Actual source code: ex48.c

petsc-master 2018-05-25
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  1: static const char help[] = "Toy hydrostatic ice flow with multigrid in 3D.\n\
  2: \n\
  3: Solves the hydrostatic (aka Blatter/Pattyn/First Order) equations for ice sheet flow\n\
  4: using multigrid.  The ice uses a power-law rheology with \"Glen\" exponent 3 (corresponds\n\
  5: to p=4/3 in a p-Laplacian).  The focus is on ISMIP-HOM experiments which assume periodic\n\
  6: boundary conditions in the x- and y-directions.\n\
  7: \n\
  8: Equations are rescaled so that the domain size and solution are O(1), details of this scaling\n\
  9: can be controlled by the options -units_meter, -units_second, and -units_kilogram.\n\
 10: \n\
 11: A VTK StructuredGrid output file can be written using the option -o filename.vts\n\
 12: \n\n";

 14: /*
 15: The equations for horizontal velocity (u,v) are

 17:   - [eta (4 u_x + 2 v_y)]_x - [eta (u_y + v_x)]_y - [eta u_z]_z + rho g s_x = 0
 18:   - [eta (4 v_y + 2 u_x)]_y - [eta (u_y + v_x)]_x - [eta v_z]_z + rho g s_y = 0

 20: where

 22:   eta = B/2 (epsilon + gamma)^((p-2)/2)

 24: is the nonlinear effective viscosity with regularization epsilon and hardness parameter B,
 25: written in terms of the second invariant

 27:   gamma = u_x^2 + v_y^2 + u_x v_y + (1/4) (u_y + v_x)^2 + (1/4) u_z^2 + (1/4) v_z^2

 29: The surface boundary conditions are the natural conditions.  The basal boundary conditions
 30: are either no-slip, or Navier (linear) slip with spatially variant friction coefficient beta^2.

 32: In the code, the equations for (u,v) are multiplied through by 1/(rho g) so that residuals are O(1).

 34: The discretization is Q1 finite elements, managed by a DMDA.  The grid is never distorted in the
 35: map (x,y) plane, but the bed and surface may be bumpy.  This is handled as usual in FEM, through
 36: the Jacobian of the coordinate transformation from a reference element to the physical element.

 38: Since ice-flow is tightly coupled in the z-direction (within columns), the DMDA is managed
 39: specially so that columns are never distributed, and are always contiguous in memory.
 40: This amounts to reversing the meaning of X,Y,Z compared to the DMDA's internal interpretation,
 41: and then indexing as vec[i][j][k].  The exotic coarse spaces require 2D DMDAs which are made to
 42: use compatible domain decomposition relative to the 3D DMDAs.

 44: There are two compile-time options:

 46:   NO_SSE2:
 47:     If the host supports SSE2, we use integration code that has been vectorized with SSE2
 48:     intrinsics, unless this macro is defined.  The intrinsics speed up integration by about
 49:     30% on my architecture (P8700, gcc-4.5 snapshot).

 51:   COMPUTE_LOWER_TRIANGULAR:
 52:     The element matrices we assemble are lower-triangular so it is not necessary to compute
 53:     all entries explicitly.  If this macro is defined, the lower-triangular entries are
 54:     computed explicitly.

 56: */

 58: #if defined(PETSC_APPLE_FRAMEWORK)
 59: #import <PETSc/petscsnes.h>
 60: #import <PETSc/petsc/private/dmdaimpl.h>     /* There is not yet a public interface to manipulate dm->ops */
 61: #else

 63:  #include <petscsnes.h>
 64: #include <petsc/private/dmdaimpl.h>     /* There is not yet a public interface to manipulate dm->ops */
 65: #endif
 66: #include <ctype.h>              /* toupper() */

 68: #if defined(__cplusplus) || defined (PETSC_HAVE_WINDOWS_COMPILERS) || defined (__PGI)
 69: /*  c++ cannot handle  [_restrict_] notation like C does */
 70: #undef PETSC_RESTRICT
 71: #define PETSC_RESTRICT
 72: #endif

 74: #if defined __SSE2__
 75: #  include <emmintrin.h>
 76: #endif

 78: /* The SSE2 kernels are only for PetscScalar=double on architectures that support it */
 79: #if !defined NO_SSE2                           \
 80:      && !defined PETSC_USE_COMPLEX             \
 81:      && !defined PETSC_USE_REAL_SINGLE         \
 82:      && !defined PETSC_USE_REAL___FLOAT128     \
 83:      && !defined PETSC_USE_REAL___FP16         \
 84:      && defined __SSE2__
 85: #define USE_SSE2_KERNELS 1
 86: #else
 87: #define USE_SSE2_KERNELS 0
 88: #endif

 90: static PetscClassId THI_CLASSID;

 92: typedef enum {QUAD_GAUSS,QUAD_LOBATTO} QuadratureType;
 93: static const char      *QuadratureTypes[] = {"gauss","lobatto","QuadratureType","QUAD_",0};
 94: PETSC_UNUSED static const PetscReal HexQWeights[8]     = {1,1,1,1,1,1,1,1};
 95: PETSC_UNUSED static const PetscReal HexQNodes[]        = {-0.57735026918962573, 0.57735026918962573};
 96: #define G 0.57735026918962573
 97: #define H (0.5*(1.+G))
 98: #define L (0.5*(1.-G))
 99: #define M (-0.5)
100: #define P (0.5)
101: /* Special quadrature: Lobatto in horizontal, Gauss in vertical */
102: static const PetscReal HexQInterp_Lobatto[8][8] = {{H,0,0,0,L,0,0,0},
103:                                                    {0,H,0,0,0,L,0,0},
104:                                                    {0,0,H,0,0,0,L,0},
105:                                                    {0,0,0,H,0,0,0,L},
106:                                                    {L,0,0,0,H,0,0,0},
107:                                                    {0,L,0,0,0,H,0,0},
108:                                                    {0,0,L,0,0,0,H,0},
109:                                                    {0,0,0,L,0,0,0,H}};
110: static const PetscReal HexQDeriv_Lobatto[8][8][3] = {
111:   {{M*H,M*H,M},{P*H,0,0}  ,{0,0,0}    ,{0,P*H,0}  ,{M*L,M*L,P},{P*L,0,0}  ,{0,0,0}    ,{0,P*L,0}  },
112:   {{M*H,0,0}  ,{P*H,M*H,M},{0,P*H,0}  ,{0,0,0}    ,{M*L,0,0}  ,{P*L,M*L,P},{0,P*L,0}  ,{0,0,0}    },
113:   {{0,0,0}    ,{0,M*H,0}  ,{P*H,P*H,M},{M*H,0,0}  ,{0,0,0}    ,{0,M*L,0}  ,{P*L,P*L,P},{M*L,0,0}  },
114:   {{0,M*H,0}  ,{0,0,0}    ,{P*H,0,0}  ,{M*H,P*H,M},{0,M*L,0}  ,{0,0,0}    ,{P*L,0,0}  ,{M*L,P*L,P}},
115:   {{M*L,M*L,M},{P*L,0,0}  ,{0,0,0}    ,{0,P*L,0}  ,{M*H,M*H,P},{P*H,0,0}  ,{0,0,0}    ,{0,P*H,0}  },
116:   {{M*L,0,0}  ,{P*L,M*L,M},{0,P*L,0}  ,{0,0,0}    ,{M*H,0,0}  ,{P*H,M*H,P},{0,P*H,0}  ,{0,0,0}    },
117:   {{0,0,0}    ,{0,M*L,0}  ,{P*L,P*L,M},{M*L,0,0}  ,{0,0,0}    ,{0,M*H,0}  ,{P*H,P*H,P},{M*H,0,0}  },
118:   {{0,M*L,0}  ,{0,0,0}    ,{P*L,0,0}  ,{M*L,P*L,M},{0,M*H,0}  ,{0,0,0}    ,{P*H,0,0}  ,{M*H,P*H,P}}};
119: /* Stanndard Gauss */
120: static const PetscReal HexQInterp_Gauss[8][8] = {{H*H*H,L*H*H,L*L*H,H*L*H, H*H*L,L*H*L,L*L*L,H*L*L},
121:                                                  {L*H*H,H*H*H,H*L*H,L*L*H, L*H*L,H*H*L,H*L*L,L*L*L},
122:                                                  {L*L*H,H*L*H,H*H*H,L*H*H, L*L*L,H*L*L,H*H*L,L*H*L},
123:                                                  {H*L*H,L*L*H,L*H*H,H*H*H, H*L*L,L*L*L,L*H*L,H*H*L},
124:                                                  {H*H*L,L*H*L,L*L*L,H*L*L, H*H*H,L*H*H,L*L*H,H*L*H},
125:                                                  {L*H*L,H*H*L,H*L*L,L*L*L, L*H*H,H*H*H,H*L*H,L*L*H},
126:                                                  {L*L*L,H*L*L,H*H*L,L*H*L, L*L*H,H*L*H,H*H*H,L*H*H},
127:                                                  {H*L*L,L*L*L,L*H*L,H*H*L, H*L*H,L*L*H,L*H*H,H*H*H}};
128: static const PetscReal HexQDeriv_Gauss[8][8][3] = {
129:   {{M*H*H,H*M*H,H*H*M},{P*H*H,L*M*H,L*H*M},{P*L*H,L*P*H,L*L*M},{M*L*H,H*P*H,H*L*M}, {M*H*L,H*M*L,H*H*P},{P*H*L,L*M*L,L*H*P},{P*L*L,L*P*L,L*L*P},{M*L*L,H*P*L,H*L*P}},
130:   {{M*H*H,L*M*H,L*H*M},{P*H*H,H*M*H,H*H*M},{P*L*H,H*P*H,H*L*M},{M*L*H,L*P*H,L*L*M}, {M*H*L,L*M*L,L*H*P},{P*H*L,H*M*L,H*H*P},{P*L*L,H*P*L,H*L*P},{M*L*L,L*P*L,L*L*P}},
131:   {{M*L*H,L*M*H,L*L*M},{P*L*H,H*M*H,H*L*M},{P*H*H,H*P*H,H*H*M},{M*H*H,L*P*H,L*H*M}, {M*L*L,L*M*L,L*L*P},{P*L*L,H*M*L,H*L*P},{P*H*L,H*P*L,H*H*P},{M*H*L,L*P*L,L*H*P}},
132:   {{M*L*H,H*M*H,H*L*M},{P*L*H,L*M*H,L*L*M},{P*H*H,L*P*H,L*H*M},{M*H*H,H*P*H,H*H*M}, {M*L*L,H*M*L,H*L*P},{P*L*L,L*M*L,L*L*P},{P*H*L,L*P*L,L*H*P},{M*H*L,H*P*L,H*H*P}},
133:   {{M*H*L,H*M*L,H*H*M},{P*H*L,L*M*L,L*H*M},{P*L*L,L*P*L,L*L*M},{M*L*L,H*P*L,H*L*M}, {M*H*H,H*M*H,H*H*P},{P*H*H,L*M*H,L*H*P},{P*L*H,L*P*H,L*L*P},{M*L*H,H*P*H,H*L*P}},
134:   {{M*H*L,L*M*L,L*H*M},{P*H*L,H*M*L,H*H*M},{P*L*L,H*P*L,H*L*M},{M*L*L,L*P*L,L*L*M}, {M*H*H,L*M*H,L*H*P},{P*H*H,H*M*H,H*H*P},{P*L*H,H*P*H,H*L*P},{M*L*H,L*P*H,L*L*P}},
135:   {{M*L*L,L*M*L,L*L*M},{P*L*L,H*M*L,H*L*M},{P*H*L,H*P*L,H*H*M},{M*H*L,L*P*L,L*H*M}, {M*L*H,L*M*H,L*L*P},{P*L*H,H*M*H,H*L*P},{P*H*H,H*P*H,H*H*P},{M*H*H,L*P*H,L*H*P}},
136:   {{M*L*L,H*M*L,H*L*M},{P*L*L,L*M*L,L*L*M},{P*H*L,L*P*L,L*H*M},{M*H*L,H*P*L,H*H*M}, {M*L*H,H*M*H,H*L*P},{P*L*H,L*M*H,L*L*P},{P*H*H,L*P*H,L*H*P},{M*H*H,H*P*H,H*H*P}}};
137: static const PetscReal (*HexQInterp)[8],(*HexQDeriv)[8][3];
138: /* Standard 2x2 Gauss quadrature for the bottom layer. */
139: static const PetscReal QuadQInterp[4][4] = {{H*H,L*H,L*L,H*L},
140:                                             {L*H,H*H,H*L,L*L},
141:                                             {L*L,H*L,H*H,L*H},
142:                                             {H*L,L*L,L*H,H*H}};
143: static const PetscReal QuadQDeriv[4][4][2] = {
144:   {{M*H,M*H},{P*H,M*L},{P*L,P*L},{M*L,P*H}},
145:   {{M*H,M*L},{P*H,M*H},{P*L,P*H},{M*L,P*L}},
146:   {{M*L,M*L},{P*L,M*H},{P*H,P*H},{M*H,P*L}},
147:   {{M*L,M*H},{P*L,M*L},{P*H,P*L},{M*H,P*H}}};
148: #undef G
149: #undef H
150: #undef L
151: #undef M
152: #undef P

154: #define HexExtract(x,i,j,k,n) do {              \
155:     (n)[0] = (x)[i][j][k];                      \
156:     (n)[1] = (x)[i+1][j][k];                    \
157:     (n)[2] = (x)[i+1][j+1][k];                  \
158:     (n)[3] = (x)[i][j+1][k];                    \
159:     (n)[4] = (x)[i][j][k+1];                    \
160:     (n)[5] = (x)[i+1][j][k+1];                  \
161:     (n)[6] = (x)[i+1][j+1][k+1];                \
162:     (n)[7] = (x)[i][j+1][k+1];                  \
163:   } while (0)

165: #define HexExtractRef(x,i,j,k,n) do {           \
166:     (n)[0] = &(x)[i][j][k];                     \
167:     (n)[1] = &(x)[i+1][j][k];                   \
168:     (n)[2] = &(x)[i+1][j+1][k];                 \
169:     (n)[3] = &(x)[i][j+1][k];                   \
170:     (n)[4] = &(x)[i][j][k+1];                   \
171:     (n)[5] = &(x)[i+1][j][k+1];                 \
172:     (n)[6] = &(x)[i+1][j+1][k+1];               \
173:     (n)[7] = &(x)[i][j+1][k+1];                 \
174:   } while (0)

176: #define QuadExtract(x,i,j,n) do {               \
177:     (n)[0] = (x)[i][j];                         \
178:     (n)[1] = (x)[i+1][j];                       \
179:     (n)[2] = (x)[i+1][j+1];                     \
180:     (n)[3] = (x)[i][j+1];                       \
181:   } while (0)

183: static void HexGrad(const PetscReal dphi[][3],const PetscReal zn[],PetscReal dz[])
184: {
185:   PetscInt i;
186:   dz[0] = dz[1] = dz[2] = 0;
187:   for (i=0; i<8; i++) {
188:     dz[0] += dphi[i][0] * zn[i];
189:     dz[1] += dphi[i][1] * zn[i];
190:     dz[2] += dphi[i][2] * zn[i];
191:   }
192: }

194: static void HexComputeGeometry(PetscInt q,PetscReal hx,PetscReal hy,const PetscReal dz[PETSC_RESTRICT],PetscReal phi[PETSC_RESTRICT],PetscReal dphi[PETSC_RESTRICT][3],PetscReal *PETSC_RESTRICT jw)
195: {
196:   const PetscReal jac[3][3]  = {{hx/2,0,0}, {0,hy/2,0}, {dz[0],dz[1],dz[2]}};
197:   const PetscReal ijac[3][3] = {{1/jac[0][0],0,0}, {0,1/jac[1][1],0}, {-jac[2][0]/(jac[0][0]*jac[2][2]),-jac[2][1]/(jac[1][1]*jac[2][2]),1/jac[2][2]}};
198:   const PetscReal jdet       = jac[0][0]*jac[1][1]*jac[2][2];
199:   PetscInt        i;

201:   for (i=0; i<8; i++) {
202:     const PetscReal *dphir = HexQDeriv[q][i];
203:     phi[i]     = HexQInterp[q][i];
204:     dphi[i][0] = dphir[0]*ijac[0][0] + dphir[1]*ijac[1][0] + dphir[2]*ijac[2][0];
205:     dphi[i][1] = dphir[0]*ijac[0][1] + dphir[1]*ijac[1][1] + dphir[2]*ijac[2][1];
206:     dphi[i][2] = dphir[0]*ijac[0][2] + dphir[1]*ijac[1][2] + dphir[2]*ijac[2][2];
207:   }
208:   *jw = 1.0 * jdet;
209: }

211: typedef struct _p_THI   *THI;
212: typedef struct _n_Units *Units;

214: typedef struct {
215:   PetscScalar u,v;
216: } Node;

218: typedef struct {
219:   PetscScalar b;                /* bed */
220:   PetscScalar h;                /* thickness */
221:   PetscScalar beta2;            /* friction */
222: } PrmNode;

224: typedef struct {
225:   PetscReal min,max,cmin,cmax;
226: } PRange;

228: typedef enum {THIASSEMBLY_TRIDIAGONAL,THIASSEMBLY_FULL} THIAssemblyMode;

230: struct _p_THI {
231:   PETSCHEADER(int);
232:   void      (*initialize)(THI,PetscReal x,PetscReal y,PrmNode *p);
233:   PetscInt  zlevels;
234:   PetscReal Lx,Ly,Lz;           /* Model domain */
235:   PetscReal alpha;              /* Bed angle */
236:   Units     units;
237:   PetscReal dirichlet_scale;
238:   PetscReal ssa_friction_scale;
239:   PRange    eta;
240:   PRange    beta2;
241:   struct {
242:     PetscReal Bd2,eps,exponent;
243:   } viscosity;
244:   struct {
245:     PetscReal irefgam,eps2,exponent,refvel,epsvel;
246:   } friction;
247:   PetscReal rhog;
248:   PetscBool no_slip;
249:   PetscBool tridiagonal;
250:   PetscBool coarse2d;
251:   PetscBool verbose;
252:   MatType   mattype;
253: };

255: struct _n_Units {
256:   /* fundamental */
257:   PetscReal meter;
258:   PetscReal kilogram;
259:   PetscReal second;
260:   /* derived */
261:   PetscReal Pascal;
262:   PetscReal year;
263: };

265: static PetscErrorCode THIJacobianLocal_3D_Full(DMDALocalInfo*,Node***,Mat,Mat,THI);
266: static PetscErrorCode THIJacobianLocal_3D_Tridiagonal(DMDALocalInfo*,Node***,Mat,Mat,THI);
267: static PetscErrorCode THIJacobianLocal_2D(DMDALocalInfo*,Node**,Mat,Mat,THI);

269: static void PrmHexGetZ(const PrmNode pn[],PetscInt k,PetscInt zm,PetscReal zn[])
270: {
271:   const PetscScalar zm1    = zm-1,
272:                     znl[8] = {pn[0].b + pn[0].h*(PetscScalar)k/zm1,
273:                               pn[1].b + pn[1].h*(PetscScalar)k/zm1,
274:                               pn[2].b + pn[2].h*(PetscScalar)k/zm1,
275:                               pn[3].b + pn[3].h*(PetscScalar)k/zm1,
276:                               pn[0].b + pn[0].h*(PetscScalar)(k+1)/zm1,
277:                               pn[1].b + pn[1].h*(PetscScalar)(k+1)/zm1,
278:                               pn[2].b + pn[2].h*(PetscScalar)(k+1)/zm1,
279:                               pn[3].b + pn[3].h*(PetscScalar)(k+1)/zm1};
280:   PetscInt i;
281:   for (i=0; i<8; i++) zn[i] = PetscRealPart(znl[i]);
282: }

284: /* Tests A and C are from the ISMIP-HOM paper (Pattyn et al. 2008) */
285: static void THIInitialize_HOM_A(THI thi,PetscReal x,PetscReal y,PrmNode *p)
286: {
287:   Units     units = thi->units;
288:   PetscReal s     = -x*PetscSinReal(thi->alpha);

290:   p->b     = s - 1000*units->meter + 500*units->meter * PetscSinReal(x*2*PETSC_PI/thi->Lx) * PetscSinReal(y*2*PETSC_PI/thi->Ly);
291:   p->h     = s - p->b;
292:   p->beta2 = 1e30;
293: }

295: static void THIInitialize_HOM_C(THI thi,PetscReal x,PetscReal y,PrmNode *p)
296: {
297:   Units     units = thi->units;
298:   PetscReal s     = -x*PetscSinReal(thi->alpha);

300:   p->b = s - 1000*units->meter;
301:   p->h = s - p->b;
302:   /* tau_b = beta2 v   is a stress (Pa) */
303:   p->beta2 = 1000 * (1 + PetscSinReal(x*2*PETSC_PI/thi->Lx)*PetscSinReal(y*2*PETSC_PI/thi->Ly)) * units->Pascal * units->year / units->meter;
304: }

306: /* These are just toys */

308: /* Same bed as test A, free slip everywhere except for a discontinuous jump to a circular sticky region in the middle. */
309: static void THIInitialize_HOM_X(THI thi,PetscReal xx,PetscReal yy,PrmNode *p)
310: {
311:   Units     units = thi->units;
312:   PetscReal x     = xx*2*PETSC_PI/thi->Lx - PETSC_PI,y = yy*2*PETSC_PI/thi->Ly - PETSC_PI; /* [-pi,pi] */
313:   PetscReal r     = PetscSqrtReal(x*x + y*y),s = -x*PetscSinReal(thi->alpha);
314:   p->b     = s - 1000*units->meter + 500*units->meter*PetscSinReal(x + PETSC_PI) * PetscSinReal(y + PETSC_PI);
315:   p->h     = s - p->b;
316:   p->beta2 = 1000 * (r < 1 ? 2 : 0) * units->Pascal * units->year / units->meter;
317: }

319: /* Like Z, but with 200 meter cliffs */
320: static void THIInitialize_HOM_Y(THI thi,PetscReal xx,PetscReal yy,PrmNode *p)
321: {
322:   Units     units = thi->units;
323:   PetscReal x     = xx*2*PETSC_PI/thi->Lx - PETSC_PI,y = yy*2*PETSC_PI/thi->Ly - PETSC_PI; /* [-pi,pi] */
324:   PetscReal r     = PetscSqrtReal(x*x + y*y),s = -x*PetscSinReal(thi->alpha);

326:   p->b = s - 1000*units->meter + 500*units->meter * PetscSinReal(x + PETSC_PI) * PetscSinReal(y + PETSC_PI);
327:   if (PetscRealPart(p->b) > -700*units->meter) p->b += 200*units->meter;
328:   p->h     = s - p->b;
329:   p->beta2 = 1000 * (1. + PetscSinReal(PetscSqrtReal(16*r))/PetscSqrtReal(1e-2 + 16*r)*PetscCosReal(x*3/2)*PetscCosReal(y*3/2)) * units->Pascal * units->year / units->meter;
330: }

332: /* Same bed as A, smoothly varying slipperiness, similar to MATLAB's "sombrero" (uncorrelated with bathymetry) */
333: static void THIInitialize_HOM_Z(THI thi,PetscReal xx,PetscReal yy,PrmNode *p)
334: {
335:   Units     units = thi->units;
336:   PetscReal x     = xx*2*PETSC_PI/thi->Lx - PETSC_PI,y = yy*2*PETSC_PI/thi->Ly - PETSC_PI; /* [-pi,pi] */
337:   PetscReal r     = PetscSqrtReal(x*x + y*y),s = -x*PetscSinReal(thi->alpha);

339:   p->b     = s - 1000*units->meter + 500*units->meter * PetscSinReal(x + PETSC_PI) * PetscSinReal(y + PETSC_PI);
340:   p->h     = s - p->b;
341:   p->beta2 = 1000 * (1. + PetscSinReal(PetscSqrtReal(16*r))/PetscSqrtReal(1e-2 + 16*r)*PetscCosReal(x*3/2)*PetscCosReal(y*3/2)) * units->Pascal * units->year / units->meter;
342: }

344: static void THIFriction(THI thi,PetscReal rbeta2,PetscReal gam,PetscReal *beta2,PetscReal *dbeta2)
345: {
346:   if (thi->friction.irefgam == 0) {
347:     Units units = thi->units;
348:     thi->friction.irefgam = 1./(0.5*PetscSqr(thi->friction.refvel * units->meter / units->year));
349:     thi->friction.eps2    = 0.5*PetscSqr(thi->friction.epsvel * units->meter / units->year) * thi->friction.irefgam;
350:   }
351:   if (thi->friction.exponent == 0) {
352:     *beta2  = rbeta2;
353:     *dbeta2 = 0;
354:   } else {
355:     *beta2  = rbeta2 * PetscPowReal(thi->friction.eps2 + gam*thi->friction.irefgam,thi->friction.exponent);
356:     *dbeta2 = thi->friction.exponent * *beta2 / (thi->friction.eps2 + gam*thi->friction.irefgam) * thi->friction.irefgam;
357:   }
358: }

360: static void THIViscosity(THI thi,PetscReal gam,PetscReal *eta,PetscReal *deta)
361: {
362:   PetscReal Bd2,eps,exponent;
363:   if (thi->viscosity.Bd2 == 0) {
364:     Units units = thi->units;
365:     const PetscReal
366:       n = 3.,                                           /* Glen exponent */
367:       p = 1. + 1./n,                                    /* for Stokes */
368:       A = 1.e-16 * PetscPowReal(units->Pascal,-n) / units->year, /* softness parameter (Pa^{-n}/s) */
369:       B = PetscPowReal(A,-1./n);                                 /* hardness parameter */
370:     thi->viscosity.Bd2      = B/2;
371:     thi->viscosity.exponent = (p-2)/2;
372:     thi->viscosity.eps      = 0.5*PetscSqr(1e-5 / units->year);
373:   }
374:   Bd2      = thi->viscosity.Bd2;
375:   exponent = thi->viscosity.exponent;
376:   eps      = thi->viscosity.eps;
377:   *eta     = Bd2 * PetscPowReal(eps + gam,exponent);
378:   *deta    = exponent * (*eta) / (eps + gam);
379: }

381: static void RangeUpdate(PetscReal *min,PetscReal *max,PetscReal x)
382: {
383:   if (x < *min) *min = x;
384:   if (x > *max) *max = x;
385: }

387: static void PRangeClear(PRange *p)
388: {
389:   p->cmin = p->min = 1e100;
390:   p->cmax = p->max = -1e100;
391: }

393: static PetscErrorCode PRangeMinMax(PRange *p,PetscReal min,PetscReal max)
394: {

397:   p->cmin = min;
398:   p->cmax = max;
399:   if (min < p->min) p->min = min;
400:   if (max > p->max) p->max = max;
401:   return(0);
402: }

404: static PetscErrorCode THIDestroy(THI *thi)
405: {

409:   if (!*thi) return(0);
410:   if (--((PetscObject)(*thi))->refct > 0) {*thi = 0; return(0);}
411:   PetscFree((*thi)->units);
412:   PetscFree((*thi)->mattype);
413:   PetscHeaderDestroy(thi);
414:   return(0);
415: }

417: static PetscErrorCode THICreate(MPI_Comm comm,THI *inthi)
418: {
419:   static PetscBool registered = PETSC_FALSE;
420:   THI              thi;
421:   Units            units;
422:   PetscErrorCode   ierr;

425:   *inthi = 0;
426:   if (!registered) {
427:     PetscClassIdRegister("Toy Hydrostatic Ice",&THI_CLASSID);
428:     registered = PETSC_TRUE;
429:   }
430:   PetscHeaderCreate(thi,THI_CLASSID,"THI","Toy Hydrostatic Ice","",comm,THIDestroy,0);

432:   PetscNew(&thi->units);
433:   units           = thi->units;
434:   units->meter    = 1e-2;
435:   units->second   = 1e-7;
436:   units->kilogram = 1e-12;

438:   PetscOptionsBegin(comm,NULL,"Scaled units options","");
439:   {
440:     PetscOptionsReal("-units_meter","1 meter in scaled length units","",units->meter,&units->meter,NULL);
441:     PetscOptionsReal("-units_second","1 second in scaled time units","",units->second,&units->second,NULL);
442:     PetscOptionsReal("-units_kilogram","1 kilogram in scaled mass units","",units->kilogram,&units->kilogram,NULL);
443:   }
444:   PetscOptionsEnd();
445:   units->Pascal = units->kilogram / (units->meter * PetscSqr(units->second));
446:   units->year   = 31556926. * units->second; /* seconds per year */

448:   thi->Lx              = 10.e3;
449:   thi->Ly              = 10.e3;
450:   thi->Lz              = 1000;
451:   thi->dirichlet_scale = 1;
452:   thi->verbose         = PETSC_FALSE;

454:   PetscOptionsBegin(comm,NULL,"Toy Hydrostatic Ice options","");
455:   {
456:     QuadratureType quad       = QUAD_GAUSS;
457:     char           homexp[]   = "A";
458:     char           mtype[256] = MATSBAIJ;
459:     PetscReal      L,m = 1.0;
460:     PetscBool      flg;
461:     L    = thi->Lx;
462:     PetscOptionsReal("-thi_L","Domain size (m)","",L,&L,&flg);
463:     if (flg) thi->Lx = thi->Ly = L;
464:     PetscOptionsReal("-thi_Lx","X Domain size (m)","",thi->Lx,&thi->Lx,NULL);
465:     PetscOptionsReal("-thi_Ly","Y Domain size (m)","",thi->Ly,&thi->Ly,NULL);
466:     PetscOptionsReal("-thi_Lz","Z Domain size (m)","",thi->Lz,&thi->Lz,NULL);
467:     PetscOptionsString("-thi_hom","ISMIP-HOM experiment (A or C)","",homexp,homexp,sizeof(homexp),NULL);
468:     switch (homexp[0] = toupper(homexp[0])) {
469:     case 'A':
470:       thi->initialize = THIInitialize_HOM_A;
471:       thi->no_slip    = PETSC_TRUE;
472:       thi->alpha      = 0.5;
473:       break;
474:     case 'C':
475:       thi->initialize = THIInitialize_HOM_C;
476:       thi->no_slip    = PETSC_FALSE;
477:       thi->alpha      = 0.1;
478:       break;
479:     case 'X':
480:       thi->initialize = THIInitialize_HOM_X;
481:       thi->no_slip    = PETSC_FALSE;
482:       thi->alpha      = 0.3;
483:       break;
484:     case 'Y':
485:       thi->initialize = THIInitialize_HOM_Y;
486:       thi->no_slip    = PETSC_FALSE;
487:       thi->alpha      = 0.5;
488:       break;
489:     case 'Z':
490:       thi->initialize = THIInitialize_HOM_Z;
491:       thi->no_slip    = PETSC_FALSE;
492:       thi->alpha      = 0.5;
493:       break;
494:     default:
495:       SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"HOM experiment '%c' not implemented",homexp[0]);
496:     }
497:     PetscOptionsEnum("-thi_quadrature","Quadrature to use for 3D elements","",QuadratureTypes,(PetscEnum)quad,(PetscEnum*)&quad,NULL);
498:     switch (quad) {
499:     case QUAD_GAUSS:
500:       HexQInterp = HexQInterp_Gauss;
501:       HexQDeriv  = HexQDeriv_Gauss;
502:       break;
503:     case QUAD_LOBATTO:
504:       HexQInterp = HexQInterp_Lobatto;
505:       HexQDeriv  = HexQDeriv_Lobatto;
506:       break;
507:     }
508:     PetscOptionsReal("-thi_alpha","Bed angle (degrees)","",thi->alpha,&thi->alpha,NULL);

510:     thi->friction.refvel = 100.;
511:     thi->friction.epsvel = 1.;

513:     PetscOptionsReal("-thi_friction_refvel","Reference velocity for sliding","",thi->friction.refvel,&thi->friction.refvel,NULL);
514:     PetscOptionsReal("-thi_friction_epsvel","Regularization velocity for sliding","",thi->friction.epsvel,&thi->friction.epsvel,NULL);
515:     PetscOptionsReal("-thi_friction_m","Friction exponent, 0=Coulomb, 1=Navier","",m,&m,NULL);

517:     thi->friction.exponent = (m-1)/2;

519:     PetscOptionsReal("-thi_dirichlet_scale","Scale Dirichlet boundary conditions by this factor","",thi->dirichlet_scale,&thi->dirichlet_scale,NULL);
520:     PetscOptionsReal("-thi_ssa_friction_scale","Scale slip boundary conditions by this factor in SSA (2D) assembly","",thi->ssa_friction_scale,&thi->ssa_friction_scale,NULL);
521:     PetscOptionsBool("-thi_coarse2d","Use a 2D coarse space corresponding to SSA","",thi->coarse2d,&thi->coarse2d,NULL);
522:     PetscOptionsBool("-thi_tridiagonal","Assemble a tridiagonal system (column coupling only) on the finest level","",thi->tridiagonal,&thi->tridiagonal,NULL);
523:     PetscOptionsFList("-thi_mat_type","Matrix type","MatSetType",MatList,mtype,(char*)mtype,sizeof(mtype),NULL);
524:     PetscStrallocpy(mtype,(char**)&thi->mattype);
525:     PetscOptionsBool("-thi_verbose","Enable verbose output (like matrix sizes and statistics)","",thi->verbose,&thi->verbose,NULL);
526:   }
527:   PetscOptionsEnd();

529:   /* dimensionalize */
530:   thi->Lx    *= units->meter;
531:   thi->Ly    *= units->meter;
532:   thi->Lz    *= units->meter;
533:   thi->alpha *= PETSC_PI / 180;

535:   PRangeClear(&thi->eta);
536:   PRangeClear(&thi->beta2);

538:   {
539:     PetscReal u       = 1000*units->meter/(3e7*units->second),
540:               gradu   = u / (100*units->meter),eta,deta,
541:               rho     = 910 * units->kilogram/PetscPowReal(units->meter,3),
542:               grav    = 9.81 * units->meter/PetscSqr(units->second),
543:               driving = rho * grav * PetscSinReal(thi->alpha) * 1000*units->meter;
544:     THIViscosity(thi,0.5*gradu*gradu,&eta,&deta);
545:     thi->rhog = rho * grav;
546:     if (thi->verbose) {
547:       PetscPrintf(PetscObjectComm((PetscObject)thi),"Units: meter %8.2g  second %8.2g  kg %8.2g  Pa %8.2g\n",(double)units->meter,(double)units->second,(double)units->kilogram,(double)units->Pascal);
548:       PetscPrintf(PetscObjectComm((PetscObject)thi),"Domain (%6.2g,%6.2g,%6.2g), pressure %8.2g, driving stress %8.2g\n",(double)thi->Lx,(double)thi->Ly,(double)thi->Lz,(double)(rho*grav*1e3*units->meter),(double)driving);
549:       PetscPrintf(PetscObjectComm((PetscObject)thi),"Large velocity 1km/a %8.2g, velocity gradient %8.2g, eta %8.2g, stress %8.2g, ratio %8.2g\n",(double)u,(double)gradu,(double)eta,(double)(2*eta*gradu),(double)(2*eta*gradu/driving));
550:       THIViscosity(thi,0.5*PetscSqr(1e-3*gradu),&eta,&deta);
551:       PetscPrintf(PetscObjectComm((PetscObject)thi),"Small velocity 1m/a  %8.2g, velocity gradient %8.2g, eta %8.2g, stress %8.2g, ratio %8.2g\n",(double)(1e-3*u),(double)(1e-3*gradu),(double)eta,(double)(2*eta*1e-3*gradu),(double)(2*eta*1e-3*gradu/driving));
552:     }
553:   }

555:   *inthi = thi;
556:   return(0);
557: }

559: static PetscErrorCode THIInitializePrm(THI thi,DM da2prm,Vec prm)
560: {
561:   PrmNode        **p;
562:   PetscInt       i,j,xs,xm,ys,ym,mx,my;

566:   DMDAGetGhostCorners(da2prm,&ys,&xs,0,&ym,&xm,0);
567:   DMDAGetInfo(da2prm,0, &my,&mx,0, 0,0,0, 0,0,0,0,0,0);
568:   DMDAVecGetArray(da2prm,prm,&p);
569:   for (i=xs; i<xs+xm; i++) {
570:     for (j=ys; j<ys+ym; j++) {
571:       PetscReal xx = thi->Lx*i/mx,yy = thi->Ly*j/my;
572:       thi->initialize(thi,xx,yy,&p[i][j]);
573:     }
574:   }
575:   DMDAVecRestoreArray(da2prm,prm,&p);
576:   return(0);
577: }

579: static PetscErrorCode THISetUpDM(THI thi,DM dm)
580: {
581:   PetscErrorCode  ierr;
582:   PetscInt        refinelevel,coarsenlevel,level,dim,Mx,My,Mz,mx,my,s;
583:   DMDAStencilType st;
584:   DM              da2prm;
585:   Vec             X;

588:   DMDAGetInfo(dm,&dim, &Mz,&My,&Mx, 0,&my,&mx, 0,&s,0,0,0,&st);
589:   if (dim == 2) {
590:     DMDAGetInfo(dm,&dim, &My,&Mx,0, &my,&mx,0, 0,&s,0,0,0,&st);
591:   }
592:   DMGetRefineLevel(dm,&refinelevel);
593:   DMGetCoarsenLevel(dm,&coarsenlevel);
594:   level = refinelevel - coarsenlevel;
595:   DMDACreate2d(PetscObjectComm((PetscObject)thi),DM_BOUNDARY_PERIODIC,DM_BOUNDARY_PERIODIC,st,My,Mx,my,mx,sizeof(PrmNode)/sizeof(PetscScalar),s,0,0,&da2prm);
596:   DMSetUp(da2prm);
597:   DMCreateLocalVector(da2prm,&X);
598:   {
599:     PetscReal Lx = thi->Lx / thi->units->meter,Ly = thi->Ly / thi->units->meter,Lz = thi->Lz / thi->units->meter;
600:     if (dim == 2) {
601:       PetscPrintf(PetscObjectComm((PetscObject)thi),"Level %D domain size (m) %8.2g x %8.2g, num elements %D x %D (%D), size (m) %g x %g\n",level,(double)Lx,(double)Ly,Mx,My,Mx*My,(double)(Lx/Mx),(double)(Ly/My));
602:     } else {
603:       PetscPrintf(PetscObjectComm((PetscObject)thi),"Level %D domain size (m) %8.2g x %8.2g x %8.2g, num elements %D x %D x %D (%D), size (m) %g x %g x %g\n",level,(double)Lx,(double)Ly,(double)Lz,Mx,My,Mz,Mx*My*Mz,(double)(Lx/Mx),(double)(Ly/My),(double)(1000./(Mz-1)));
604:     }
605:   }
606:   THIInitializePrm(thi,da2prm,X);
607:   if (thi->tridiagonal) {       /* Reset coarse Jacobian evaluation */
608:     DMDASNESSetJacobianLocal(dm,(DMDASNESJacobian)THIJacobianLocal_3D_Full,thi);
609:   }
610:   if (thi->coarse2d) {
611:     DMDASNESSetJacobianLocal(dm,(DMDASNESJacobian)THIJacobianLocal_2D,thi);
612:   }
613:   PetscObjectCompose((PetscObject)dm,"DMDA2Prm",(PetscObject)da2prm);
614:   PetscObjectCompose((PetscObject)dm,"DMDA2Prm_Vec",(PetscObject)X);
615:   DMDestroy(&da2prm);
616:   VecDestroy(&X);
617:   return(0);
618: }

620: static PetscErrorCode DMCoarsenHook_THI(DM dmf,DM dmc,void *ctx)
621: {
622:   THI            thi = (THI)ctx;
624:   PetscInt       rlevel,clevel;

627:   THISetUpDM(thi,dmc);
628:   DMGetRefineLevel(dmc,&rlevel);
629:   DMGetCoarsenLevel(dmc,&clevel);
630:   if (rlevel-clevel == 0) {DMSetMatType(dmc,MATAIJ);}
631:   DMCoarsenHookAdd(dmc,DMCoarsenHook_THI,NULL,thi);
632:   return(0);
633: }

635: static PetscErrorCode DMRefineHook_THI(DM dmc,DM dmf,void *ctx)
636: {
637:   THI            thi = (THI)ctx;

641:   THISetUpDM(thi,dmf);
642:   DMSetMatType(dmf,thi->mattype);
643:   DMRefineHookAdd(dmf,DMRefineHook_THI,NULL,thi);
644:   /* With grid sequencing, a formerly-refined DM will later be coarsened by PCSetUp_MG */
645:   DMCoarsenHookAdd(dmf,DMCoarsenHook_THI,NULL,thi);
646:   return(0);
647: }

649: static PetscErrorCode THIDAGetPrm(DM da,PrmNode ***prm)
650: {
652:   DM             da2prm;
653:   Vec            X;

656:   PetscObjectQuery((PetscObject)da,"DMDA2Prm",(PetscObject*)&da2prm);
657:   if (!da2prm) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"No DMDA2Prm composed with given DMDA");
658:   PetscObjectQuery((PetscObject)da,"DMDA2Prm_Vec",(PetscObject*)&X);
659:   if (!X) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"No DMDA2Prm_Vec composed with given DMDA");
660:   DMDAVecGetArray(da2prm,X,prm);
661:   return(0);
662: }

664: static PetscErrorCode THIDARestorePrm(DM da,PrmNode ***prm)
665: {
667:   DM             da2prm;
668:   Vec            X;

671:   PetscObjectQuery((PetscObject)da,"DMDA2Prm",(PetscObject*)&da2prm);
672:   if (!da2prm) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"No DMDA2Prm composed with given DMDA");
673:   PetscObjectQuery((PetscObject)da,"DMDA2Prm_Vec",(PetscObject*)&X);
674:   if (!X) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"No DMDA2Prm_Vec composed with given DMDA");
675:   DMDAVecRestoreArray(da2prm,X,prm);
676:   return(0);
677: }

679: static PetscErrorCode THIInitial(SNES snes,Vec X,void *ctx)
680: {
681:   THI            thi;
682:   PetscInt       i,j,k,xs,xm,ys,ym,zs,zm,mx,my;
683:   PetscReal      hx,hy;
684:   PrmNode        **prm;
685:   Node           ***x;
687:   DM             da;

690:   SNESGetDM(snes,&da);
691:   DMGetApplicationContext(da,&thi);
692:   DMDAGetInfo(da,0, 0,&my,&mx, 0,0,0, 0,0,0,0,0,0);
693:   DMDAGetCorners(da,&zs,&ys,&xs,&zm,&ym,&xm);
694:   DMDAVecGetArray(da,X,&x);
695:   THIDAGetPrm(da,&prm);
696:   hx   = thi->Lx / mx;
697:   hy   = thi->Ly / my;
698:   for (i=xs; i<xs+xm; i++) {
699:     for (j=ys; j<ys+ym; j++) {
700:       for (k=zs; k<zs+zm; k++) {
701:         const PetscScalar zm1      = zm-1,
702:                           drivingx = thi->rhog * (prm[i+1][j].b+prm[i+1][j].h - prm[i-1][j].b-prm[i-1][j].h) / (2*hx),
703:                           drivingy = thi->rhog * (prm[i][j+1].b+prm[i][j+1].h - prm[i][j-1].b-prm[i][j-1].h) / (2*hy);
704:         x[i][j][k].u = 0. * drivingx * prm[i][j].h*(PetscScalar)k/zm1;
705:         x[i][j][k].v = 0. * drivingy * prm[i][j].h*(PetscScalar)k/zm1;
706:       }
707:     }
708:   }
709:   DMDAVecRestoreArray(da,X,&x);
710:   THIDARestorePrm(da,&prm);
711:   return(0);
712: }

714: static void PointwiseNonlinearity(THI thi,const Node n[PETSC_RESTRICT],const PetscReal phi[PETSC_RESTRICT],PetscReal dphi[PETSC_RESTRICT][3],PetscScalar *PETSC_RESTRICT u,PetscScalar *PETSC_RESTRICT v,PetscScalar du[PETSC_RESTRICT],PetscScalar dv[PETSC_RESTRICT],PetscReal *eta,PetscReal *deta)
715: {
716:   PetscInt    l,ll;
717:   PetscScalar gam;

719:   du[0] = du[1] = du[2] = 0;
720:   dv[0] = dv[1] = dv[2] = 0;
721:   *u    = 0;
722:   *v    = 0;
723:   for (l=0; l<8; l++) {
724:     *u += phi[l] * n[l].u;
725:     *v += phi[l] * n[l].v;
726:     for (ll=0; ll<3; ll++) {
727:       du[ll] += dphi[l][ll] * n[l].u;
728:       dv[ll] += dphi[l][ll] * n[l].v;
729:     }
730:   }
731:   gam = PetscSqr(du[0]) + PetscSqr(dv[1]) + du[0]*dv[1] + 0.25*PetscSqr(du[1]+dv[0]) + 0.25*PetscSqr(du[2]) + 0.25*PetscSqr(dv[2]);
732:   THIViscosity(thi,PetscRealPart(gam),eta,deta);
733: }

735: static void PointwiseNonlinearity2D(THI thi,Node n[],PetscReal phi[],PetscReal dphi[4][2],PetscScalar *u,PetscScalar *v,PetscScalar du[],PetscScalar dv[],PetscReal *eta,PetscReal *deta)
736: {
737:   PetscInt    l,ll;
738:   PetscScalar gam;

740:   du[0] = du[1] = 0;
741:   dv[0] = dv[1] = 0;
742:   *u    = 0;
743:   *v    = 0;
744:   for (l=0; l<4; l++) {
745:     *u += phi[l] * n[l].u;
746:     *v += phi[l] * n[l].v;
747:     for (ll=0; ll<2; ll++) {
748:       du[ll] += dphi[l][ll] * n[l].u;
749:       dv[ll] += dphi[l][ll] * n[l].v;
750:     }
751:   }
752:   gam = PetscSqr(du[0]) + PetscSqr(dv[1]) + du[0]*dv[1] + 0.25*PetscSqr(du[1]+dv[0]);
753:   THIViscosity(thi,PetscRealPart(gam),eta,deta);
754: }

756: static PetscErrorCode THIFunctionLocal(DMDALocalInfo *info,Node ***x,Node ***f,THI thi)
757: {
758:   PetscInt       xs,ys,xm,ym,zm,i,j,k,q,l;
759:   PetscReal      hx,hy,etamin,etamax,beta2min,beta2max;
760:   PrmNode        **prm;

764:   xs = info->zs;
765:   ys = info->ys;
766:   xm = info->zm;
767:   ym = info->ym;
768:   zm = info->xm;
769:   hx = thi->Lx / info->mz;
770:   hy = thi->Ly / info->my;

772:   etamin   = 1e100;
773:   etamax   = 0;
774:   beta2min = 1e100;
775:   beta2max = 0;

777:   THIDAGetPrm(info->da,&prm);

779:   for (i=xs; i<xs+xm; i++) {
780:     for (j=ys; j<ys+ym; j++) {
781:       PrmNode pn[4];
782:       QuadExtract(prm,i,j,pn);
783:       for (k=0; k<zm-1; k++) {
784:         PetscInt  ls = 0;
785:         Node      n[8],*fn[8];
786:         PetscReal zn[8],etabase = 0;
787:         PrmHexGetZ(pn,k,zm,zn);
788:         HexExtract(x,i,j,k,n);
789:         HexExtractRef(f,i,j,k,fn);
790:         if (thi->no_slip && k == 0) {
791:           for (l=0; l<4; l++) n[l].u = n[l].v = 0;
792:           /* The first 4 basis functions lie on the bottom layer, so their contribution is exactly 0, hence we can skip them */
793:           ls = 4;
794:         }
795:         for (q=0; q<8; q++) {
796:           PetscReal   dz[3],phi[8],dphi[8][3],jw,eta,deta;
797:           PetscScalar du[3],dv[3],u,v;
798:           HexGrad(HexQDeriv[q],zn,dz);
799:           HexComputeGeometry(q,hx,hy,dz,phi,dphi,&jw);
800:           PointwiseNonlinearity(thi,n,phi,dphi,&u,&v,du,dv,&eta,&deta);
801:           jw /= thi->rhog;      /* scales residuals to be O(1) */
802:           if (q == 0) etabase = eta;
803:           RangeUpdate(&etamin,&etamax,eta);
804:           for (l=ls; l<8; l++) { /* test functions */
805:             const PetscReal ds[2] = {-PetscSinReal(thi->alpha),0};
806:             const PetscReal pp    = phi[l],*dp = dphi[l];
807:             fn[l]->u += dp[0]*jw*eta*(4.*du[0]+2.*dv[1]) + dp[1]*jw*eta*(du[1]+dv[0]) + dp[2]*jw*eta*du[2] + pp*jw*thi->rhog*ds[0];
808:             fn[l]->v += dp[1]*jw*eta*(2.*du[0]+4.*dv[1]) + dp[0]*jw*eta*(du[1]+dv[0]) + dp[2]*jw*eta*dv[2] + pp*jw*thi->rhog*ds[1];
809:           }
810:         }
811:         if (k == 0) { /* we are on a bottom face */
812:           if (thi->no_slip) {
813:             /* Note: Non-Galerkin coarse grid operators are very sensitive to the scaling of Dirichlet boundary
814:             * conditions.  After shenanigans above, etabase contains the effective viscosity at the closest quadrature
815:             * point to the bed.  We want the diagonal entry in the Dirichlet condition to have similar magnitude to the
816:             * diagonal entry corresponding to the adjacent node.  The fundamental scaling of the viscous part is in
817:             * diagu, diagv below.  This scaling is easy to recognize by considering the finite difference operator after
818:             * scaling by element size.  The no-slip Dirichlet condition is scaled by this factor, and also in the
819:             * assembled matrix (see the similar block in THIJacobianLocal).
820:             *
821:             * Note that the residual at this Dirichlet node is linear in the state at this node, but also depends
822:             * (nonlinearly in general) on the neighboring interior nodes through the local viscosity.  This will make
823:             * a matrix-free Jacobian have extra entries in the corresponding row.  We assemble only the diagonal part,
824:             * so the solution will exactly satisfy the boundary condition after the first linear iteration.
825:             */
826:             const PetscReal   hz    = PetscRealPart(pn[0].h)/(zm-1.);
827:             const PetscScalar diagu = 2*etabase/thi->rhog*(hx*hy/hz + hx*hz/hy + 4*hy*hz/hx),diagv = 2*etabase/thi->rhog*(hx*hy/hz + 4*hx*hz/hy + hy*hz/hx);
828:             fn[0]->u = thi->dirichlet_scale*diagu*x[i][j][k].u;
829:             fn[0]->v = thi->dirichlet_scale*diagv*x[i][j][k].v;
830:           } else {              /* Integrate over bottom face to apply boundary condition */
831:             for (q=0; q<4; q++) {
832:               const PetscReal jw = 0.25*hx*hy/thi->rhog,*phi = QuadQInterp[q];
833:               PetscScalar     u  =0,v=0,rbeta2=0;
834:               PetscReal       beta2,dbeta2;
835:               for (l=0; l<4; l++) {
836:                 u      += phi[l]*n[l].u;
837:                 v      += phi[l]*n[l].v;
838:                 rbeta2 += phi[l]*pn[l].beta2;
839:               }
840:               THIFriction(thi,PetscRealPart(rbeta2),PetscRealPart(u*u+v*v)/2,&beta2,&dbeta2);
841:               RangeUpdate(&beta2min,&beta2max,beta2);
842:               for (l=0; l<4; l++) {
843:                 const PetscReal pp = phi[l];
844:                 fn[ls+l]->u += pp*jw*beta2*u;
845:                 fn[ls+l]->v += pp*jw*beta2*v;
846:               }
847:             }
848:           }
849:         }
850:       }
851:     }
852:   }

854:   THIDARestorePrm(info->da,&prm);

856:   PRangeMinMax(&thi->eta,etamin,etamax);
857:   PRangeMinMax(&thi->beta2,beta2min,beta2max);
858:   return(0);
859: }

861: static PetscErrorCode THIMatrixStatistics(THI thi,Mat B,PetscViewer viewer)
862: {
864:   PetscReal      nrm;
865:   PetscInt       m;
866:   PetscMPIInt    rank;

869:   MatNorm(B,NORM_FROBENIUS,&nrm);
870:   MatGetSize(B,&m,0);
871:   MPI_Comm_rank(PetscObjectComm((PetscObject)B),&rank);
872:   if (!rank) {
873:     PetscScalar val0,val2;
874:     MatGetValue(B,0,0,&val0);
875:     MatGetValue(B,2,2,&val2);
876:     PetscViewerASCIIPrintf(viewer,"Matrix dim %D norm %8.2e (0,0) %8.2e  (2,2) %8.2e %8.2e <= eta <= %8.2e %8.2e <= beta2 <= %8.2e\n",m,(double)nrm,(double)PetscRealPart(val0),(double)PetscRealPart(val2),(double)thi->eta.cmin,(double)thi->eta.cmax,(double)thi->beta2.cmin,(double)thi->beta2.cmax);
877:   }
878:   return(0);
879: }

881: static PetscErrorCode THISurfaceStatistics(DM da,Vec X,PetscReal *min,PetscReal *max,PetscReal *mean)
882: {
884:   Node           ***x;
885:   PetscInt       i,j,xs,ys,zs,xm,ym,zm,mx,my,mz;
886:   PetscReal      umin = 1e100,umax=-1e100;
887:   PetscScalar    usum = 0.0,gusum;

890:   *min = *max = *mean = 0;
891:   DMDAGetInfo(da,0, &mz,&my,&mx, 0,0,0, 0,0,0,0,0,0);
892:   DMDAGetCorners(da,&zs,&ys,&xs,&zm,&ym,&xm);
893:   if (zs != 0 || zm != mz) SETERRQ(PETSC_COMM_SELF,1,"Unexpected decomposition");
894:   DMDAVecGetArray(da,X,&x);
895:   for (i=xs; i<xs+xm; i++) {
896:     for (j=ys; j<ys+ym; j++) {
897:       PetscReal u = PetscRealPart(x[i][j][zm-1].u);
898:       RangeUpdate(&umin,&umax,u);
899:       usum += u;
900:     }
901:   }
902:   DMDAVecRestoreArray(da,X,&x);
903:   MPI_Allreduce(&umin,min,1,MPIU_REAL,MPIU_MIN,PetscObjectComm((PetscObject)da));
904:   MPI_Allreduce(&umax,max,1,MPIU_REAL,MPIU_MAX,PetscObjectComm((PetscObject)da));
905:   MPI_Allreduce(&usum,&gusum,1,MPIU_SCALAR,MPIU_SUM,PetscObjectComm((PetscObject)da));
906:   *mean = PetscRealPart(gusum) / (mx*my);
907:   return(0);
908: }

910: static PetscErrorCode THISolveStatistics(THI thi,SNES snes,PetscInt coarsened,const char name[])
911: {
912:   MPI_Comm       comm;
913:   Vec            X;
914:   DM             dm;

918:   PetscObjectGetComm((PetscObject)thi,&comm);
919:   SNESGetSolution(snes,&X);
920:   SNESGetDM(snes,&dm);
921:   PetscPrintf(comm,"Solution statistics after solve: %s\n",name);
922:   {
923:     PetscInt            its,lits;
924:     SNESConvergedReason reason;
925:     SNESGetIterationNumber(snes,&its);
926:     SNESGetConvergedReason(snes,&reason);
927:     SNESGetLinearSolveIterations(snes,&lits);
928:     PetscPrintf(comm,"%s: Number of SNES iterations = %D, total linear iterations = %D\n",SNESConvergedReasons[reason],its,lits);
929:   }
930:   {
931:     PetscReal         nrm2,tmin[3]={1e100,1e100,1e100},tmax[3]={-1e100,-1e100,-1e100},min[3],max[3];
932:     PetscInt          i,j,m;
933:     const PetscScalar *x;
934:     VecNorm(X,NORM_2,&nrm2);
935:     VecGetLocalSize(X,&m);
936:     VecGetArrayRead(X,&x);
937:     for (i=0; i<m; i+=2) {
938:       PetscReal u = PetscRealPart(x[i]),v = PetscRealPart(x[i+1]),c = PetscSqrtReal(u*u+v*v);
939:       tmin[0] = PetscMin(u,tmin[0]);
940:       tmin[1] = PetscMin(v,tmin[1]);
941:       tmin[2] = PetscMin(c,tmin[2]);
942:       tmax[0] = PetscMax(u,tmax[0]);
943:       tmax[1] = PetscMax(v,tmax[1]);
944:       tmax[2] = PetscMax(c,tmax[2]);
945:     }
946:     VecRestoreArrayRead(X,&x);
947:     MPI_Allreduce(tmin,min,3,MPIU_REAL,MPIU_MIN,PetscObjectComm((PetscObject)thi));
948:     MPI_Allreduce(tmax,max,3,MPIU_REAL,MPIU_MAX,PetscObjectComm((PetscObject)thi));
949:     /* Dimensionalize to meters/year */
950:     nrm2 *= thi->units->year / thi->units->meter;
951:     for (j=0; j<3; j++) {
952:       min[j] *= thi->units->year / thi->units->meter;
953:       max[j] *= thi->units->year / thi->units->meter;
954:     }
955:     if (min[0] == 0.0) min[0] = 0.0;
956:     PetscPrintf(comm,"|X|_2 %g   %g <= u <=  %g   %g <= v <=  %g   %g <= c <=  %g \n",(double)nrm2,(double)min[0],(double)max[0],(double)min[1],(double)max[1],(double)min[2],(double)max[2]);
957:     {
958:       PetscReal umin,umax,umean;
959:       THISurfaceStatistics(dm,X,&umin,&umax,&umean);
960:       umin  *= thi->units->year / thi->units->meter;
961:       umax  *= thi->units->year / thi->units->meter;
962:       umean *= thi->units->year / thi->units->meter;
963:       PetscPrintf(comm,"Surface statistics: u in [%12.6e, %12.6e] mean %12.6e\n",(double)umin,(double)umax,(double)umean);
964:     }
965:     /* These values stay nondimensional */
966:     PetscPrintf(comm,"Global eta range   %g to %g converged range %g to %g\n",(double)thi->eta.min,(double)thi->eta.max,(double)thi->eta.cmin,(double)thi->eta.cmax);
967:     PetscPrintf(comm,"Global beta2 range %g to %g converged range %g to %g\n",(double)thi->beta2.min,(double)thi->beta2.max,(double)thi->beta2.cmin,(double)thi->beta2.cmax);
968:   }
969:   return(0);
970: }

972: static PetscErrorCode THIJacobianLocal_2D(DMDALocalInfo *info,Node **x,Mat J,Mat B,THI thi)
973: {
974:   PetscInt       xs,ys,xm,ym,i,j,q,l,ll;
975:   PetscReal      hx,hy;
976:   PrmNode        **prm;

980:   xs = info->ys;
981:   ys = info->xs;
982:   xm = info->ym;
983:   ym = info->xm;
984:   hx = thi->Lx / info->my;
985:   hy = thi->Ly / info->mx;

987:   MatZeroEntries(B);
988:   THIDAGetPrm(info->da,&prm);

990:   for (i=xs; i<xs+xm; i++) {
991:     for (j=ys; j<ys+ym; j++) {
992:       Node        n[4];
993:       PrmNode     pn[4];
994:       PetscScalar Ke[4*2][4*2];
995:       QuadExtract(prm,i,j,pn);
996:       QuadExtract(x,i,j,n);
997:       PetscMemzero(Ke,sizeof(Ke));
998:       for (q=0; q<4; q++) {
999:         PetscReal   phi[4],dphi[4][2],jw,eta,deta,beta2,dbeta2;
1000:         PetscScalar u,v,du[2],dv[2],h = 0,rbeta2 = 0;
1001:         for (l=0; l<4; l++) {
1002:           phi[l]     = QuadQInterp[q][l];
1003:           dphi[l][0] = QuadQDeriv[q][l][0]*2./hx;
1004:           dphi[l][1] = QuadQDeriv[q][l][1]*2./hy;
1005:           h         += phi[l] * pn[l].h;
1006:           rbeta2    += phi[l] * pn[l].beta2;
1007:         }
1008:         jw = 0.25*hx*hy / thi->rhog; /* rhog is only scaling */
1009:         PointwiseNonlinearity2D(thi,n,phi,dphi,&u,&v,du,dv,&eta,&deta);
1010:         THIFriction(thi,PetscRealPart(rbeta2),PetscRealPart(u*u+v*v)/2,&beta2,&dbeta2);
1011:         for (l=0; l<4; l++) {
1012:           const PetscReal pp = phi[l],*dp = dphi[l];
1013:           for (ll=0; ll<4; ll++) {
1014:             const PetscReal ppl = phi[ll],*dpl = dphi[ll];
1015:             PetscScalar     dgdu,dgdv;
1016:             dgdu = 2.*du[0]*dpl[0] + dv[1]*dpl[0] + 0.5*(du[1]+dv[0])*dpl[1];
1017:             dgdv = 2.*dv[1]*dpl[1] + du[0]*dpl[1] + 0.5*(du[1]+dv[0])*dpl[0];
1018:             /* Picard part */
1019:             Ke[l*2+0][ll*2+0] += dp[0]*jw*eta*4.*dpl[0] + dp[1]*jw*eta*dpl[1] + pp*jw*(beta2/h)*ppl*thi->ssa_friction_scale;
1020:             Ke[l*2+0][ll*2+1] += dp[0]*jw*eta*2.*dpl[1] + dp[1]*jw*eta*dpl[0];
1021:             Ke[l*2+1][ll*2+0] += dp[1]*jw*eta*2.*dpl[0] + dp[0]*jw*eta*dpl[1];
1022:             Ke[l*2+1][ll*2+1] += dp[1]*jw*eta*4.*dpl[1] + dp[0]*jw*eta*dpl[0] + pp*jw*(beta2/h)*ppl*thi->ssa_friction_scale;
1023:             /* extra Newton terms */
1024:             Ke[l*2+0][ll*2+0] += dp[0]*jw*deta*dgdu*(4.*du[0]+2.*dv[1]) + dp[1]*jw*deta*dgdu*(du[1]+dv[0]) + pp*jw*(dbeta2/h)*u*u*ppl*thi->ssa_friction_scale;
1025:             Ke[l*2+0][ll*2+1] += dp[0]*jw*deta*dgdv*(4.*du[0]+2.*dv[1]) + dp[1]*jw*deta*dgdv*(du[1]+dv[0]) + pp*jw*(dbeta2/h)*u*v*ppl*thi->ssa_friction_scale;
1026:             Ke[l*2+1][ll*2+0] += dp[1]*jw*deta*dgdu*(4.*dv[1]+2.*du[0]) + dp[0]*jw*deta*dgdu*(du[1]+dv[0]) + pp*jw*(dbeta2/h)*v*u*ppl*thi->ssa_friction_scale;
1027:             Ke[l*2+1][ll*2+1] += dp[1]*jw*deta*dgdv*(4.*dv[1]+2.*du[0]) + dp[0]*jw*deta*dgdv*(du[1]+dv[0]) + pp*jw*(dbeta2/h)*v*v*ppl*thi->ssa_friction_scale;
1028:           }
1029:         }
1030:       }
1031:       {
1032:         const MatStencil rc[4] = {{0,i,j,0},{0,i+1,j,0},{0,i+1,j+1,0},{0,i,j+1,0}};
1033:         MatSetValuesBlockedStencil(B,4,rc,4,rc,&Ke[0][0],ADD_VALUES);
1034:       }
1035:     }
1036:   }
1037:   THIDARestorePrm(info->da,&prm);

1039:   MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
1040:   MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
1041:   MatSetOption(B,MAT_SYMMETRIC,PETSC_TRUE);
1042:   if (thi->verbose) {THIMatrixStatistics(thi,B,PETSC_VIEWER_STDOUT_WORLD);}
1043:   return(0);
1044: }

1046: static PetscErrorCode THIJacobianLocal_3D(DMDALocalInfo *info,Node ***x,Mat B,THI thi,THIAssemblyMode amode)
1047: {
1048:   PetscInt       xs,ys,xm,ym,zm,i,j,k,q,l,ll;
1049:   PetscReal      hx,hy;
1050:   PrmNode        **prm;

1054:   xs = info->zs;
1055:   ys = info->ys;
1056:   xm = info->zm;
1057:   ym = info->ym;
1058:   zm = info->xm;
1059:   hx = thi->Lx / info->mz;
1060:   hy = thi->Ly / info->my;

1062:   MatZeroEntries(B);
1063:   MatSetOption(B,MAT_SUBSET_OFF_PROC_ENTRIES,PETSC_TRUE);
1064:   THIDAGetPrm(info->da,&prm);

1066:   for (i=xs; i<xs+xm; i++) {
1067:     for (j=ys; j<ys+ym; j++) {
1068:       PrmNode pn[4];
1069:       QuadExtract(prm,i,j,pn);
1070:       for (k=0; k<zm-1; k++) {
1071:         Node        n[8];
1072:         PetscReal   zn[8],etabase = 0;
1073:         PetscScalar Ke[8*2][8*2];
1074:         PetscInt    ls = 0;

1076:         PrmHexGetZ(pn,k,zm,zn);
1077:         HexExtract(x,i,j,k,n);
1078:         PetscMemzero(Ke,sizeof(Ke));
1079:         if (thi->no_slip && k == 0) {
1080:           for (l=0; l<4; l++) n[l].u = n[l].v = 0;
1081:           ls = 4;
1082:         }
1083:         for (q=0; q<8; q++) {
1084:           PetscReal   dz[3],phi[8],dphi[8][3],jw,eta,deta;
1085:           PetscScalar du[3],dv[3],u,v;
1086:           HexGrad(HexQDeriv[q],zn,dz);
1087:           HexComputeGeometry(q,hx,hy,dz,phi,dphi,&jw);
1088:           PointwiseNonlinearity(thi,n,phi,dphi,&u,&v,du,dv,&eta,&deta);
1089:           jw /= thi->rhog;      /* residuals are scaled by this factor */
1090:           if (q == 0) etabase = eta;
1091:           for (l=ls; l<8; l++) { /* test functions */
1092:             const PetscReal *PETSC_RESTRICT dp = dphi[l];
1093: #if USE_SSE2_KERNELS
1094:             /* gcc (up to my 4.5 snapshot) is really bad at hoisting intrinsics so we do it manually */
1095:             __m128d
1096:               p4         = _mm_set1_pd(4),p2 = _mm_set1_pd(2),p05 = _mm_set1_pd(0.5),
1097:               p42        = _mm_setr_pd(4,2),p24 = _mm_shuffle_pd(p42,p42,_MM_SHUFFLE2(0,1)),
1098:               du0        = _mm_set1_pd(du[0]),du1 = _mm_set1_pd(du[1]),du2 = _mm_set1_pd(du[2]),
1099:               dv0        = _mm_set1_pd(dv[0]),dv1 = _mm_set1_pd(dv[1]),dv2 = _mm_set1_pd(dv[2]),
1100:               jweta      = _mm_set1_pd(jw*eta),jwdeta = _mm_set1_pd(jw*deta),
1101:               dp0        = _mm_set1_pd(dp[0]),dp1 = _mm_set1_pd(dp[1]),dp2 = _mm_set1_pd(dp[2]),
1102:               dp0jweta   = _mm_mul_pd(dp0,jweta),dp1jweta = _mm_mul_pd(dp1,jweta),dp2jweta = _mm_mul_pd(dp2,jweta),
1103:               p4du0p2dv1 = _mm_add_pd(_mm_mul_pd(p4,du0),_mm_mul_pd(p2,dv1)), /* 4 du0 + 2 dv1 */
1104:               p4dv1p2du0 = _mm_add_pd(_mm_mul_pd(p4,dv1),_mm_mul_pd(p2,du0)), /* 4 dv1 + 2 du0 */
1105:               pdu2dv2    = _mm_unpacklo_pd(du2,dv2),                          /* [du2, dv2] */
1106:               du1pdv0    = _mm_add_pd(du1,dv0),                               /* du1 + dv0 */
1107:               t1         = _mm_mul_pd(dp0,p4du0p2dv1),                        /* dp0 (4 du0 + 2 dv1) */
1108:               t2         = _mm_mul_pd(dp1,p4dv1p2du0);                        /* dp1 (4 dv1 + 2 du0) */

1110: #endif
1111: #if defined COMPUTE_LOWER_TRIANGULAR  /* The element matrices are always symmetric so computing the lower-triangular part is not necessary */
1112:             for (ll=ls; ll<8; ll++) { /* trial functions */
1113: #else
1114:             for (ll=l; ll<8; ll++) {
1115: #endif
1116:               const PetscReal *PETSC_RESTRICT dpl = dphi[ll];
1117:               if (amode == THIASSEMBLY_TRIDIAGONAL && (l-ll)%4) continue; /* these entries would not be inserted */
1118: #if !USE_SSE2_KERNELS
1119:               /* The analytic Jacobian in nice, easy-to-read form */
1120:               {
1121:                 PetscScalar dgdu,dgdv;
1122:                 dgdu = 2.*du[0]*dpl[0] + dv[1]*dpl[0] + 0.5*(du[1]+dv[0])*dpl[1] + 0.5*du[2]*dpl[2];
1123:                 dgdv = 2.*dv[1]*dpl[1] + du[0]*dpl[1] + 0.5*(du[1]+dv[0])*dpl[0] + 0.5*dv[2]*dpl[2];
1124:                 /* Picard part */
1125:                 Ke[l*2+0][ll*2+0] += dp[0]*jw*eta*4.*dpl[0] + dp[1]*jw*eta*dpl[1] + dp[2]*jw*eta*dpl[2];
1126:                 Ke[l*2+0][ll*2+1] += dp[0]*jw*eta*2.*dpl[1] + dp[1]*jw*eta*dpl[0];
1127:                 Ke[l*2+1][ll*2+0] += dp[1]*jw*eta*2.*dpl[0] + dp[0]*jw*eta*dpl[1];
1128:                 Ke[l*2+1][ll*2+1] += dp[1]*jw*eta*4.*dpl[1] + dp[0]*jw*eta*dpl[0] + dp[2]*jw*eta*dpl[2];
1129:                 /* extra Newton terms */
1130:                 Ke[l*2+0][ll*2+0] += dp[0]*jw*deta*dgdu*(4.*du[0]+2.*dv[1]) + dp[1]*jw*deta*dgdu*(du[1]+dv[0]) + dp[2]*jw*deta*dgdu*du[2];
1131:                 Ke[l*2+0][ll*2+1] += dp[0]*jw*deta*dgdv*(4.*du[0]+2.*dv[1]) + dp[1]*jw*deta*dgdv*(du[1]+dv[0]) + dp[2]*jw*deta*dgdv*du[2];
1132:                 Ke[l*2+1][ll*2+0] += dp[1]*jw*deta*dgdu*(4.*dv[1]+2.*du[0]) + dp[0]*jw*deta*dgdu*(du[1]+dv[0]) + dp[2]*jw*deta*dgdu*dv[2];
1133:                 Ke[l*2+1][ll*2+1] += dp[1]*jw*deta*dgdv*(4.*dv[1]+2.*du[0]) + dp[0]*jw*deta*dgdv*(du[1]+dv[0]) + dp[2]*jw*deta*dgdv*dv[2];
1134:               }
1135: #else
1136:               /* This SSE2 code is an exact replica of above, but uses explicit packed instructions for some speed
1137:               * benefit.  On my hardware, these intrinsics are almost twice as fast as above, reducing total assembly cost
1138:               * by 25 to 30 percent. */
1139:               {
1140:                 __m128d
1141:                   keu   = _mm_loadu_pd(&Ke[l*2+0][ll*2+0]),
1142:                   kev   = _mm_loadu_pd(&Ke[l*2+1][ll*2+0]),
1143:                   dpl01 = _mm_loadu_pd(&dpl[0]),dpl10 = _mm_shuffle_pd(dpl01,dpl01,_MM_SHUFFLE2(0,1)),dpl2 = _mm_set_sd(dpl[2]),
1144:                   t0,t3,pdgduv;
1145:                 keu = _mm_add_pd(keu,_mm_add_pd(_mm_mul_pd(_mm_mul_pd(dp0jweta,p42),dpl01),
1146:                                                 _mm_add_pd(_mm_mul_pd(dp1jweta,dpl10),
1147:                                                            _mm_mul_pd(dp2jweta,dpl2))));
1148:                 kev = _mm_add_pd(kev,_mm_add_pd(_mm_mul_pd(_mm_mul_pd(dp1jweta,p24),dpl01),
1149:                                                 _mm_add_pd(_mm_mul_pd(dp0jweta,dpl10),
1150:                                                            _mm_mul_pd(dp2jweta,_mm_shuffle_pd(dpl2,dpl2,_MM_SHUFFLE2(0,1))))));
1151:                 pdgduv = _mm_mul_pd(p05,_mm_add_pd(_mm_add_pd(_mm_mul_pd(p42,_mm_mul_pd(du0,dpl01)),
1152:                                                               _mm_mul_pd(p24,_mm_mul_pd(dv1,dpl01))),
1153:                                                    _mm_add_pd(_mm_mul_pd(du1pdv0,dpl10),
1154:                                                               _mm_mul_pd(pdu2dv2,_mm_set1_pd(dpl[2]))))); /* [dgdu, dgdv] */
1155:                 t0 = _mm_mul_pd(jwdeta,pdgduv);  /* jw deta [dgdu, dgdv] */
1156:                 t3 = _mm_mul_pd(t0,du1pdv0);     /* t0 (du1 + dv0) */
1157:                 _mm_storeu_pd(&Ke[l*2+0][ll*2+0],_mm_add_pd(keu,_mm_add_pd(_mm_mul_pd(t1,t0),
1158:                                                                            _mm_add_pd(_mm_mul_pd(dp1,t3),
1159:                                                                                       _mm_mul_pd(t0,_mm_mul_pd(dp2,du2))))));
1160:                 _mm_storeu_pd(&Ke[l*2+1][ll*2+0],_mm_add_pd(kev,_mm_add_pd(_mm_mul_pd(t2,t0),
1161:                                                                            _mm_add_pd(_mm_mul_pd(dp0,t3),
1162:                                                                                       _mm_mul_pd(t0,_mm_mul_pd(dp2,dv2))))));
1163:               }
1164: #endif
1165:             }
1166:           }
1167:         }
1168:         if (k == 0) { /* on a bottom face */
1169:           if (thi->no_slip) {
1170:             const PetscReal   hz    = PetscRealPart(pn[0].h)/(zm-1);
1171:             const PetscScalar diagu = 2*etabase/thi->rhog*(hx*hy/hz + hx*hz/hy + 4*hy*hz/hx),diagv = 2*etabase/thi->rhog*(hx*hy/hz + 4*hx*hz/hy + hy*hz/hx);
1172:             Ke[0][0] = thi->dirichlet_scale*diagu;
1173:             Ke[1][1] = thi->dirichlet_scale*diagv;
1174:           } else {
1175:             for (q=0; q<4; q++) {
1176:               const PetscReal jw = 0.25*hx*hy/thi->rhog,*phi = QuadQInterp[q];
1177:               PetscScalar     u  =0,v=0,rbeta2=0;
1178:               PetscReal       beta2,dbeta2;
1179:               for (l=0; l<4; l++) {
1180:                 u      += phi[l]*n[l].u;
1181:                 v      += phi[l]*n[l].v;
1182:                 rbeta2 += phi[l]*pn[l].beta2;
1183:               }
1184:               THIFriction(thi,PetscRealPart(rbeta2),PetscRealPart(u*u+v*v)/2,&beta2,&dbeta2);
1185:               for (l=0; l<4; l++) {
1186:                 const PetscReal pp = phi[l];
1187:                 for (ll=0; ll<4; ll++) {
1188:                   const PetscReal ppl = phi[ll];
1189:                   Ke[l*2+0][ll*2+0] += pp*jw*beta2*ppl + pp*jw*dbeta2*u*u*ppl;
1190:                   Ke[l*2+0][ll*2+1] +=                   pp*jw*dbeta2*u*v*ppl;
1191:                   Ke[l*2+1][ll*2+0] +=                   pp*jw*dbeta2*v*u*ppl;
1192:                   Ke[l*2+1][ll*2+1] += pp*jw*beta2*ppl + pp*jw*dbeta2*v*v*ppl;
1193:                 }
1194:               }
1195:             }
1196:           }
1197:         }
1198:         {
1199:           const MatStencil rc[8] = {{i,j,k,0},{i+1,j,k,0},{i+1,j+1,k,0},{i,j+1,k,0},{i,j,k+1,0},{i+1,j,k+1,0},{i+1,j+1,k+1,0},{i,j+1,k+1,0}};
1200:           if (amode == THIASSEMBLY_TRIDIAGONAL) {
1201:             for (l=0; l<4; l++) { /* Copy out each of the blocks, discarding horizontal coupling */
1202:               const PetscInt   l4     = l+4;
1203:               const MatStencil rcl[2] = {{rc[l].k,rc[l].j,rc[l].i,0},{rc[l4].k,rc[l4].j,rc[l4].i,0}};
1204: #if defined COMPUTE_LOWER_TRIANGULAR
1205:               const PetscScalar Kel[4][4] = {{Ke[2*l+0][2*l+0] ,Ke[2*l+0][2*l+1] ,Ke[2*l+0][2*l4+0] ,Ke[2*l+0][2*l4+1]},
1206:                                              {Ke[2*l+1][2*l+0] ,Ke[2*l+1][2*l+1] ,Ke[2*l+1][2*l4+0] ,Ke[2*l+1][2*l4+1]},
1207:                                              {Ke[2*l4+0][2*l+0],Ke[2*l4+0][2*l+1],Ke[2*l4+0][2*l4+0],Ke[2*l4+0][2*l4+1]},
1208:                                              {Ke[2*l4+1][2*l+0],Ke[2*l4+1][2*l+1],Ke[2*l4+1][2*l4+0],Ke[2*l4+1][2*l4+1]}};
1209: #else
1210:               /* Same as above except for the lower-left block */
1211:               const PetscScalar Kel[4][4] = {{Ke[2*l+0][2*l+0] ,Ke[2*l+0][2*l+1] ,Ke[2*l+0][2*l4+0] ,Ke[2*l+0][2*l4+1]},
1212:                                              {Ke[2*l+1][2*l+0] ,Ke[2*l+1][2*l+1] ,Ke[2*l+1][2*l4+0] ,Ke[2*l+1][2*l4+1]},
1213:                                              {Ke[2*l+0][2*l4+0],Ke[2*l+1][2*l4+0],Ke[2*l4+0][2*l4+0],Ke[2*l4+0][2*l4+1]},
1214:                                              {Ke[2*l+0][2*l4+1],Ke[2*l+1][2*l4+1],Ke[2*l4+1][2*l4+0],Ke[2*l4+1][2*l4+1]}};
1215: #endif
1216:               MatSetValuesBlockedStencil(B,2,rcl,2,rcl,&Kel[0][0],ADD_VALUES);
1217:             }
1218:           } else {
1219: #if !defined COMPUTE_LOWER_TRIANGULAR /* fill in lower-triangular part, this is really cheap compared to computing the entries */
1220:             for (l=0; l<8; l++) {
1221:               for (ll=l+1; ll<8; ll++) {
1222:                 Ke[ll*2+0][l*2+0] = Ke[l*2+0][ll*2+0];
1223:                 Ke[ll*2+1][l*2+0] = Ke[l*2+0][ll*2+1];
1224:                 Ke[ll*2+0][l*2+1] = Ke[l*2+1][ll*2+0];
1225:                 Ke[ll*2+1][l*2+1] = Ke[l*2+1][ll*2+1];
1226:               }
1227:             }
1228: #endif
1229:             MatSetValuesBlockedStencil(B,8,rc,8,rc,&Ke[0][0],ADD_VALUES);
1230:           }
1231:         }
1232:       }
1233:     }
1234:   }
1235:   THIDARestorePrm(info->da,&prm);

1237:   MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
1238:   MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
1239:   MatSetOption(B,MAT_SYMMETRIC,PETSC_TRUE);
1240:   if (thi->verbose) {THIMatrixStatistics(thi,B,PETSC_VIEWER_STDOUT_WORLD);}
1241:   return(0);
1242: }

1244: static PetscErrorCode THIJacobianLocal_3D_Full(DMDALocalInfo *info,Node ***x,Mat A,Mat B,THI thi)
1245: {

1249:   THIJacobianLocal_3D(info,x,B,thi,THIASSEMBLY_FULL);
1250:   return(0);
1251: }

1253: static PetscErrorCode THIJacobianLocal_3D_Tridiagonal(DMDALocalInfo *info,Node ***x,Mat A,Mat B,THI thi)
1254: {

1258:   THIJacobianLocal_3D(info,x,B,thi,THIASSEMBLY_TRIDIAGONAL);
1259:   return(0);
1260: }

1262: static PetscErrorCode DMRefineHierarchy_THI(DM dac0,PetscInt nlevels,DM hierarchy[])
1263: {
1264:   PetscErrorCode  ierr;
1265:   THI             thi;
1266:   PetscInt        dim,M,N,m,n,s,dof;
1267:   DM              dac,daf;
1268:   DMDAStencilType st;
1269:   DM_DA           *ddf,*ddc;

1272:   PetscObjectQuery((PetscObject)dac0,"THI",(PetscObject*)&thi);
1273:   if (!thi) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Cannot refine this DMDA, missing composed THI instance");
1274:   if (nlevels > 1) {
1275:     DMRefineHierarchy(dac0,nlevels-1,hierarchy);
1276:     dac  = hierarchy[nlevels-2];
1277:   } else {
1278:     dac = dac0;
1279:   }
1280:   DMDAGetInfo(dac,&dim, &N,&M,0, &n,&m,0, &dof,&s,0,0,0,&st);
1281:   if (dim != 2) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"This function can only refine 2D DMDAs");

1283:   /* Creates a 3D DMDA with the same map-plane layout as the 2D one, with contiguous columns */
1284:   DMDACreate3d(PetscObjectComm((PetscObject)dac),DM_BOUNDARY_NONE,DM_BOUNDARY_PERIODIC,DM_BOUNDARY_PERIODIC,st,thi->zlevels,N,M,1,n,m,dof,s,NULL,NULL,NULL,&daf);
1285:   DMSetUp(daf);

1287:   daf->ops->creatematrix        = dac->ops->creatematrix;
1288:   daf->ops->createinterpolation = dac->ops->createinterpolation;
1289:   daf->ops->getcoloring         = dac->ops->getcoloring;
1290:   ddf                           = (DM_DA*)daf->data;
1291:   ddc                           = (DM_DA*)dac->data;
1292:   ddf->interptype               = ddc->interptype;

1294:   DMDASetFieldName(daf,0,"x-velocity");
1295:   DMDASetFieldName(daf,1,"y-velocity");

1297:   hierarchy[nlevels-1] = daf;
1298:   return(0);
1299: }

1301: static PetscErrorCode DMCreateInterpolation_DA_THI(DM dac,DM daf,Mat *A,Vec *scale)
1302: {
1304:   PetscInt       dim;

1311:   DMDAGetInfo(daf,&dim,0,0,0,0,0,0,0,0,0,0,0,0);
1312:   if (dim  == 2) {
1313:     /* We are in the 2D problem and use normal DMDA interpolation */
1314:     DMCreateInterpolation(dac,daf,A,scale);
1315:   } else {
1316:     PetscInt i,j,k,xs,ys,zs,xm,ym,zm,mx,my,mz,rstart,cstart;
1317:     Mat      B;

1319:     DMDAGetInfo(daf,0, &mz,&my,&mx, 0,0,0, 0,0,0,0,0,0);
1320:     DMDAGetCorners(daf,&zs,&ys,&xs,&zm,&ym,&xm);
1321:     if (zs != 0) SETERRQ(PETSC_COMM_SELF,1,"unexpected");
1322:     MatCreate(PetscObjectComm((PetscObject)daf),&B);
1323:     MatSetSizes(B,xm*ym*zm,xm*ym,mx*my*mz,mx*my);

1325:     MatSetType(B,MATAIJ);
1326:     MatSeqAIJSetPreallocation(B,1,NULL);
1327:     MatMPIAIJSetPreallocation(B,1,NULL,0,NULL);
1328:     MatGetOwnershipRange(B,&rstart,NULL);
1329:     MatGetOwnershipRangeColumn(B,&cstart,NULL);
1330:     for (i=xs; i<xs+xm; i++) {
1331:       for (j=ys; j<ys+ym; j++) {
1332:         for (k=zs; k<zs+zm; k++) {
1333:           PetscInt    i2  = i*ym+j,i3 = i2*zm+k;
1334:           PetscScalar val = ((k == 0 || k == mz-1) ? 0.5 : 1.) / (mz-1.); /* Integration using trapezoid rule */
1335:           MatSetValue(B,cstart+i3,rstart+i2,val,INSERT_VALUES);
1336:         }
1337:       }
1338:     }
1339:     MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
1340:     MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
1341:     MatCreateMAIJ(B,sizeof(Node)/sizeof(PetscScalar),A);
1342:     MatDestroy(&B);
1343:   }
1344:   return(0);
1345: }

1347: static PetscErrorCode DMCreateMatrix_THI_Tridiagonal(DM da,Mat *J)
1348: {
1349:   PetscErrorCode         ierr;
1350:   Mat                    A;
1351:   PetscInt               xm,ym,zm,dim,dof = 2,starts[3],dims[3];
1352:   ISLocalToGlobalMapping ltog;

1355:   DMDAGetInfo(da,&dim, 0,0,0, 0,0,0, 0,0,0,0,0,0);
1356:   if (dim != 3) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Expected DMDA to be 3D");
1357:   DMDAGetCorners(da,0,0,0,&zm,&ym,&xm);
1358:   DMGetLocalToGlobalMapping(da,&ltog);
1359:   MatCreate(PetscObjectComm((PetscObject)da),&A);
1360:   MatSetSizes(A,dof*xm*ym*zm,dof*xm*ym*zm,PETSC_DETERMINE,PETSC_DETERMINE);
1361:   MatSetType(A,da->mattype);
1362:   MatSetFromOptions(A);
1363:   MatSeqAIJSetPreallocation(A,3*2,NULL);
1364:   MatMPIAIJSetPreallocation(A,3*2,NULL,0,NULL);
1365:   MatSeqBAIJSetPreallocation(A,2,3,NULL);
1366:   MatMPIBAIJSetPreallocation(A,2,3,NULL,0,NULL);
1367:   MatSeqSBAIJSetPreallocation(A,2,2,NULL);
1368:   MatMPISBAIJSetPreallocation(A,2,2,NULL,0,NULL);
1369:   MatSetLocalToGlobalMapping(A,ltog,ltog);
1370:   DMDAGetGhostCorners(da,&starts[0],&starts[1],&starts[2],&dims[0],&dims[1],&dims[2]);
1371:   MatSetStencil(A,dim,dims,starts,dof);
1372:   *J   = A;
1373:   return(0);
1374: }

1376: static PetscErrorCode THIDAVecView_VTK_XML(THI thi,DM da,Vec X,const char filename[])
1377: {
1378:   const PetscInt    dof   = 2;
1379:   Units             units = thi->units;
1380:   MPI_Comm          comm;
1381:   PetscErrorCode    ierr;
1382:   PetscViewer       viewer;
1383:   PetscMPIInt       rank,size,tag,nn,nmax;
1384:   PetscInt          mx,my,mz,r,range[6];
1385:   const PetscScalar *x;

1388:   PetscObjectGetComm((PetscObject)thi,&comm);
1389:   DMDAGetInfo(da,0, &mz,&my,&mx, 0,0,0, 0,0,0,0,0,0);
1390:   MPI_Comm_size(comm,&size);
1391:   MPI_Comm_rank(comm,&rank);
1392:   PetscViewerASCIIOpen(comm,filename,&viewer);
1393:   PetscViewerASCIIPrintf(viewer,"<VTKFile type=\"StructuredGrid\" version=\"0.1\" byte_order=\"LittleEndian\">\n");
1394:   PetscViewerASCIIPrintf(viewer,"  <StructuredGrid WholeExtent=\"%d %D %d %D %d %D\">\n",0,mz-1,0,my-1,0,mx-1);

1396:   DMDAGetCorners(da,range,range+1,range+2,range+3,range+4,range+5);
1397:   PetscMPIIntCast(range[3]*range[4]*range[5]*dof,&nn);
1398:   MPI_Reduce(&nn,&nmax,1,MPI_INT,MPI_MAX,0,comm);
1399:   tag  = ((PetscObject) viewer)->tag;
1400:   VecGetArrayRead(X,&x);
1401:   if (!rank) {
1402:     PetscScalar *array;
1403:     PetscMalloc1(nmax,&array);
1404:     for (r=0; r<size; r++) {
1405:       PetscInt          i,j,k,xs,xm,ys,ym,zs,zm;
1406:       const PetscScalar *ptr;
1407:       MPI_Status        status;
1408:       if (r) {
1409:         MPI_Recv(range,6,MPIU_INT,r,tag,comm,MPI_STATUS_IGNORE);
1410:       }
1411:       zs = range[0];ys = range[1];xs = range[2];zm = range[3];ym = range[4];xm = range[5];
1412:       if (xm*ym*zm*dof > nmax) SETERRQ(PETSC_COMM_SELF,1,"should not happen");
1413:       if (r) {
1414:         MPI_Recv(array,nmax,MPIU_SCALAR,r,tag,comm,&status);
1415:         MPI_Get_count(&status,MPIU_SCALAR,&nn);
1416:         if (nn != xm*ym*zm*dof) SETERRQ(PETSC_COMM_SELF,1,"should not happen");
1417:         ptr = array;
1418:       } else ptr = x;
1419:       PetscViewerASCIIPrintf(viewer,"    <Piece Extent=\"%D %D %D %D %D %D\">\n",zs,zs+zm-1,ys,ys+ym-1,xs,xs+xm-1);

1421:       PetscViewerASCIIPrintf(viewer,"      <Points>\n");
1422:       PetscViewerASCIIPrintf(viewer,"        <DataArray type=\"Float32\" NumberOfComponents=\"3\" format=\"ascii\">\n");
1423:       for (i=xs; i<xs+xm; i++) {
1424:         for (j=ys; j<ys+ym; j++) {
1425:           for (k=zs; k<zs+zm; k++) {
1426:             PrmNode   p;
1427:             PetscReal xx = thi->Lx*i/mx,yy = thi->Ly*j/my,zz;
1428:             thi->initialize(thi,xx,yy,&p);
1429:             zz   = PetscRealPart(p.b) + PetscRealPart(p.h)*k/(mz-1);
1430:             PetscViewerASCIIPrintf(viewer,"%f %f %f\n",(double)xx,(double)yy,(double)zz);
1431:           }
1432:         }
1433:       }
1434:       PetscViewerASCIIPrintf(viewer,"        </DataArray>\n");
1435:       PetscViewerASCIIPrintf(viewer,"      </Points>\n");

1437:       PetscViewerASCIIPrintf(viewer,"      <PointData>\n");
1438:       PetscViewerASCIIPrintf(viewer,"        <DataArray type=\"Float32\" Name=\"velocity\" NumberOfComponents=\"3\" format=\"ascii\">\n");
1439:       for (i=0; i<nn; i+=dof) {
1440:         PetscViewerASCIIPrintf(viewer,"%f %f %f\n",(double)(PetscRealPart(ptr[i])*units->year/units->meter),(double)(PetscRealPart(ptr[i+1])*units->year/units->meter),0.0);
1441:       }
1442:       PetscViewerASCIIPrintf(viewer,"        </DataArray>\n");

1444:       PetscViewerASCIIPrintf(viewer,"        <DataArray type=\"Int32\" Name=\"rank\" NumberOfComponents=\"1\" format=\"ascii\">\n");
1445:       for (i=0; i<nn; i+=dof) {
1446:         PetscViewerASCIIPrintf(viewer,"%D\n",r);
1447:       }
1448:       PetscViewerASCIIPrintf(viewer,"        </DataArray>\n");
1449:       PetscViewerASCIIPrintf(viewer,"      </PointData>\n");

1451:       PetscViewerASCIIPrintf(viewer,"    </Piece>\n");
1452:     }
1453:     PetscFree(array);
1454:   } else {
1455:     MPI_Send(range,6,MPIU_INT,0,tag,comm);
1456:     MPI_Send((PetscScalar*)x,nn,MPIU_SCALAR,0,tag,comm);
1457:   }
1458:   VecRestoreArrayRead(X,&x);
1459:   PetscViewerASCIIPrintf(viewer,"  </StructuredGrid>\n");
1460:   PetscViewerASCIIPrintf(viewer,"</VTKFile>\n");
1461:   PetscViewerDestroy(&viewer);
1462:   return(0);
1463: }

1465: int main(int argc,char *argv[])
1466: {
1467:   MPI_Comm       comm;
1468:   THI            thi;
1470:   DM             da;
1471:   SNES           snes;

1473:   PetscInitialize(&argc,&argv,0,help);
1474:   comm = PETSC_COMM_WORLD;

1476:   THICreate(comm,&thi);
1477:   {
1478:     PetscInt M = 3,N = 3,P = 2;
1479:     PetscOptionsBegin(comm,NULL,"Grid resolution options","");
1480:     {
1481:       PetscOptionsInt("-M","Number of elements in x-direction on coarse level","",M,&M,NULL);
1482:       N    = M;
1483:       PetscOptionsInt("-N","Number of elements in y-direction on coarse level (if different from M)","",N,&N,NULL);
1484:       if (thi->coarse2d) {
1485:         PetscOptionsInt("-zlevels","Number of elements in z-direction on fine level","",thi->zlevels,&thi->zlevels,NULL);
1486:       } else {
1487:         PetscOptionsInt("-P","Number of elements in z-direction on coarse level","",P,&P,NULL);
1488:       }
1489:     }
1490:     PetscOptionsEnd();
1491:     if (thi->coarse2d) {
1492:       DMDACreate2d(comm,DM_BOUNDARY_PERIODIC,DM_BOUNDARY_PERIODIC,DMDA_STENCIL_BOX,N,M,PETSC_DETERMINE,PETSC_DETERMINE,sizeof(Node)/sizeof(PetscScalar),1,0,0,&da);
1493:       DMSetFromOptions(da);
1494:       DMSetUp(da);
1495:       da->ops->refinehierarchy     = DMRefineHierarchy_THI;
1496:       da->ops->createinterpolation = DMCreateInterpolation_DA_THI;

1498:       PetscObjectCompose((PetscObject)da,"THI",(PetscObject)thi);
1499:     } else {
1500:       DMDACreate3d(comm,DM_BOUNDARY_NONE,DM_BOUNDARY_PERIODIC,DM_BOUNDARY_PERIODIC, DMDA_STENCIL_BOX,P,N,M,1,PETSC_DETERMINE,PETSC_DETERMINE,sizeof(Node)/sizeof(PetscScalar),1,0,0,0,&da);
1501:       DMSetFromOptions(da);
1502:       DMSetUp(da);
1503:     }
1504:     DMDASetFieldName(da,0,"x-velocity");
1505:     DMDASetFieldName(da,1,"y-velocity");
1506:   }
1507:   THISetUpDM(thi,da);
1508:   if (thi->tridiagonal) da->ops->creatematrix = DMCreateMatrix_THI_Tridiagonal;

1510:   {                             /* Set the fine level matrix type if -da_refine */
1511:     PetscInt rlevel,clevel;
1512:     DMGetRefineLevel(da,&rlevel);
1513:     DMGetCoarsenLevel(da,&clevel);
1514:     if (rlevel - clevel > 0) {DMSetMatType(da,thi->mattype);}
1515:   }

1517:   DMDASNESSetFunctionLocal(da,ADD_VALUES,(DMDASNESFunction)THIFunctionLocal,thi);
1518:   if (thi->tridiagonal) {
1519:     DMDASNESSetJacobianLocal(da,(DMDASNESJacobian)THIJacobianLocal_3D_Tridiagonal,thi);
1520:   } else {
1521:     DMDASNESSetJacobianLocal(da,(DMDASNESJacobian)THIJacobianLocal_3D_Full,thi);
1522:   }
1523:   DMCoarsenHookAdd(da,DMCoarsenHook_THI,NULL,thi);
1524:   DMRefineHookAdd(da,DMRefineHook_THI,NULL,thi);

1526:   DMSetApplicationContext(da,thi);

1528:   SNESCreate(comm,&snes);
1529:   SNESSetDM(snes,da);
1530:   DMDestroy(&da);
1531:   SNESSetComputeInitialGuess(snes,THIInitial,NULL);
1532:   SNESSetFromOptions(snes);

1534:   SNESSolve(snes,NULL,NULL);

1536:   THISolveStatistics(thi,snes,0,"Full");

1538:   {
1539:     PetscBool flg;
1540:     char      filename[PETSC_MAX_PATH_LEN] = "";
1541:     PetscOptionsGetString(NULL,NULL,"-o",filename,sizeof(filename),&flg);
1542:     if (flg) {
1543:       Vec X;
1544:       DM  dm;
1545:       SNESGetSolution(snes,&X);
1546:       SNESGetDM(snes,&dm);
1547:       THIDAVecView_VTK_XML(thi,dm,X,filename);
1548:     }
1549:   }

1551:   DMDestroy(&da);
1552:   SNESDestroy(&snes);
1553:   THIDestroy(&thi);
1554:   PetscFinalize();
1555:   return ierr;
1556: }


1559: /*TEST

1561:    build:
1562:       requires: c99

1564:    test:
1565:       args: -M 6 -P 4 -da_refine 1 -snes_monitor_short -snes_converged_reason -ksp_monitor_short -ksp_converged_reason -thi_mat_type sbaij -ksp_type fgmres -pc_type mg -pc_mg_type full -mg_levels_ksp_type gmres -mg_levels_ksp_max_it 1 -mg_levels_pc_type icc
1566:       requires: !single

1568:    test:
1569:       suffix: 2
1570:       nsize: 2
1571:       args: -M 6 -P 4 -thi_hom z -snes_monitor_short -snes_converged_reason -ksp_monitor_short -ksp_converged_reason -thi_mat_type sbaij -ksp_type fgmres -pc_type mg -pc_mg_type full -mg_levels_ksp_type gmres -mg_levels_ksp_max_it 1 -mg_levels_pc_type asm -mg_levels_pc_asm_blocks 6 -mg_levels_0_pc_type redundant -snes_grid_sequence 1 -mat_partitioning_type current -ksp_atol -1
1572:       requires: !single

1574:    test:
1575:       suffix: 3
1576:       nsize: 3
1577:       args: -M 7 -P 4 -thi_hom z -da_refine 1 -snes_monitor_short -snes_converged_reason -ksp_monitor_short -ksp_converged_reason -thi_mat_type baij -ksp_type fgmres -pc_type mg -pc_mg_type full -mg_levels_pc_asm_type restrict -mg_levels_pc_type asm -mg_levels_pc_asm_blocks 9 -mg_levels_ksp_type gmres -mg_levels_ksp_max_it 1 -mat_partitioning_type current
1578:       requires: !single

1580:    test:
1581:       suffix: 4
1582:       nsize: 6
1583:       args: -M 4 -P 2 -da_refine_hierarchy_x 1,1,3 -da_refine_hierarchy_y 2,2,1 -da_refine_hierarchy_z 2,2,1 -snes_grid_sequence 3 -ksp_converged_reason -ksp_type fgmres -ksp_rtol 1e-2 -pc_type mg -mg_levels_ksp_type gmres -mg_levels_ksp_max_it 1 -mg_levels_pc_type bjacobi -mg_levels_1_sub_pc_type cholesky -pc_mg_type multiplicative -snes_converged_reason -snes_stol 1e-12 -thi_L 80e3 -thi_alpha 0.05 -thi_friction_m 1 -thi_hom x -snes_view -mg_levels_0_pc_type redundant -mg_levels_0_ksp_type preonly -ksp_atol -1
1584:       requires: !single

1586:    test:
1587:       suffix: 5
1588:       nsize: 6
1589:       args: -M 12 -P 5 -snes_monitor_short -ksp_converged_reason -pc_type asm -pc_asm_type restrict -dm_mat_type {{aij baij sbaij}}
1590:       requires: !single

1592: TEST*/