[3] | 1 | MODULE solmat |
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| 2 | !!====================================================================== |
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| 3 | !! *** MODULE solmat *** |
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| 4 | !! solver : construction of the matrix |
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| 5 | !!====================================================================== |
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[1601] | 6 | !! History : 1.0 ! 1988-04 (G. Madec) Original code |
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| 7 | !! ! 1993-03 (M. Guyon) symetrical conditions |
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| 8 | !! ! 1993-06 (M. Guyon) suppress pointers |
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| 9 | !! ! 1996-05 (G. Madec) merge sor and pcg formulations |
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| 10 | !! ! 1996-11 (A. Weaver) correction to preconditioning |
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| 11 | !! NEMO 1.0 ! 1902-08 (G. Madec) F90: Free form |
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| 12 | !! - ! 1902-11 (C. Talandier, A-M. Treguier) Free surface & Open boundaries |
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| 13 | !! 2.0 ! 2005-09 (R. Benshila) add sol_exd for extra outer halo |
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| 14 | !! - ! 2005-11 (V. Garnier) Surface pressure gradient organization |
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| 15 | !! 3.2 ! 2009-06 (S. Masson) distributed restart using iom |
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| 16 | !! - ! 2009-07 (R. Benshila) suppression of rigid-lid option |
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[2528] | 17 | !! 3.3 ! 2010-09 (D. Storkey) update for BDY module. |
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[508] | 18 | !!---------------------------------------------------------------------- |
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[3] | 19 | |
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| 20 | !!---------------------------------------------------------------------- |
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[1601] | 21 | !! sol_mat : Construction of the matrix of used by the elliptic solvers |
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| 22 | !! sol_exd : |
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[3] | 23 | !!---------------------------------------------------------------------- |
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| 24 | USE oce ! ocean dynamics and active tracers |
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| 25 | USE dom_oce ! ocean space and time domain |
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| 26 | USE sol_oce ! ocean solver |
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| 27 | USE phycst ! physical constants |
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[2528] | 28 | USE bdy_oce ! unstructured open boundary conditions |
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[312] | 29 | USE lbclnk ! lateral boudary conditions |
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[3] | 30 | USE lib_mpp ! distributed memory computing |
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[4153] | 31 | USE c1d ! 1D vertical configuration |
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[413] | 32 | USE in_out_manager ! I/O manager |
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[3294] | 33 | USE timing ! timing |
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[3] | 34 | |
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| 35 | IMPLICIT NONE |
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| 36 | PRIVATE |
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| 37 | |
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[1601] | 38 | PUBLIC sol_mat ! routine called by inisol.F90 |
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| 39 | |
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[3] | 40 | !!---------------------------------------------------------------------- |
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[2528] | 41 | !! NEMO/OPA 3.3 , NEMO Consortium (2010) |
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[1152] | 42 | !! $Id$ |
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[2715] | 43 | !! Software governed by the CeCILL licence (NEMOGCM/NEMO_CeCILL.txt) |
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[3] | 44 | !!---------------------------------------------------------------------- |
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| 45 | CONTAINS |
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| 46 | |
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[413] | 47 | SUBROUTINE sol_mat( kt ) |
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[3] | 48 | !!---------------------------------------------------------------------- |
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| 49 | !! *** ROUTINE sol_mat *** |
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| 50 | !! |
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| 51 | !! ** Purpose : Construction of the matrix of used by the elliptic |
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[1601] | 52 | !! solvers (either sor or pcg methods). |
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[3] | 53 | !! |
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[1601] | 54 | !! ** Method : The matrix is built for the divergence of the transport |
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| 55 | !! system. a diagonal preconditioning matrix is also defined. |
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[3] | 56 | !! |
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| 57 | !! ** Action : - gcp : extra-diagonal elements of the matrix |
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| 58 | !! - gcdmat : preconditioning matrix (diagonal elements) |
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| 59 | !! - gcdprc : inverse of the preconditioning matrix |
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| 60 | !!---------------------------------------------------------------------- |
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[413] | 61 | INTEGER, INTENT(in) :: kt |
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[1601] | 62 | !! |
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[3] | 63 | INTEGER :: ji, jj ! dummy loop indices |
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| 64 | REAL(wp) :: zcoefs, zcoefw, zcoefe, zcoefn ! temporary scalars |
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[16] | 65 | REAL(wp) :: z2dt, zcoef |
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[3] | 66 | !!---------------------------------------------------------------------- |
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[3294] | 67 | ! |
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| 68 | IF( nn_timing == 1 ) CALL timing_start('sol_mat') |
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| 69 | ! |
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[3] | 70 | |
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| 71 | ! 1. Construction of the matrix |
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| 72 | ! ----------------------------- |
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[1601] | 73 | zcoef = 0.e0 ! initialize to zero |
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[3] | 74 | gcp(:,:,1) = 0.e0 |
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| 75 | gcp(:,:,2) = 0.e0 |
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| 76 | gcp(:,:,3) = 0.e0 |
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| 77 | gcp(:,:,4) = 0.e0 |
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[1601] | 78 | ! |
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[3] | 79 | gcdprc(:,:) = 0.e0 |
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| 80 | gcdmat(:,:) = 0.e0 |
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[1601] | 81 | ! |
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| 82 | IF( neuler == 0 .AND. kt == nit000 ) THEN ; z2dt = rdt |
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| 83 | ELSE ; z2dt = 2. * rdt |
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[413] | 84 | ENDIF |
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[3] | 85 | |
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[2528] | 86 | #if defined key_dynspg_flt && ! defined key_bdy |
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[3] | 87 | |
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[1601] | 88 | DO jj = 2, jpjm1 ! matrix of free surface elliptic system |
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[3] | 89 | DO ji = 2, jpim1 |
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[1601] | 90 | zcoef = z2dt * z2dt * grav * bmask(ji,jj) |
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[5870] | 91 | zcoefs = -zcoef * hv(ji ,jj-1) * e1_e2v(ji ,jj-1) ! south coefficient |
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| 92 | zcoefw = -zcoef * hu(ji-1,jj ) * e2_e1u(ji-1,jj ) ! west coefficient |
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| 93 | zcoefe = -zcoef * hu(ji ,jj ) * e2_e1u(ji ,jj ) ! east coefficient |
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| 94 | zcoefn = -zcoef * hv(ji ,jj ) * e1_e2v(ji ,jj ) ! north coefficient |
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[3] | 95 | gcp(ji,jj,1) = zcoefs |
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| 96 | gcp(ji,jj,2) = zcoefw |
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| 97 | gcp(ji,jj,3) = zcoefe |
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| 98 | gcp(ji,jj,4) = zcoefn |
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[5870] | 99 | gcdmat(ji,jj) = e1e2t(ji,jj) * bmask(ji,jj) & ! diagonal coefficient |
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[16] | 100 | & - zcoefs -zcoefw -zcoefe -zcoefn |
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[3] | 101 | END DO |
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| 102 | END DO |
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[2528] | 103 | |
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| 104 | # elif defined key_dynspg_flt && defined key_bdy |
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| 105 | |
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| 106 | ! defined gcdmat in the case of unstructured open boundaries |
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| 107 | DO jj = 2, jpjm1 |
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| 108 | DO ji = 2, jpim1 |
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| 109 | zcoef = z2dt * z2dt * grav * bmask(ji,jj) |
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| 110 | |
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| 111 | ! south coefficient |
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[5870] | 112 | zcoefs = -zcoef * hv(ji,jj-1) * e1_e2v(ji,jj-1) |
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[2528] | 113 | zcoefs = zcoefs * bdyvmask(ji,jj-1) |
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| 114 | gcp(ji,jj,1) = zcoefs |
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| 115 | |
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| 116 | ! west coefficient |
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[5870] | 117 | zcoefw = -zcoef * hu(ji-1,jj) * e2_e1u(ji-1,jj) |
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[2528] | 118 | zcoefw = zcoefw * bdyumask(ji-1,jj) |
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| 119 | gcp(ji,jj,2) = zcoefw |
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| 120 | |
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| 121 | ! east coefficient |
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[5870] | 122 | zcoefe = -zcoef * hu(ji,jj) * e2_e1u(ji,jj) |
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[2528] | 123 | zcoefe = zcoefe * bdyumask(ji,jj) |
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| 124 | gcp(ji,jj,3) = zcoefe |
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| 125 | |
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| 126 | ! north coefficient |
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[5870] | 127 | zcoefn = -zcoef * hv(ji,jj) * e1_e2v(ji,jj) |
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[2528] | 128 | zcoefn = zcoefn * bdyvmask(ji,jj) |
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| 129 | gcp(ji,jj,4) = zcoefn |
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| 130 | |
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| 131 | ! diagonal coefficient |
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[5870] | 132 | gcdmat(ji,jj) = e1e2t(ji,jj)*bmask(ji,jj) - zcoefs -zcoefw -zcoefe -zcoefn |
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[2528] | 133 | END DO |
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| 134 | END DO |
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| 135 | |
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[1601] | 136 | #endif |
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[3] | 137 | |
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[2031] | 138 | IF( .NOT. Agrif_Root() ) THEN |
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[1601] | 139 | ! |
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| 140 | IF( nbondi == -1 .OR. nbondi == 2 ) bmask(2 ,: ) = 0.e0 |
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| 141 | IF( nbondi == 1 .OR. nbondi == 2 ) bmask(nlci-1,: ) = 0.e0 |
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| 142 | IF( nbondj == -1 .OR. nbondj == 2 ) bmask(: ,2 ) = 0.e0 |
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| 143 | IF( nbondj == 1 .OR. nbondj == 2 ) bmask(: ,nlcj-1) = 0.e0 |
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| 144 | ! |
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| 145 | DO jj = 2, jpjm1 |
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| 146 | DO ji = 2, jpim1 |
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| 147 | zcoef = z2dt * z2dt * grav * bmask(ji,jj) |
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| 148 | ! south coefficient |
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| 149 | IF( ( nbondj == -1 .OR. nbondj == 2 ) .AND. ( jj == 3 ) ) THEN |
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[5870] | 150 | zcoefs = -zcoef * hv(ji,jj-1) * e1_e2v(ji,jj-1)*(1.-vmask(ji,jj-1,1)) |
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[1601] | 151 | ELSE |
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[5870] | 152 | zcoefs = -zcoef * hv(ji,jj-1) * e1_e2v(ji,jj-1) |
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[1601] | 153 | END IF |
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| 154 | gcp(ji,jj,1) = zcoefs |
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| 155 | ! |
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| 156 | ! west coefficient |
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| 157 | IF( ( nbondi == -1 .OR. nbondi == 2 ) .AND. ( ji == 3 ) ) THEN |
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[5870] | 158 | zcoefw = -zcoef * hu(ji-1,jj) * e2_e1u(ji-1,jj)*(1.-umask(ji-1,jj,1)) |
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[1601] | 159 | ELSE |
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[5870] | 160 | zcoefw = -zcoef * hu(ji-1,jj) * e2_e1u(ji-1,jj) |
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[1601] | 161 | END IF |
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| 162 | gcp(ji,jj,2) = zcoefw |
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| 163 | ! |
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| 164 | ! east coefficient |
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| 165 | IF( ( nbondi == 1 .OR. nbondi == 2 ) .AND. ( ji == nlci-2 ) ) THEN |
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[5870] | 166 | zcoefe = -zcoef * hu(ji,jj) * e2_e1u(ji,jj)*(1.-umask(ji,jj,1)) |
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[1601] | 167 | ELSE |
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[5870] | 168 | zcoefe = -zcoef * hu(ji,jj) * e2_e1u(ji,jj) |
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[1601] | 169 | END IF |
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| 170 | gcp(ji,jj,3) = zcoefe |
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| 171 | ! |
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| 172 | ! north coefficient |
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| 173 | IF( ( nbondj == 1 .OR. nbondj == 2 ) .AND. ( jj == nlcj-2 ) ) THEN |
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[5870] | 174 | zcoefn = -zcoef * hv(ji,jj) * e1_e2v(ji,jj)*(1.-vmask(ji,jj,1)) |
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[1601] | 175 | ELSE |
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[5870] | 176 | zcoefn = -zcoef * hv(ji,jj) * e1_e2v(ji,jj) |
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[1601] | 177 | END IF |
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| 178 | gcp(ji,jj,4) = zcoefn |
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| 179 | ! |
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| 180 | ! diagonal coefficient |
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[5870] | 181 | gcdmat(ji,jj) = e1e2t(ji,jj)*bmask(ji,jj) - zcoefs -zcoefw -zcoefe -zcoefn |
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[1601] | 182 | END DO |
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[389] | 183 | END DO |
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[1601] | 184 | ! |
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| 185 | ENDIF |
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[389] | 186 | |
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[3] | 187 | ! 2. Boundary conditions |
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| 188 | ! ---------------------- |
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| 189 | |
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| 190 | ! Cyclic east-west boundary conditions |
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| 191 | ! ji=2 is the column east of ji=jpim1 and reciprocally, |
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| 192 | ! ji=jpim1 is the column west of ji=2 |
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| 193 | ! all the coef are already set to zero as bmask is initialized to |
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| 194 | ! zero for ji=1 and ji=jpj in dommsk. |
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| 195 | |
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| 196 | ! Symetrical conditions |
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| 197 | ! free surface: no specific action |
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| 198 | ! bsf system: n-s gradient of bsf = 0 along j=2 (perhaps a bug !!!!!!) |
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| 199 | ! the diagonal coefficient of the southern grid points must be modify to |
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| 200 | ! account for the existence of the south symmetric bassin. |
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| 201 | |
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| 202 | ! North fold boundary condition |
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| 203 | ! all the coef are already set to zero as bmask is initialized to |
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| 204 | ! zero on duplicated lignes and portion of lignes |
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| 205 | |
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| 206 | ! 3. Preconditioned matrix |
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| 207 | ! ------------------------ |
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| 208 | |
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[1556] | 209 | ! SOR and PCG solvers |
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[4153] | 210 | IF( lk_c1d ) CALL lbc_lnk( gcdmat, 'T', 1._wp ) ! 1D case bmask =/0 but gcdmat not define everywhere |
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[1556] | 211 | DO jj = 1, jpj |
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| 212 | DO ji = 1, jpi |
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| 213 | IF( bmask(ji,jj) /= 0.e0 ) gcdprc(ji,jj) = 1.e0 / gcdmat(ji,jj) |
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[3] | 214 | END DO |
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[1556] | 215 | END DO |
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[3] | 216 | |
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[1556] | 217 | gcp(:,:,1) = gcp(:,:,1) * gcdprc(:,:) |
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| 218 | gcp(:,:,2) = gcp(:,:,2) * gcdprc(:,:) |
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| 219 | gcp(:,:,3) = gcp(:,:,3) * gcdprc(:,:) |
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| 220 | gcp(:,:,4) = gcp(:,:,4) * gcdprc(:,:) |
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[1601] | 221 | IF( nn_solv == 2 ) gccd(:,:) = rn_sor * gcp(:,:,2) |
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[3] | 222 | |
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[1601] | 223 | IF( nn_solv == 2 .AND. MAX( jpr2di, jpr2dj ) > 0) THEN |
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[3609] | 224 | CALL lbc_lnk_e( gcp (:,:,1), c_solver_pt, 1., jpr2di, jpr2dj ) ! lateral boundary conditions |
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| 225 | CALL lbc_lnk_e( gcp (:,:,2), c_solver_pt, 1., jpr2di, jpr2dj ) ! lateral boundary conditions |
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| 226 | CALL lbc_lnk_e( gcp (:,:,3), c_solver_pt, 1., jpr2di, jpr2dj ) ! lateral boundary conditions |
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| 227 | CALL lbc_lnk_e( gcp (:,:,4), c_solver_pt, 1., jpr2di, jpr2dj ) ! lateral boundary conditions |
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| 228 | CALL lbc_lnk_e( gcdprc(:,:) , c_solver_pt, 1., jpr2di, jpr2dj ) ! lateral boundary conditions |
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| 229 | CALL lbc_lnk_e( gcdmat(:,:) , c_solver_pt, 1., jpr2di, jpr2dj ) ! lateral boundary conditions |
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[1556] | 230 | IF( npolj /= 0 ) CALL sol_exd( gcp , c_solver_pt ) ! switch northernelements |
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| 231 | END IF |
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| 232 | |
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[3] | 233 | ! 4. Initialization the arrays used in pcg |
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| 234 | ! ---------------------------------------- |
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| 235 | gcb (:,:) = 0.e0 |
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| 236 | gcr (:,:) = 0.e0 |
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| 237 | gcdes(:,:) = 0.e0 |
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| 238 | gccd (:,:) = 0.e0 |
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[1556] | 239 | ! |
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[3294] | 240 | IF( nn_timing == 1 ) CALL timing_stop('sol_mat') |
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| 241 | ! |
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[3] | 242 | END SUBROUTINE sol_mat |
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| 243 | |
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[312] | 244 | |
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| 245 | SUBROUTINE sol_exd( pt3d, cd_type ) |
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| 246 | !!---------------------------------------------------------------------- |
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| 247 | !! *** routine sol_exd *** |
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| 248 | !! |
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| 249 | !! ** Purpose : Reorder gcb coefficient on the extra outer halo |
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| 250 | !! at north fold in case of T or F pivot |
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| 251 | !! |
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| 252 | !! ** Method : Perform a circular permutation of the coefficients on |
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| 253 | !! the total area strictly above the pivot point, |
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| 254 | !! and on the semi-row of the pivot point |
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| 255 | !!---------------------------------------------------------------------- |
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[1601] | 256 | CHARACTER(len=1) , INTENT( in ) :: cd_type ! define the nature of pt2d array grid-points |
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| 257 | ! ! = T , U , V , F , W |
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| 258 | ! ! = S : T-point, north fold treatment |
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| 259 | ! ! = G : F-point, north fold treatment |
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| 260 | ! ! = I : sea-ice velocity at F-point with index shift |
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| 261 | REAL(wp), DIMENSION(1-jpr2di:jpi+jpr2di,1-jpr2dj:jpj+jpr2dj,4), INTENT(inout) :: pt3d ! 2D field to be treated |
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| 262 | !! |
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| 263 | INTEGER :: ji, jk ! dummy loop indices |
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[2715] | 264 | INTEGER :: iloc ! local integers |
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| 265 | REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:,:) :: ztab ! workspace allocated one for all |
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[312] | 266 | !!---------------------------------------------------------------------- |
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| 267 | |
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[2715] | 268 | IF( .NOT. ALLOCATED( ztab ) ) THEN |
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| 269 | ALLOCATE( ztab(1-jpr2di:jpi+jpr2di,1-jpr2dj:jpj+jpr2dj,4), STAT=iloc ) |
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| 270 | IF( lk_mpp ) CALL mpp_sum ( iloc ) |
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| 271 | IF( iloc /= 0 ) CALL ctl_stop('STOP', 'sol_exd: failed to allocate array') |
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| 272 | ENDIF |
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| 273 | |
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[312] | 274 | ztab = pt3d |
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| 275 | |
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[1601] | 276 | SELECT CASE ( npolj ) ! north fold type |
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| 277 | ! |
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| 278 | CASE ( 3 , 4 ) !== T pivot ==! |
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[312] | 279 | iloc = jpiglo/2 +1 |
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[1601] | 280 | ! |
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| 281 | SELECT CASE ( cd_type ) |
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| 282 | ! |
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[2528] | 283 | CASE ( 'T' , 'U', 'W' ) |
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[1601] | 284 | DO jk = 1, 4 |
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| 285 | DO ji = 1-jpr2di, nlci+jpr2di |
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| 286 | pt3d(ji,nlcj:nlcj+jpr2dj,jk) = ztab(ji,nlcj:nlcj+jpr2dj,jk+3-2*MOD(jk+3,4)) |
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| 287 | END DO |
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| 288 | END DO |
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| 289 | DO jk =1, 4 |
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| 290 | DO ji = nlci+jpr2di, 1-jpr2di, -1 |
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| 291 | IF( ( ji .LT. mi0(iloc) .AND. mi0(iloc) /= 1 ) & |
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| 292 | & .OR. ( mi0(iloc) == jpi+1 ) ) EXIT |
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[312] | 293 | pt3d(ji,nlcj-1,jk) = ztab(ji,nlcj-1,jk+3-2*MOD(jk+3,4)) |
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[1601] | 294 | END DO |
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| 295 | END DO |
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| 296 | ! |
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[2528] | 297 | CASE ( 'F' , 'I', 'V' ) |
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[1601] | 298 | DO jk =1, 4 |
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| 299 | DO ji = 1-jpr2di, nlci+jpr2di |
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| 300 | pt3d(ji,nlcj-1:nlcj+jpr2dj,jk) = ztab(ji,nlcj-1:nlcj+jpr2dj,jk+3-2*MOD(jk+3,4)) |
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| 301 | END DO |
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| 302 | END DO |
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| 303 | ! |
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| 304 | END SELECT ! cd_type |
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| 305 | ! |
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| 306 | CASE ( 5 , 6 ) !== F pivot ==! |
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| 307 | iloc=jpiglo/2 |
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| 308 | ! |
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| 309 | SELECT CASE (cd_type ) |
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| 310 | ! |
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[2528] | 311 | CASE ( 'T' , 'U', 'W') |
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[1601] | 312 | DO jk =1, 4 |
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| 313 | DO ji = 1-jpr2di, nlci+jpr2di |
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| 314 | pt3d(ji,nlcj:nlcj+jpr2dj,jk) = ztab(ji,nlcj:nlcj+jpr2dj,jk+3-2*MOD(jk+3,4)) |
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| 315 | END DO |
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| 316 | END DO |
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| 317 | ! |
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[2528] | 318 | CASE ( 'F' , 'I', 'V' ) |
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[1601] | 319 | DO jk =1, 4 |
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| 320 | DO ji = 1-jpr2di, nlci+jpr2di |
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| 321 | pt3d(ji,nlcj:nlcj+jpr2dj,jk) = ztab(ji,nlcj:nlcj+jpr2dj,jk+3-2*MOD(jk+3,4)) |
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| 322 | END DO |
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| 323 | END DO |
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| 324 | DO jk =1, 4 |
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| 325 | DO ji = nlci+jpr2di, 1-jpr2di, -1 |
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| 326 | IF( ( ji .LT. mi0(iloc) .AND. mi0(iloc) /= 1 ) .OR. ( mi0(iloc) == jpi+1 ) ) EXIT |
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[312] | 327 | pt3d(ji,nlcj-1,jk) = ztab(ji,nlcj-1,jk+3-2*MOD(jk+3,4)) |
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[1601] | 328 | END DO |
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| 329 | END DO |
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| 330 | ! |
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| 331 | END SELECT ! cd_type |
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| 332 | ! |
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| 333 | END SELECT ! npolj |
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[1556] | 334 | ! |
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[312] | 335 | END SUBROUTINE sol_exd |
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| 336 | |
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[3] | 337 | !!====================================================================== |
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| 338 | END MODULE solmat |
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