 | !! ! 96-11 (A. Weaver) correction to preconditioning |
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| 83 | !! 8.5 ! 02-08 (G. Madec) F90: Free form |
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| 84 | !!---------------------------------------------------------------------- |
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| 85 | !! * Arguments |
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| 86 | INTEGER, INTENT( inout ) :: kindic ! solver indicator, < 0 if the conver- |
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| 87 | ! ! gence is not reached: the model is |
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| 88 | ! ! stopped in step |
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| 89 | ! ! set to zero before the call of solpcg |
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| 90 | |
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| 91 | !! * Local declarations |
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| 92 | INTEGER :: ji, jj, jn ! dummy loop indices |
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| 93 | REAL(wp) :: zgcad ! temporary scalars |
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| 94 | !!---------------------------------------------------------------------- |
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| 95 | |
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| 96 | ! !================ |
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| 97 | DO jn = 1, nmax ! Iterative loop |
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| 98 | ! !================ |
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| 99 | |
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| [16] | 100 | IF( jn == 1 ) THEN ! Initialization of the algorithm |
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| [3] | 101 | |
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| [16] | 102 | CALL lbc_lnk( gcx, c_solver_pt, 1. ) ! lateral boundary condition |
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| 103 | |
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| [3] | 104 | ! gcr = gcb-a.gcx |
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| 105 | ! gcdes = gsr |
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| 106 | DO jj = 2, jpjm1 |
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| 107 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| [16] | 108 | zgcad = bmask(ji,jj) * ( gcb(ji,jj ) - gcx(ji ,jj ) & |
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| 109 | & - gcp(ji,jj,1) * gcx(ji ,jj-1) & |
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| 110 | & - gcp(ji,jj,2) * gcx(ji-1,jj ) & |
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| 111 | & - gcp(ji,jj,3) * gcx(ji+1,jj ) & |
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| 112 | & - gcp(ji,jj,4) * gcx(ji ,jj+1) ) |
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| [3] | 113 | gcr (ji,jj) = zgcad |
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| 114 | gcdes(ji,jj) = zgcad |
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| 115 | END DO |
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| 116 | END DO |
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| 117 | |
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| 118 | rnorme = SUM( gcr(:,:) * gcdmat(:,:) * gcr(:,:) ) |
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| [16] | 119 | IF( lk_mpp ) CALL mpp_sum( rnorme ) ! sum over the global domain |
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| [3] | 120 | rr = rnorme |
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| 121 | |
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| [16] | 122 | ENDIF |
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| [3] | 123 | |
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| [16] | 124 | ! ! Algorithm |
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| [3] | 125 | |
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| [16] | 126 | CALL lbc_lnk( gcdes, c_solver_pt, 1. ) ! lateral boundary condition |
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| [3] | 127 | |
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| [16] | 128 | ! ... gccd = matrix . gcdes |
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| 129 | DO jj = 2, jpjm1 |
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| 130 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 131 | gccd(ji,jj) = bmask(ji,jj)*( gcdes(ji,jj) & |
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| 132 | & +gcp(ji,jj,1)*gcdes(ji,jj-1)+gcp(ji,jj,2)*gcdes(ji-1,jj) & |
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| 133 | & +gcp(ji,jj,4)*gcdes(ji,jj+1)+gcp(ji,jj,3)*gcdes(ji+1,jj) ) |
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| 134 | END DO |
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| 135 | END DO |
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| 136 | |
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| 137 | ! alph = (gcr,gcr)/(gcdes,gccd) |
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| 138 | radd = SUM( gcdes(:,:) * gcdmat(:,:) * gccd(:,:) ) |
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| 139 | IF( lk_mpp ) CALL mpp_sum( radd ) ! sum over the global domain |
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| 140 | alph = rr / radd |
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| 141 | |
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| 142 | ! gcx = gcx + alph * gcdes |
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| 143 | ! gcr = gcr - alph * gccd |
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| 144 | DO jj = 2, jpjm1 |
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| 145 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 146 | gcx(ji,jj) = bmask(ji,jj) * ( gcx(ji,jj) + alph * gcdes(ji,jj) ) |
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| 147 | gcr(ji,jj) = bmask(ji,jj) * ( gcr(ji,jj) - alph * gccd (ji,jj) ) |
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| 148 | END DO |
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| 149 | END DO |
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| [3] | 150 | |
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| [16] | 151 | ! rnorme = (gcr,gcr) |
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| 152 | rnorme = SUM( gcr(:,:) * gcdmat(:,:) * gcr(:,:) ) |
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| 153 | IF( lk_mpp ) CALL mpp_sum( rnorme ) ! sum over the global domain |
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| [3] | 154 | |
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| [16] | 155 | ! test of convergence |
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| 156 | IF( rnorme < epsr .OR. jn == nmax ) THEN |
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| 157 | res = SQRT( rnorme ) |
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| 158 | niter = jn |
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| 159 | ncut = 999 |
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| 160 | ENDIF |
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| [3] | 161 | |
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| [16] | 162 | ! beta = (rk+1,rk+1)/(rk,rk) |
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| 163 | beta = rnorme / rr |
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| 164 | rr = rnorme |
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| [3] | 165 | |
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| [16] | 166 | ! indicator of non-convergence or explosion |
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| 167 | IF( jn == nmax .OR. SQRT(epsr)/eps > 1.e+20 ) kindic = -2 |
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| 168 | IF( ncut == 999 ) GOTO 999 |
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| [3] | 169 | |
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| [16] | 170 | ! gcdes = gcr + beta * gcdes |
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| 171 | DO jj = 2, jpjm1 |
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| 172 | DO ji = fs_2, fs_jpim1 ! vector opt. |
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| 173 | gcdes(ji,jj) = bmask(ji,jj)*( gcr(ji,jj) + beta * gcdes(ji,jj) ) |
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| 174 | END DO |
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| 175 | END DO |
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| [3] | 176 | |
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| [16] | 177 | ! !================ |
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| 178 | END DO ! End Loop |
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| 179 | ! !================ |
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| [3] | 180 | |
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| [16] | 181 | 999 CONTINUE |
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| [3] | 182 | |
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| 183 | |
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| [16] | 184 | ! Output in gcx with lateral b.c. applied |
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| 185 | ! --------------------------------------- |
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| [3] | 186 | |
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| [16] | 187 | CALL lbc_lnk( gcx, c_solver_pt, 1. ) |
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| [3] | 188 | |
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| 189 | END SUBROUTINE sol_pcg |
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| 190 | |
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| 191 | !!===================================================================== |
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| 192 | END MODULE solpcg |
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