Actual source code: ex14.c

petsc-3.4.4 2014-03-13
  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: */

 46: #include <petscts.h>
 47: #include <petscdmda.h>
 48: #include <petscdmcomposite.h>
 49: #include <ctype.h>              /* toupper() */

 51: #if defined __SSE2__
 52: #  include <emmintrin.h>
 53: #endif

 55: /* The SSE2 kernels are only for PetscScalar=double on architectures that support it */
 56: #define USE_SSE2_KERNELS (!defined NO_SSE2                              \
 57:                           && !defined PETSC_USE_COMPLEX                 \
 58:                           && !defined PETSC_USE_REAL_SINGLE           \
 59:                           && defined __SSE2__)

 61: #if !defined __STDC_VERSION__ || __STDC_VERSION__ < 199901L
 62: #  if defined __cplusplus       /* C++ restrict is nonstandard and compilers have inconsistent rules about where it can be used */
 63: #    define restrict
 64: #  else
 65: #    define restrict PETSC_RESTRICT
 66: #  endif
 67: #endif

 69: static PetscClassId THI_CLASSID;

 71: typedef enum {QUAD_GAUSS,QUAD_LOBATTO} QuadratureType;
 72: static const char *QuadratureTypes[] = {"gauss","lobatto","QuadratureType","QUAD_",0};
 73: static const PetscReal HexQWeights[8] = {1,1,1,1,1,1,1,1};
 74: static const PetscReal HexQNodes[]    = {-0.57735026918962573, 0.57735026918962573};
 75: #define G 0.57735026918962573
 76: #define H (0.5*(1.+G))
 77: #define L (0.5*(1.-G))
 78: #define M (-0.5)
 79: #define P (0.5)
 80: /* Special quadrature: Lobatto in horizontal, Gauss in vertical */
 81: static const PetscReal HexQInterp_Lobatto[8][8] = {{H,0,0,0,L,0,0,0},
 82:                                                    {0,H,0,0,0,L,0,0},
 83:                                                    {0,0,H,0,0,0,L,0},
 84:                                                    {0,0,0,H,0,0,0,L},
 85:                                                    {L,0,0,0,H,0,0,0},
 86:                                                    {0,L,0,0,0,H,0,0},
 87:                                                    {0,0,L,0,0,0,H,0},
 88:                                                    {0,0,0,L,0,0,0,H}};
 89: static const PetscReal HexQDeriv_Lobatto[8][8][3] = {
 90:   {{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}  },
 91:   {{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}    },
 92:   {{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}  },
 93:   {{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}},
 94:   {{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}  },
 95:   {{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}    },
 96:   {{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}  },
 97:   {{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}}};
 98: /* Stanndard Gauss */
 99: 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},
100:                                                  {L*H*H,H*H*H,H*L*H,L*L*H, L*H*L,H*H*L,H*L*L,L*L*L},
101:                                                  {L*L*H,H*L*H,H*H*H,L*H*H, L*L*L,H*L*L,H*H*L,L*H*L},
102:                                                  {H*L*H,L*L*H,L*H*H,H*H*H, H*L*L,L*L*L,L*H*L,H*H*L},
103:                                                  {H*H*L,L*H*L,L*L*L,H*L*L, H*H*H,L*H*H,L*L*H,H*L*H},
104:                                                  {L*H*L,H*H*L,H*L*L,L*L*L, L*H*H,H*H*H,H*L*H,L*L*H},
105:                                                  {L*L*L,H*L*L,H*H*L,L*H*L, L*L*H,H*L*H,H*H*H,L*H*H},
106:                                                  {H*L*L,L*L*L,L*H*L,H*H*L, H*L*H,L*L*H,L*H*H,H*H*H}};
107: static const PetscReal HexQDeriv_Gauss[8][8][3] = {
108:   {{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}},
109:   {{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}},
110:   {{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}},
111:   {{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}},
112:   {{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}},
113:   {{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}},
114:   {{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}},
115:   {{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}}};
116: static const PetscReal (*HexQInterp)[8],(*HexQDeriv)[8][3];
117: /* Standard 2x2 Gauss quadrature for the bottom layer. */
118: static const PetscReal QuadQInterp[4][4] = {{H*H,L*H,L*L,H*L},
119:                                             {L*H,H*H,H*L,L*L},
120:                                             {L*L,H*L,H*H,L*H},
121:                                             {H*L,L*L,L*H,H*H}};
122: static const PetscReal QuadQDeriv[4][4][2] = {
123:   {{M*H,M*H},{P*H,M*L},{P*L,P*L},{M*L,P*H}},
124:   {{M*H,M*L},{P*H,M*H},{P*L,P*H},{M*L,P*L}},
125:   {{M*L,M*L},{P*L,M*H},{P*H,P*H},{M*H,P*L}},
126:   {{M*L,M*H},{P*L,M*L},{P*H,P*L},{M*H,P*H}}};
127: #undef G
128: #undef H
129: #undef L
130: #undef M
131: #undef P

133: #define HexExtract(x,i,j,k,n) do {              \
134:     (n)[0] = (x)[i][j][k];                      \
135:     (n)[1] = (x)[i+1][j][k];                    \
136:     (n)[2] = (x)[i+1][j+1][k];                  \
137:     (n)[3] = (x)[i][j+1][k];                    \
138:     (n)[4] = (x)[i][j][k+1];                    \
139:     (n)[5] = (x)[i+1][j][k+1];                  \
140:     (n)[6] = (x)[i+1][j+1][k+1];                \
141:     (n)[7] = (x)[i][j+1][k+1];                  \
142:   } while (0)

144: #define HexExtractRef(x,i,j,k,n) do {           \
145:     (n)[0] = &(x)[i][j][k];                     \
146:     (n)[1] = &(x)[i+1][j][k];                   \
147:     (n)[2] = &(x)[i+1][j+1][k];                 \
148:     (n)[3] = &(x)[i][j+1][k];                   \
149:     (n)[4] = &(x)[i][j][k+1];                   \
150:     (n)[5] = &(x)[i+1][j][k+1];                 \
151:     (n)[6] = &(x)[i+1][j+1][k+1];               \
152:     (n)[7] = &(x)[i][j+1][k+1];                 \
153:   } while (0)

155: #define QuadExtract(x,i,j,n) do {               \
156:     (n)[0] = (x)[i][j];                         \
157:     (n)[1] = (x)[i+1][j];                       \
158:     (n)[2] = (x)[i+1][j+1];                     \
159:     (n)[3] = (x)[i][j+1];                       \
160:   } while (0)

162: static PetscScalar Sqr(PetscScalar a) {return a*a;}

164: static void HexGrad(const PetscReal dphi[][3],const PetscReal zn[],PetscReal dz[])
165: {
166:   PetscInt i;
167:   dz[0] = dz[1] = dz[2] = 0;
168:   for (i=0; i<8; i++) {
169:     dz[0] += dphi[i][0] * zn[i];
170:     dz[1] += dphi[i][1] * zn[i];
171:     dz[2] += dphi[i][2] * zn[i];
172:   }
173: }

175: static void HexComputeGeometry(PetscInt q,PetscReal hx,PetscReal hy,const PetscReal dz[restrict],PetscReal phi[restrict],PetscReal dphi[restrict][3],PetscReal *restrict jw)
176: {
177:   const PetscReal
178:     jac[3][3] = {{hx/2,0,0}, {0,hy/2,0}, {dz[0],dz[1],dz[2]}}
179:   ,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]}}
180:   ,jdet = jac[0][0]*jac[1][1]*jac[2][2];
181:   PetscInt i;

183:   for (i=0; i<8; i++) {
184:     const PetscReal *dphir = HexQDeriv[q][i];
185:     phi[i] = HexQInterp[q][i];
186:     dphi[i][0] = dphir[0]*ijac[0][0] + dphir[1]*ijac[1][0] + dphir[2]*ijac[2][0];
187:     dphi[i][1] = dphir[0]*ijac[0][1] + dphir[1]*ijac[1][1] + dphir[2]*ijac[2][1];
188:     dphi[i][2] = dphir[0]*ijac[0][2] + dphir[1]*ijac[1][2] + dphir[2]*ijac[2][2];
189:   }
190:   *jw = 1.0 * jdet;
191: }

193: typedef struct _p_THI   *THI;
194: typedef struct _n_Units *Units;

196: typedef struct {
197:   PetscScalar u,v;
198: } Node;

200: typedef struct {
201:   PetscScalar b;                /* bed */
202:   PetscScalar h;                /* thickness */
203:   PetscScalar beta2;            /* friction */
204: } PrmNode;

206: #define FieldSize(ntype) ((PetscInt)(sizeof(ntype)/sizeof(PetscScalar)))
207: #define FieldOffset(ntype,member) ((PetscInt)(offsetof(ntype,member)/sizeof(PetscScalar)))
208: #define FieldIndex(ntype,i,member) ((PetscInt)((i)*FieldSize(ntype) + FieldOffset(ntype,member)))
209: #define NODE_SIZE FieldSize(Node)
210: #define PRMNODE_SIZE FieldSize(PrmNode)

212: typedef struct {
213:   PetscReal min,max,cmin,cmax;
214: } PRange;

216: struct _p_THI {
217:   PETSCHEADER(int);
218:   void      (*initialize)(THI,PetscReal x,PetscReal y,PrmNode *p);
219:   PetscInt  nlevels;
220:   PetscInt  zlevels;
221:   PetscReal Lx,Ly,Lz;           /* Model domain */
222:   PetscReal alpha;              /* Bed angle */
223:   Units     units;
224:   PetscReal dirichlet_scale;
225:   PetscReal ssa_friction_scale;
226:   PetscReal inertia;
227:   PRange    eta;
228:   PRange    beta2;
229:   struct {
230:     PetscReal Bd2,eps,exponent,glen_n;
231:   } viscosity;
232:   struct {
233:     PetscReal irefgam,eps2,exponent;
234:   } friction;
235:   struct {
236:     PetscReal rate,exponent,refvel;
237:   } erosion;
238:   PetscReal rhog;
239:   PetscBool no_slip;
240:   PetscBool verbose;
241:   MatType   mattype;
242:   char      *monitor_basename;
243:   PetscInt  monitor_interval;
244: };

246: struct _n_Units {
247:   /* fundamental */
248:   PetscReal meter;
249:   PetscReal kilogram;
250:   PetscReal second;
251:   /* derived */
252:   PetscReal Pascal;
253:   PetscReal year;
254: };

256: static void PrmHexGetZ(const PrmNode pn[],PetscInt k,PetscInt zm,PetscReal zn[])
257: {
258:   const PetscScalar zm1 = zm-1,
259:     znl[8] = {pn[0].b + pn[0].h*(PetscScalar)k/zm1,
260:               pn[1].b + pn[1].h*(PetscScalar)k/zm1,
261:               pn[2].b + pn[2].h*(PetscScalar)k/zm1,
262:               pn[3].b + pn[3].h*(PetscScalar)k/zm1,
263:               pn[0].b + pn[0].h*(PetscScalar)(k+1)/zm1,
264:               pn[1].b + pn[1].h*(PetscScalar)(k+1)/zm1,
265:               pn[2].b + pn[2].h*(PetscScalar)(k+1)/zm1,
266:               pn[3].b + pn[3].h*(PetscScalar)(k+1)/zm1};
267:   PetscInt i;
268:   for (i=0; i<8; i++) zn[i] = PetscRealPart(znl[i]);
269: }

273: /* Compute a gradient of all the 2D fields at four quadrature points.  Output for [quadrature_point][direction].field_name */
274: static PetscErrorCode QuadComputeGrad4(const PetscReal dphi[][4][2],PetscReal hx,PetscReal hy,const PrmNode pn[4],PrmNode dp[4][2])
275: {
277:   PetscInt       q,i,f;
278:   const PetscScalar (*restrict pg)[PRMNODE_SIZE] = (const PetscScalar(*)[PRMNODE_SIZE])pn; /* Get generic array pointers to the node */
279:   PetscScalar (*restrict dpg)[2][PRMNODE_SIZE]   = (PetscScalar(*)[2][PRMNODE_SIZE])dp;

282:   PetscMemzero(dpg,4*sizeof(dpg[0]));
283:   for (q=0; q<4; q++) {
284:     for (i=0; i<4; i++) {
285:       for (f=0; f<PRMNODE_SIZE; f++) {
286:         dpg[q][0][f] += dphi[q][i][0]/hx * pg[i][f];
287:         dpg[q][1][f] += dphi[q][i][1]/hy * pg[i][f];
288:       }
289:     }
290:   }
291:   return(0);
292: }

294: static inline PetscReal StaggeredMidpoint2D(PetscScalar a,PetscScalar b,PetscScalar c,PetscScalar d)
295: {return 0.5*PetscRealPart(0.75*a + 0.75*b + 0.25*c + 0.25*d);}
296: static inline PetscReal UpwindFlux1D(PetscReal u,PetscReal hL,PetscReal hR)
297: {return (u > 0) ? hL*u : hR*u;}

299: #define UpwindFluxXW(x3,x2,h,i,j,k,dj) UpwindFlux1D(StaggeredMidpoint2D(x3[i][j][k].u,x3[i-1][j][k].u, x3[i-1][j+dj][k].u,x3[i][k+dj][k].u), \
300:                                                     PetscRealPart(0.75*x2[i-1][j  ].h+0.25*x2[i-1][j+dj].h), PetscRealPart(0.75*x2[i  ][j  ].h+0.25*x2[i  ][j+dj].h))
301: #define UpwindFluxXE(x3,x2,h,i,j,k,dj) UpwindFlux1D(StaggeredMidpoint2D(x3[i][j][k].u,x3[i+1][j][k].u, x3[i+1][j+dj][k].u,x3[i][k+dj][k].u), \
302:                                                     PetscRealPart(0.75*x2[i  ][j  ].h+0.25*x2[i  ][j+dj].h), PetscRealPart(0.75*x2[i+1][j  ].h+0.25*x2[i+1][j+dj].h))
303: #define UpwindFluxYS(x3,x2,h,i,j,k,di) UpwindFlux1D(StaggeredMidpoint2D(x3[i][j][k].v,x3[i][j-1][k].v, x3[i+di][j-1][k].v,x3[i+di][j][k].v), \
304:                                                     PetscRealPart(0.75*x2[i  ][j-1].h+0.25*x2[i+di][j-1].h), PetscRealPart(0.75*x2[i  ][j  ].h+0.25*x2[i+di][j  ].h))
305: #define UpwindFluxYN(x3,x2,h,i,j,k,di) UpwindFlux1D(StaggeredMidpoint2D(x3[i][j][k].v,x3[i][j+1][k].v, x3[i+di][j+1][k].v,x3[i+di][j][k].v), \
306:                                                     PetscRealPart(0.75*x2[i  ][j  ].h+0.25*x2[i+di][j  ].h), PetscRealPart(0.75*x2[i  ][j+1].h+0.25*x2[i+di][j+1].h))

308: static void PrmNodeGetFaceMeasure(const PrmNode **p,PetscInt i,PetscInt j,PetscScalar h[])
309: {
310:   /* West */
311:   h[0] = StaggeredMidpoint2D(p[i][j].h,p[i-1][j].h,p[i-1][j-1].h,p[i][j-1].h);
312:   h[1] = StaggeredMidpoint2D(p[i][j].h,p[i-1][j].h,p[i-1][j+1].h,p[i][j+1].h);
313:   /* East */
314:   h[2] = StaggeredMidpoint2D(p[i][j].h,p[i+1][j].h,p[i+1][j+1].h,p[i][j+1].h);
315:   h[3] = StaggeredMidpoint2D(p[i][j].h,p[i+1][j].h,p[i+1][j-1].h,p[i][j-1].h);
316:   /* South */
317:   h[4] = StaggeredMidpoint2D(p[i][j].h,p[i][j-1].h,p[i+1][j-1].h,p[i+1][j].h);
318:   h[5] = StaggeredMidpoint2D(p[i][j].h,p[i][j-1].h,p[i-1][j-1].h,p[i-1][j].h);
319:   /* North */
320:   h[6] = StaggeredMidpoint2D(p[i][j].h,p[i][j+1].h,p[i-1][j+1].h,p[i-1][j].h);
321:   h[7] = StaggeredMidpoint2D(p[i][j].h,p[i][j+1].h,p[i+1][j+1].h,p[i+1][j].h);
322: }

324: /* Tests A and C are from the ISMIP-HOM paper (Pattyn et al. 2008) */
325: static void THIInitialize_HOM_A(THI thi,PetscReal x,PetscReal y,PrmNode *p)
326: {
327:   Units units = thi->units;
328:   PetscReal s = -x*sin(thi->alpha);
329:   p->b = s - 1000*units->meter + 500*units->meter * sin(x*2*PETSC_PI/thi->Lx) * sin(y*2*PETSC_PI/thi->Ly);
330:   p->h = s - p->b;
331:   p->beta2 = -1e-10;             /* This value is not used, but it should not be huge because that would change the finite difference step size  */
332: }

334: static void THIInitialize_HOM_C(THI thi,PetscReal x,PetscReal y,PrmNode *p)
335: {
336:   Units units = thi->units;
337:   PetscReal s = -x*sin(thi->alpha);
338:   p->b = s - 1000*units->meter;
339:   p->h = s - p->b;
340:   /* tau_b = beta2 v   is a stress (Pa).
341:    * This is a big number in our units (it needs to balance the driving force from the surface), so we scale it by 1/rhog, just like the residual. */
342:   p->beta2 = 1000 * (1 + sin(x*2*PETSC_PI/thi->Lx)*sin(y*2*PETSC_PI/thi->Ly)) * units->Pascal * units->year / units->meter / thi->rhog;
343: }

345: /* These are just toys */

347: /* From Fred Herman */
348: static void THIInitialize_HOM_F(THI thi,PetscReal x,PetscReal y,PrmNode *p)
349: {
350:   Units units = thi->units;
351:   PetscReal s = -x*sin(thi->alpha);
352:   p->b = s - 1000*units->meter + 100*units->meter * sin(x*2*PETSC_PI/thi->Lx);/* * sin(y*2*PETSC_PI/thi->Ly); */
353:   p->h = s - p->b;
354:   p->h = (1-(atan((x-thi->Lx/2)/1.)+PETSC_PI/2.)/PETSC_PI)*500*units->meter+1*units->meter;
355:   s = PetscRealPart(p->b + p->h);
356:   p->beta2 = -1e-10;
357:   /*  p->beta2 = 1000 * units->Pascal * units->year / units->meter; */
358: }

360: /* Same bed as test A, free slip everywhere except for a discontinuous jump to a circular sticky region in the middle. */
361: static void THIInitialize_HOM_X(THI thi,PetscReal xx,PetscReal yy,PrmNode *p)
362: {
363:   Units units = thi->units;
364:   PetscReal x = xx*2*PETSC_PI/thi->Lx - PETSC_PI,y = yy*2*PETSC_PI/thi->Ly - PETSC_PI; /* [-pi,pi] */
365:   PetscReal r = PetscSqrtReal(x*x + y*y),s = -x*sin(thi->alpha);
366:   p->b = s - 1000*units->meter + 500*units->meter * sin(x + PETSC_PI) * sin(y + PETSC_PI);
367:   p->h = s - p->b;
368:   p->beta2 = 1000 * (r < 1 ? 2 : 0) * units->Pascal * units->year / units->meter / thi->rhog;
369: }

371: /* Like Z, but with 200 meter cliffs */
372: static void THIInitialize_HOM_Y(THI thi,PetscReal xx,PetscReal yy,PrmNode *p)
373: {
374:   Units units = thi->units;
375:   PetscReal x = xx*2*PETSC_PI/thi->Lx - PETSC_PI,y = yy*2*PETSC_PI/thi->Ly - PETSC_PI; /* [-pi,pi] */
376:   PetscReal r = PetscSqrtReal(x*x + y*y),s = -x*sin(thi->alpha);
377:   p->b = s - 1000*units->meter + 500*units->meter * sin(x + PETSC_PI) * sin(y + PETSC_PI);
378:   if (PetscRealPart(p->b) > -700*units->meter) p->b += 200*units->meter;
379:   p->h = s - p->b;
380:   p->beta2 = 1000 * (1. + sin(PetscSqrtReal(16*r))/PetscSqrtReal(1e-2 + 16*r)*cos(x*3/2)*cos(y*3/2)) * units->Pascal * units->year / units->meter / thi->rhog;
381: }

383: /* Same bed as A, smoothly varying slipperiness, similar to MATLAB's "sombrero" (uncorrelated with bathymetry) */
384: static void THIInitialize_HOM_Z(THI thi,PetscReal xx,PetscReal yy,PrmNode *p)
385: {
386:   Units units = thi->units;
387:   PetscReal x = xx*2*PETSC_PI/thi->Lx - PETSC_PI,y = yy*2*PETSC_PI/thi->Ly - PETSC_PI; /* [-pi,pi] */
388:   PetscReal r = PetscSqrtReal(x*x + y*y),s = -x*sin(thi->alpha);
389:   p->b = s - 1000*units->meter + 500*units->meter * sin(x + PETSC_PI) * sin(y + PETSC_PI);
390:   p->h = s - p->b;
391:   p->beta2 = 1000 * (1. + sin(PetscSqrtReal(16*r))/PetscSqrtReal(1e-2 + 16*r)*cos(x*3/2)*cos(y*3/2)) * units->Pascal * units->year / units->meter / thi->rhog;
392: }

394: static void THIFriction(THI thi,PetscReal rbeta2,PetscReal gam,PetscReal *beta2,PetscReal *dbeta2)
395: {
396:   if (thi->friction.irefgam == 0) {
397:     Units units = thi->units;
398:     thi->friction.irefgam = 1./(0.5*PetscSqr(100 * units->meter / units->year));
399:     thi->friction.eps2 = 0.5*PetscSqr(1.e-4 / thi->friction.irefgam);
400:   }
401:   if (thi->friction.exponent == 0) {
402:     *beta2  = rbeta2;
403:     *dbeta2 = 0;
404:   } else {
405:     *beta2  = rbeta2 * pow(thi->friction.eps2 + gam*thi->friction.irefgam,thi->friction.exponent);
406:     *dbeta2 = thi->friction.exponent * *beta2 / (thi->friction.eps2 + gam*thi->friction.irefgam) * thi->friction.irefgam;
407:   }
408: }

410: static void THIViscosity(THI thi,PetscReal gam,PetscReal *eta,PetscReal *deta)
411: {
412:   PetscReal Bd2,eps,exponent;
413:   if (thi->viscosity.Bd2 == 0) {
414:     Units units = thi->units;
415:     const PetscReal
416:       n = thi->viscosity.glen_n,                        /* Glen exponent */
417:       p = 1. + 1./n,                                    /* for Stokes */
418:       A = 1.e-16 * pow(units->Pascal,-n) / units->year, /* softness parameter (Pa^{-n}/s) */
419:       B = pow(A,-1./n);                                 /* hardness parameter */
420:     thi->viscosity.Bd2      = B/2;
421:     thi->viscosity.exponent = (p-2)/2;
422:     thi->viscosity.eps      = 0.5*PetscSqr(1e-5 / units->year);
423:   }
424:   Bd2      = thi->viscosity.Bd2;
425:   exponent = thi->viscosity.exponent;
426:   eps      = thi->viscosity.eps;
427:   *eta     = Bd2 * pow(eps + gam,exponent);
428:   *deta    = exponent * (*eta) / (eps + gam);
429: }

431: static void THIErosion(THI thi,const Node *vel,PetscScalar *erate,Node *derate)
432: {
433:   const PetscScalar magref2 = 1.e-10 + (PetscSqr(vel->u) + PetscSqr(vel->v)) / PetscSqr(thi->erosion.refvel),
434:                     rate    = -thi->erosion.rate*PetscPowScalar(magref2, 0.5*thi->erosion.exponent);
435:   if (erate) *erate = rate;
436:   if (derate) {
437:     if (thi->erosion.exponent == 1) {
438:       derate->u = 0;
439:       derate->v = 0;
440:     } else {
441:       derate->u = 0.5*thi->erosion.exponent * rate / magref2 * 2. * vel->u / PetscSqr(thi->erosion.refvel);
442:       derate->v = 0.5*thi->erosion.exponent * rate / magref2 * 2. * vel->v / PetscSqr(thi->erosion.refvel);
443:     }
444:   }
445: }

447: static void RangeUpdate(PetscReal *min,PetscReal *max,PetscReal x)
448: {
449:   if (x < *min) *min = x;
450:   if (x > *max) *max = x;
451: }

453: static void PRangeClear(PRange *p)
454: {
455:   p->cmin = p->min = 1e100;
456:   p->cmax = p->max = -1e100;
457: }

461: static PetscErrorCode PRangeMinMax(PRange *p,PetscReal min,PetscReal max)
462: {

465:   p->cmin = min;
466:   p->cmax = max;
467:   if (min < p->min) p->min = min;
468:   if (max > p->max) p->max = max;
469:   return(0);
470: }

474: static PetscErrorCode THIDestroy(THI *thi)
475: {

479:   if (--((PetscObject)(*thi))->refct > 0) return(0);
480:   PetscFree((*thi)->units);
481:   PetscFree((*thi)->mattype);
482:   PetscFree((*thi)->monitor_basename);
483:   PetscHeaderDestroy(thi);
484:   return(0);
485: }

489: static PetscErrorCode THICreate(MPI_Comm comm,THI *inthi)
490: {
491:   static PetscBool registered = PETSC_FALSE;
492:   THI              thi;
493:   Units            units;
494:   char             monitor_basename[PETSC_MAX_PATH_LEN] = "thi-";
495:   PetscErrorCode   ierr;

498:   *inthi = 0;
499:   if (!registered) {
500:     PetscClassIdRegister("Toy Hydrostatic Ice",&THI_CLASSID);
501:     registered = PETSC_TRUE;
502:   }
503:   PetscHeaderCreate(thi,_p_THI,0,THI_CLASSID,"THI","Toy Hydrostatic Ice","THI",comm,THIDestroy,0);

505:   PetscNew(struct _n_Units,&thi->units);

507:   units           = thi->units;
508:   units->meter    = 1e-2;
509:   units->second   = 1e-7;
510:   units->kilogram = 1e-12;

512:   PetscOptionsBegin(comm,NULL,"Scaled units options","");
513:   {
514:     PetscOptionsReal("-units_meter","1 meter in scaled length units","",units->meter,&units->meter,NULL);
515:     PetscOptionsReal("-units_second","1 second in scaled time units","",units->second,&units->second,NULL);
516:     PetscOptionsReal("-units_kilogram","1 kilogram in scaled mass units","",units->kilogram,&units->kilogram,NULL);
517:   }
518:   PetscOptionsEnd();
519:   units->Pascal = units->kilogram / (units->meter * PetscSqr(units->second));
520:   units->year   = 31556926. * units->second, /* seconds per year */

522:   thi->Lx              = 10.e3;
523:   thi->Ly              = 10.e3;
524:   thi->Lz              = 1000;
525:   thi->nlevels         = 1;
526:   thi->dirichlet_scale = 1;
527:   thi->verbose         = PETSC_FALSE;

529:   thi->viscosity.glen_n = 3.;
530:   thi->erosion.rate     = 1e-3; /* m/a */
531:   thi->erosion.exponent = 1.;
532:   thi->erosion.refvel   = 1.;   /* m/a */

534:   PetscOptionsBegin(comm,NULL,"Toy Hydrostatic Ice options","");
535:   {
536:     QuadratureType quad       = QUAD_GAUSS;
537:     char           homexp[]   = "A";
538:     char           mtype[256] = MATSBAIJ;
539:     PetscReal      L,m = 1.0;
540:     PetscBool      flg;
541:     L    = thi->Lx;
542:     PetscOptionsReal("-thi_L","Domain size (m)","",L,&L,&flg);
543:     if (flg) thi->Lx = thi->Ly = L;
544:     PetscOptionsReal("-thi_Lx","X Domain size (m)","",thi->Lx,&thi->Lx,NULL);
545:     PetscOptionsReal("-thi_Ly","Y Domain size (m)","",thi->Ly,&thi->Ly,NULL);
546:     PetscOptionsReal("-thi_Lz","Z Domain size (m)","",thi->Lz,&thi->Lz,NULL);
547:     PetscOptionsString("-thi_hom","ISMIP-HOM experiment (A or C)","",homexp,homexp,sizeof(homexp),NULL);
548:     switch (homexp[0] = toupper(homexp[0])) {
549:     case 'A':
550:       thi->initialize = THIInitialize_HOM_A;
551:       thi->no_slip    = PETSC_TRUE;
552:       thi->alpha      = 0.5;
553:       break;
554:     case 'C':
555:       thi->initialize = THIInitialize_HOM_C;
556:       thi->no_slip    = PETSC_FALSE;
557:       thi->alpha      = 0.1;
558:       break;
559:     case 'F':
560:       thi->initialize = THIInitialize_HOM_F;
561:       thi->no_slip    = PETSC_FALSE;
562:       thi->alpha      = 0.5;
563:       break;
564:     case 'X':
565:       thi->initialize = THIInitialize_HOM_X;
566:       thi->no_slip    = PETSC_FALSE;
567:       thi->alpha      = 0.3;
568:       break;
569:     case 'Y':
570:       thi->initialize = THIInitialize_HOM_Y;
571:       thi->no_slip    = PETSC_FALSE;
572:       thi->alpha      = 0.5;
573:       break;
574:     case 'Z':
575:       thi->initialize = THIInitialize_HOM_Z;
576:       thi->no_slip    = PETSC_FALSE;
577:       thi->alpha      = 0.5;
578:       break;
579:     default:
580:       SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"HOM experiment '%c' not implemented",homexp[0]);
581:     }
582:     PetscOptionsEnum("-thi_quadrature","Quadrature to use for 3D elements","",QuadratureTypes,(PetscEnum)quad,(PetscEnum*)&quad,NULL);
583:     switch (quad) {
584:     case QUAD_GAUSS:
585:       HexQInterp = HexQInterp_Gauss;
586:       HexQDeriv  = HexQDeriv_Gauss;
587:       break;
588:     case QUAD_LOBATTO:
589:       HexQInterp = HexQInterp_Lobatto;
590:       HexQDeriv  = HexQDeriv_Lobatto;
591:       break;
592:     }
593:     PetscOptionsReal("-thi_alpha","Bed angle (degrees)","",thi->alpha,&thi->alpha,NULL);
594:     PetscOptionsReal("-thi_viscosity_glen_n","Exponent in Glen flow law, 1=linear, infty=ideal plastic",NULL,thi->viscosity.glen_n,&thi->viscosity.glen_n,NULL);
595:     PetscOptionsReal("-thi_friction_m","Friction exponent, 0=Coulomb, 1=Navier","",m,&m,NULL);
596:     thi->friction.exponent = (m-1)/2;
597:     PetscOptionsReal("-thi_erosion_rate","Rate of erosion relative to sliding velocity at reference velocity (m/a)",NULL,thi->erosion.rate,&thi->erosion.rate,NULL);
598:     PetscOptionsReal("-thi_erosion_exponent","Power of sliding velocity appearing in erosion relation",NULL,thi->erosion.exponent,&thi->erosion.exponent,NULL);
599:     PetscOptionsReal("-thi_erosion_refvel","Reference sliding velocity for erosion (m/a)",NULL,thi->erosion.refvel,&thi->erosion.refvel,NULL);
600:     thi->erosion.rate   *= units->meter / units->year;
601:     thi->erosion.refvel *= units->meter / units->year;
602:     PetscOptionsReal("-thi_dirichlet_scale","Scale Dirichlet boundary conditions by this factor","",thi->dirichlet_scale,&thi->dirichlet_scale,NULL);
603:     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);
604:     PetscOptionsReal("-thi_inertia","Coefficient of accelaration term in velocity system, physical is almost zero",NULL,thi->inertia,&thi->inertia,NULL);
605:     PetscOptionsInt("-thi_nlevels","Number of levels of refinement","",thi->nlevels,&thi->nlevels,NULL);
606:     PetscOptionsList("-thi_mat_type","Matrix type","MatSetType",MatList,mtype,(char*)mtype,sizeof(mtype),NULL);
607:     PetscStrallocpy(mtype,&thi->mattype);
608:     PetscOptionsBool("-thi_verbose","Enable verbose output (like matrix sizes and statistics)","",thi->verbose,&thi->verbose,NULL);
609:     PetscOptionsString("-thi_monitor","Basename to write state files to",NULL,monitor_basename,monitor_basename,sizeof(monitor_basename),&flg);
610:     if (flg) {
611:       PetscStrallocpy(monitor_basename,&thi->monitor_basename);
612:       thi->monitor_interval = 1;
613:       PetscOptionsInt("-thi_monitor_interval","Frequency at which to write state files",NULL,thi->monitor_interval,&thi->monitor_interval,NULL);
614:     }
615:   }
616:   PetscOptionsEnd();

618:   /* dimensionalize */
619:   thi->Lx    *= units->meter;
620:   thi->Ly    *= units->meter;
621:   thi->Lz    *= units->meter;
622:   thi->alpha *= PETSC_PI / 180;

624:   PRangeClear(&thi->eta);
625:   PRangeClear(&thi->beta2);

627:   {
628:     PetscReal u       = 1000*units->meter/(3e7*units->second),
629:               gradu   = u / (100*units->meter),eta,deta,
630:               rho     = 910 * units->kilogram/pow(units->meter,3),
631:               grav    = 9.81 * units->meter/PetscSqr(units->second),
632:               driving = rho * grav * sin(thi->alpha) * 1000*units->meter;
633:     THIViscosity(thi,0.5*gradu*gradu,&eta,&deta);
634:     thi->rhog = rho * grav;
635:     if (thi->verbose) {
636:       PetscPrintf(PetscObjectComm((PetscObject)thi),"Units: meter %8.2g  second %8.2g  kg %8.2g  Pa %8.2g\n",units->meter,units->second,units->kilogram,units->Pascal);
637:       PetscPrintf(PetscObjectComm((PetscObject)thi),"Domain (%6.2g,%6.2g,%6.2g), pressure %8.2g, driving stress %8.2g\n",thi->Lx,thi->Ly,thi->Lz,rho*grav*1e3*units->meter,driving);
638:       PetscPrintf(PetscObjectComm((PetscObject)thi),"Large velocity 1km/a %8.2g, velocity gradient %8.2g, eta %8.2g, stress %8.2g, ratio %8.2g\n",u,gradu,eta,2*eta*gradu,2*eta*gradu/driving);
639:       THIViscosity(thi,0.5*PetscSqr(1e-3*gradu),&eta,&deta);
640:       PetscPrintf(PetscObjectComm((PetscObject)thi),"Small velocity 1m/a  %8.2g, velocity gradient %8.2g, eta %8.2g, stress %8.2g, ratio %8.2g\n",1e-3*u,1e-3*gradu,eta,2*eta*1e-3*gradu,2*eta*1e-3*gradu/driving);
641:     }
642:   }

644:   *inthi = thi;
645:   return(0);
646: }

650: /* Our problem is periodic, but the domain has a mean slope of alpha so the bed does not line up between the upstream
651:  * and downstream ends of the domain.  This function fixes the ghost values so that the domain appears truly periodic in
652:  * the horizontal. */
653: static PetscErrorCode THIFixGhosts(THI thi,DM da3,DM da2,Vec X3,Vec X2)
654: {
656:   DMDALocalInfo  info;
657:   PrmNode        **x2;
658:   PetscInt       i,j;

661:   DMDAGetLocalInfo(da3,&info);
662:   /* VecView(X2,PETSC_VIEWER_STDOUT_WORLD); */
663:   DMDAVecGetArray(da2,X2,&x2);
664:   for (i=info.gzs; i<info.gzs+info.gzm; i++) {
665:     if (i > -1 && i < info.mz) continue;
666:     for (j=info.gys; j<info.gys+info.gym; j++) {
667:       x2[i][j].b += sin(thi->alpha) * thi->Lx * (i<0 ? 1.0 : -1.0);
668:     }
669:   }
670:   DMDAVecRestoreArray(da2,X2,&x2);
671:   /* VecView(X2,PETSC_VIEWER_STDOUT_WORLD); */
672:   return(0);
673: }

677: static PetscErrorCode THIInitializePrm(THI thi,DM da2prm,PrmNode **p)
678: {
679:   PetscInt       i,j,xs,xm,ys,ym,mx,my;

683:   DMDAGetGhostCorners(da2prm,&ys,&xs,0,&ym,&xm,0);
684:   DMDAGetInfo(da2prm,0, &my,&mx,0, 0,0,0, 0,0,0,0,0,0);
685:   for (i=xs; i<xs+xm; i++) {
686:     for (j=ys; j<ys+ym; j++) {
687:       PetscReal xx = thi->Lx*i/mx,yy = thi->Ly*j/my;
688:       thi->initialize(thi,xx,yy,&p[i][j]);
689:     }
690:   }
691:   return(0);
692: }

696: static PetscErrorCode THIInitial(THI thi,DM pack,Vec X)
697: {
698:   DM             da3,da2;
699:   PetscInt       i,j,k,xs,xm,ys,ym,zs,zm,mx,my;
700:   PetscReal      hx,hy;
701:   PrmNode        **prm;
702:   Node           ***x;
703:   Vec            X3g,X2g,X2;

707:   DMCompositeGetEntries(pack,&da3,&da2);
708:   DMCompositeGetAccess(pack,X,&X3g,&X2g);
709:   DMGetLocalVector(da2,&X2);

711:   DMDAGetInfo(da3,0, 0,&my,&mx, 0,0,0, 0,0,0,0,0,0);
712:   DMDAGetCorners(da3,&zs,&ys,&xs,&zm,&ym,&xm);
713:   DMDAVecGetArray(da3,X3g,&x);
714:   DMDAVecGetArray(da2,X2,&prm);

716:   THIInitializePrm(thi,da2,prm);

718:   hx = thi->Lx / mx;
719:   hy = thi->Ly / my;
720:   for (i=xs; i<xs+xm; i++) {
721:     for (j=ys; j<ys+ym; j++) {
722:       for (k=zs; k<zs+zm; k++) {
723:         const PetscScalar zm1      = zm-1,
724:                           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),
725:                           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);
726:         x[i][j][k].u = 0. * drivingx * prm[i][j].h*(PetscScalar)k/zm1;
727:         x[i][j][k].v = 0. * drivingy * prm[i][j].h*(PetscScalar)k/zm1;
728:       }
729:     }
730:   }

732:   DMDAVecRestoreArray(da3,X3g,&x);
733:   DMDAVecRestoreArray(da2,X2,&prm);

735:   DMLocalToGlobalBegin(da2,X2,INSERT_VALUES,X2g);
736:   DMLocalToGlobalEnd  (da2,X2,INSERT_VALUES,X2g);
737:   DMRestoreLocalVector(da2,&X2);

739:   DMCompositeRestoreAccess(pack,X,&X3g,&X2g);
740:   return(0);
741: }

743: static void PointwiseNonlinearity(THI thi,const Node n[restrict 8],const PetscReal phi[restrict 3],PetscReal dphi[restrict 8][3],PetscScalar *restrict u,PetscScalar *restrict v,PetscScalar du[restrict 3],PetscScalar dv[restrict 3],PetscReal *eta,PetscReal *deta)
744: {
745:   PetscInt    l,ll;
746:   PetscScalar gam;

748:   du[0] = du[1] = du[2] = 0;
749:   dv[0] = dv[1] = dv[2] = 0;
750:   *u    = 0;
751:   *v    = 0;
752:   for (l=0; l<8; l++) {
753:     *u += phi[l] * n[l].u;
754:     *v += phi[l] * n[l].v;
755:     for (ll=0; ll<3; ll++) {
756:       du[ll] += dphi[l][ll] * n[l].u;
757:       dv[ll] += dphi[l][ll] * n[l].v;
758:     }
759:   }
760:   gam = Sqr(du[0]) + Sqr(dv[1]) + du[0]*dv[1] + 0.25*Sqr(du[1]+dv[0]) + 0.25*Sqr(du[2]) + 0.25*Sqr(dv[2]);
761:   THIViscosity(thi,PetscRealPart(gam),eta,deta);
762: }

766: static PetscErrorCode THIFunctionLocal_3D(DMDALocalInfo *info,const Node ***x,const PrmNode **prm,const Node ***xdot,Node ***f,THI thi)
767: {
768:   PetscInt       xs,ys,xm,ym,zm,i,j,k,q,l;
769:   PetscReal      hx,hy,etamin,etamax,beta2min,beta2max;

773:   xs = info->zs;
774:   ys = info->ys;
775:   xm = info->zm;
776:   ym = info->ym;
777:   zm = info->xm;
778:   hx = thi->Lx / info->mz;
779:   hy = thi->Ly / info->my;

781:   etamin   = 1e100;
782:   etamax   = 0;
783:   beta2min = 1e100;
784:   beta2max = 0;

786:   for (i=xs; i<xs+xm; i++) {
787:     for (j=ys; j<ys+ym; j++) {
788:       PrmNode pn[4],dpn[4][2];
789:       QuadExtract(prm,i,j,pn);
790:       QuadComputeGrad4(QuadQDeriv,hx,hy,pn,dpn);
791:       for (k=0; k<zm-1; k++) {
792:         PetscInt  ls = 0;
793:         Node      n[8],ndot[8],*fn[8];
794:         PetscReal zn[8],etabase = 0;
795:         PrmHexGetZ(pn,k,zm,zn);
796:         HexExtract(x,i,j,k,n);
797:         HexExtract(xdot,i,j,k,ndot);
798:         HexExtractRef(f,i,j,k,fn);
799:         if (thi->no_slip && k == 0) {
800:           for (l=0; l<4; l++) n[l].u = n[l].v = 0;
801:           /* The first 4 basis functions lie on the bottom layer, so their contribution is exactly 0, hence we can skip them */
802:           ls = 4;
803:         }
804:         for (q=0; q<8; q++) {
805:           PetscReal   dz[3],phi[8],dphi[8][3],jw,eta,deta;
806:           PetscScalar du[3],dv[3],u,v,udot=0,vdot=0;
807:           for (l=ls; l<8; l++) {
808:             udot += HexQInterp[q][l]*ndot[l].u;
809:             vdot += HexQInterp[q][l]*ndot[l].v;
810:           }
811:           HexGrad(HexQDeriv[q],zn,dz);
812:           HexComputeGeometry(q,hx,hy,dz,phi,dphi,&jw);
813:           PointwiseNonlinearity(thi,n,phi,dphi,&u,&v,du,dv,&eta,&deta);
814:           jw /= thi->rhog;      /* scales residuals to be O(1) */
815:           if (q == 0) etabase = eta;
816:           RangeUpdate(&etamin,&etamax,eta);
817:           for (l=ls; l<8; l++) { /* test functions */
818:             const PetscScalar ds[2] = {dpn[q%4][0].h+dpn[q%4][0].b, dpn[q%4][1].h+dpn[q%4][1].b};
819:             const PetscReal   pp    = phi[l],*dp = dphi[l];
820:             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];
821:             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];
822:             fn[l]->u += pp*jw*udot*thi->inertia*pp;
823:             fn[l]->v += pp*jw*vdot*thi->inertia*pp;
824:           }
825:         }
826:         if (k == 0) { /* we are on a bottom face */
827:           if (thi->no_slip) {
828:             /* Note: Non-Galerkin coarse grid operators are very sensitive to the scaling of Dirichlet boundary
829:             * conditions.  After shenanigans above, etabase contains the effective viscosity at the closest quadrature
830:             * point to the bed.  We want the diagonal entry in the Dirichlet condition to have similar magnitude to the
831:             * diagonal entry corresponding to the adjacent node.  The fundamental scaling of the viscous part is in
832:             * diagu, diagv below.  This scaling is easy to recognize by considering the finite difference operator after
833:             * scaling by element size.  The no-slip Dirichlet condition is scaled by this factor, and also in the
834:             * assembled matrix (see the similar block in THIJacobianLocal).
835:             *
836:             * Note that the residual at this Dirichlet node is linear in the state at this node, but also depends
837:             * (nonlinearly in general) on the neighboring interior nodes through the local viscosity.  This will make
838:             * a matrix-free Jacobian have extra entries in the corresponding row.  We assemble only the diagonal part,
839:             * so the solution will exactly satisfy the boundary condition after the first linear iteration.
840:             */
841:             const PetscReal   hz    = PetscRealPart(pn[0].h)/(zm-1.);
842:             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);
843:             fn[0]->u = thi->dirichlet_scale*diagu*x[i][j][k].u;
844:             fn[0]->v = thi->dirichlet_scale*diagv*x[i][j][k].v;
845:           } else {              /* Integrate over bottom face to apply boundary condition */
846:             for (q=0; q<4; q++) { /* We remove the explicit scaling of the residual by 1/rhog because beta2 already has that scaling to be O(1) */
847:               const PetscReal jw = 0.25*hx*hy,*phi = QuadQInterp[q];
848:               PetscScalar     u  =0,v=0,rbeta2=0;
849:               PetscReal       beta2,dbeta2;
850:               for (l=0; l<4; l++) {
851:                 u     += phi[l]*n[l].u;
852:                 v     += phi[l]*n[l].v;
853:                 rbeta2 += phi[l]*pn[l].beta2;
854:               }
855:               THIFriction(thi,PetscRealPart(rbeta2),PetscRealPart(u*u+v*v)/2,&beta2,&dbeta2);
856:               RangeUpdate(&beta2min,&beta2max,beta2);
857:               for (l=0; l<4; l++) {
858:                 const PetscReal pp = phi[l];
859:                 fn[ls+l]->u += pp*jw*beta2*u;
860:                 fn[ls+l]->v += pp*jw*beta2*v;
861:               }
862:             }
863:           }
864:         }
865:       }
866:     }
867:   }

869:   PRangeMinMax(&thi->eta,etamin,etamax);
870:   PRangeMinMax(&thi->beta2,beta2min,beta2max);
871:   return(0);
872: }

876: static PetscErrorCode THIFunctionLocal_2D(DMDALocalInfo *info,const Node ***x,const PrmNode **prm,const PrmNode **prmdot,PrmNode **f,THI thi)
877: {
878:   PetscInt xs,ys,xm,ym,zm,i,j,k;

881:   xs = info->zs;
882:   ys = info->ys;
883:   xm = info->zm;
884:   ym = info->ym;
885:   zm = info->xm;

887:   for (i=xs; i<xs+xm; i++) {
888:     for (j=ys; j<ys+ym; j++) {
889:       PetscScalar div = 0,erate,h[8];
890:       PrmNodeGetFaceMeasure(prm,i,j,h);
891:       for (k=0; k<zm; k++) {
892:         PetscScalar weight = (k==0 || k == zm-1) ? 0.5/(zm-1) : 1.0/(zm-1);
893:         if (0) {                /* centered flux */
894:           div += (- weight*h[0] * StaggeredMidpoint2D(x[i][j][k].u,x[i-1][j][k].u, x[i-1][j-1][k].u,x[i][j-1][k].u)
895:                   - weight*h[1] * StaggeredMidpoint2D(x[i][j][k].u,x[i-1][j][k].u, x[i-1][j+1][k].u,x[i][j+1][k].u)
896:                   + weight*h[2] * StaggeredMidpoint2D(x[i][j][k].u,x[i+1][j][k].u, x[i+1][j+1][k].u,x[i][j+1][k].u)
897:                   + weight*h[3] * StaggeredMidpoint2D(x[i][j][k].u,x[i+1][j][k].u, x[i+1][j-1][k].u,x[i][j-1][k].u)
898:                   - weight*h[4] * StaggeredMidpoint2D(x[i][j][k].v,x[i][j-1][k].v, x[i+1][j-1][k].v,x[i+1][j][k].v)
899:                   - weight*h[5] * StaggeredMidpoint2D(x[i][j][k].v,x[i][j-1][k].v, x[i-1][j-1][k].v,x[i-1][j][k].v)
900:                   + weight*h[6] * StaggeredMidpoint2D(x[i][j][k].v,x[i][j+1][k].v, x[i-1][j+1][k].v,x[i-1][j][k].v)
901:                   + weight*h[7] * StaggeredMidpoint2D(x[i][j][k].v,x[i][j+1][k].v, x[i+1][j+1][k].v,x[i+1][j][k].v));
902:         } else {                /* Upwind flux */
903:           div += weight*(-UpwindFluxXW(x,prm,h,i,j,k, 1)
904:                          -UpwindFluxXW(x,prm,h,i,j,k,-1)
905:                          +UpwindFluxXE(x,prm,h,i,j,k, 1)
906:                          +UpwindFluxXE(x,prm,h,i,j,k,-1)
907:                          -UpwindFluxYS(x,prm,h,i,j,k, 1)
908:                          -UpwindFluxYS(x,prm,h,i,j,k,-1)
909:                          +UpwindFluxYN(x,prm,h,i,j,k, 1)
910:                          +UpwindFluxYN(x,prm,h,i,j,k,-1));
911:         }
912:       }
913:       /* printf("div[%d][%d] %g\n",i,j,div); */
914:       THIErosion(thi,&x[i][j][0],&erate,NULL);
915:       f[i][j].b     = prmdot[i][j].b - erate;
916:       f[i][j].h     = prmdot[i][j].h + div;
917:       f[i][j].beta2 = prmdot[i][j].beta2;
918:     }
919:   }
920:   return(0);
921: }

925: static PetscErrorCode THIFunction(TS ts,PetscReal t,Vec X,Vec Xdot,Vec F,void *ctx)
926: {
928:   THI            thi = (THI)ctx;
929:   DM             pack,da3,da2;
930:   Vec            X3,X2,Xdot3,Xdot2,F3,F2,F3g,F2g;
931:   const Node     ***x3,***xdot3;
932:   const PrmNode  **x2,**xdot2;
933:   Node           ***f3;
934:   PrmNode        **f2;
935:   DMDALocalInfo  info3;

938:   TSGetDM(ts,&pack);
939:   DMCompositeGetEntries(pack,&da3,&da2);
940:   DMDAGetLocalInfo(da3,&info3);
941:   DMCompositeGetLocalVectors(pack,&X3,&X2);
942:   DMCompositeGetLocalVectors(pack,&Xdot3,&Xdot2);
943:   DMCompositeScatter(pack,X,X3,X2);
944:   THIFixGhosts(thi,da3,da2,X3,X2);
945:   DMCompositeScatter(pack,Xdot,Xdot3,Xdot2);

947:   DMGetLocalVector(da3,&F3);
948:   DMGetLocalVector(da2,&F2);
949:   VecZeroEntries(F3);

951:   DMDAVecGetArray(da3,X3,&x3);
952:   DMDAVecGetArray(da2,X2,&x2);
953:   DMDAVecGetArray(da3,Xdot3,&xdot3);
954:   DMDAVecGetArray(da2,Xdot2,&xdot2);
955:   DMDAVecGetArray(da3,F3,&f3);
956:   DMDAVecGetArray(da2,F2,&f2);

958:   THIFunctionLocal_3D(&info3,x3,x2,xdot3,f3,thi);
959:   THIFunctionLocal_2D(&info3,x3,x2,xdot2,f2,thi);

961:   DMDAVecRestoreArray(da3,X3,&x3);
962:   DMDAVecRestoreArray(da2,X2,&x2);
963:   DMDAVecRestoreArray(da3,Xdot3,&xdot3);
964:   DMDAVecRestoreArray(da2,Xdot2,&xdot2);
965:   DMDAVecRestoreArray(da3,F3,&f3);
966:   DMDAVecRestoreArray(da2,F2,&f2);

968:   DMCompositeRestoreLocalVectors(pack,&X3,&X2);
969:   DMCompositeRestoreLocalVectors(pack,&Xdot3,&Xdot2);

971:   VecZeroEntries(F);
972:   DMCompositeGetAccess(pack,F,&F3g,&F2g);
973:   DMLocalToGlobalBegin(da3,F3,ADD_VALUES,F3g);
974:   DMLocalToGlobalEnd  (da3,F3,ADD_VALUES,F3g);
975:   DMLocalToGlobalBegin(da2,F2,INSERT_VALUES,F2g);
976:   DMLocalToGlobalEnd  (da2,F2,INSERT_VALUES,F2g);

978:   if (thi->verbose) {
979:     PetscViewer viewer;
980:     PetscViewerASCIIGetStdout(PetscObjectComm((PetscObject)thi),&viewer);
981:     PetscViewerASCIIPrintf(viewer,"3D_Velocity residual (bs=2):\n");
982:     PetscViewerASCIIPushTab(viewer);
983:     VecView(F3,viewer);
984:     PetscViewerASCIIPopTab(viewer);
985:     PetscViewerASCIIPrintf(viewer,"2D_Fields residual (bs=3):\n");
986:     PetscViewerASCIIPushTab(viewer);
987:     VecView(F2,viewer);
988:     PetscViewerASCIIPopTab(viewer);
989:   }

991:   DMCompositeRestoreAccess(pack,F,&F3g,&F2g);

993:   DMRestoreLocalVector(da3,&F3);
994:   DMRestoreLocalVector(da2,&F2);
995:   return(0);
996: }

1000: static PetscErrorCode THIMatrixStatistics(THI thi,Mat B,PetscViewer viewer)
1001: {
1003:   PetscReal      nrm;
1004:   PetscInt       m;
1005:   PetscMPIInt    rank;

1008:   MatNorm(B,NORM_FROBENIUS,&nrm);
1009:   MatGetSize(B,&m,0);
1010:   MPI_Comm_rank(PetscObjectComm((PetscObject)B),&rank);
1011:   if (!rank) {
1012:     PetscScalar val0,val2;
1013:     MatGetValue(B,0,0,&val0);
1014:     MatGetValue(B,2,2,&val2);
1015:     PetscViewerASCIIPrintf(viewer,"Matrix dim %8d  norm %8.2e, (0,0) %8.2e  (2,2) %8.2e, eta [%8.2e,%8.2e] beta2 [%8.2e,%8.2e]\n",m,nrm,PetscRealPart(val0),PetscRealPart(val2),thi->eta.cmin,thi->eta.cmax,thi->beta2.cmin,thi->beta2.cmax);
1016:   }
1017:   return(0);
1018: }

1022: static PetscErrorCode THISurfaceStatistics(DM pack,Vec X,PetscReal *min,PetscReal *max,PetscReal *mean)
1023: {
1025:   DM             da3,da2;
1026:   Vec            X3,X2;
1027:   Node           ***x;
1028:   PetscInt       i,j,xs,ys,zs,xm,ym,zm,mx,my,mz;
1029:   PetscReal      umin = 1e100,umax=-1e100;
1030:   PetscScalar    usum =0.0,gusum;

1033:   DMCompositeGetEntries(pack,&da3,&da2);
1034:   DMCompositeGetAccess(pack,X,&X3,&X2);
1035:   *min = *max = *mean = 0;
1036:   DMDAGetInfo(da3,0, &mz,&my,&mx, 0,0,0, 0,0,0,0,0,0);
1037:   DMDAGetCorners(da3,&zs,&ys,&xs,&zm,&ym,&xm);
1038:   if (zs != 0 || zm != mz) SETERRQ(PETSC_COMM_SELF,1,"Unexpected decomposition");
1039:   DMDAVecGetArray(da3,X3,&x);
1040:   for (i=xs; i<xs+xm; i++) {
1041:     for (j=ys; j<ys+ym; j++) {
1042:       PetscReal u = PetscRealPart(x[i][j][zm-1].u);
1043:       RangeUpdate(&umin,&umax,u);
1044:       usum += u;
1045:     }
1046:   }
1047:   DMDAVecRestoreArray(da3,X3,&x);
1048:   DMCompositeRestoreAccess(pack,X,&X3,&X2);

1050:   MPI_Allreduce(&umin,min,1,MPIU_REAL,MPIU_MIN,PetscObjectComm((PetscObject)da3));
1051:   MPI_Allreduce(&umax,max,1,MPIU_REAL,MPIU_MAX,PetscObjectComm((PetscObject)da3));
1052:   MPI_Allreduce(&usum,&gusum,1,MPIU_SCALAR,MPIU_SUM,PetscObjectComm((PetscObject)da3));
1053:   *mean = PetscRealPart(gusum) / (mx*my);
1054:   return(0);
1055: }

1059: static PetscErrorCode THISolveStatistics(THI thi,TS ts,PetscInt coarsened,const char name[])
1060: {
1061:   MPI_Comm       comm;
1062:   DM             pack;
1063:   Vec            X,X3,X2;

1067:   PetscObjectGetComm((PetscObject)thi,&comm);
1068:   TSGetDM(ts,&pack);
1069:   TSGetSolution(ts,&X);
1070:   DMCompositeGetAccess(pack,X,&X3,&X2);
1071:   PetscPrintf(comm,"Solution statistics after solve: %s\n",name);
1072:   {
1073:     PetscInt            its,lits;
1074:     SNESConvergedReason reason;
1075:     SNES                snes;
1076:     TSGetSNES(ts,&snes);
1077:     SNESGetIterationNumber(snes,&its);
1078:     SNESGetConvergedReason(snes,&reason);
1079:     SNESGetLinearSolveIterations(snes,&lits);
1080:     PetscPrintf(comm,"%s: Number of SNES iterations = %d, total linear iterations = %d\n",SNESConvergedReasons[reason],its,lits);
1081:   }
1082:   {
1083:     PetscReal   nrm2,tmin[3]={1e100,1e100,1e100},tmax[3]={-1e100,-1e100,-1e100},min[3],max[3];
1084:     PetscInt    i,j,m;
1085:     PetscScalar *x;
1086:     VecNorm(X3,NORM_2,&nrm2);
1087:     VecGetLocalSize(X3,&m);
1088:     VecGetArray(X3,&x);
1089:     for (i=0; i<m; i+=2) {
1090:       PetscReal u = PetscRealPart(x[i]),v = PetscRealPart(x[i+1]),c = PetscSqrtReal(u*u+v*v);
1091:       tmin[0] = PetscMin(u,tmin[0]);
1092:       tmin[1] = PetscMin(v,tmin[1]);
1093:       tmin[2] = PetscMin(c,tmin[2]);
1094:       tmax[0] = PetscMax(u,tmax[0]);
1095:       tmax[1] = PetscMax(v,tmax[1]);
1096:       tmax[2] = PetscMax(c,tmax[2]);
1097:     }
1098:     VecRestoreArray(X,&x);
1099:     MPI_Allreduce(tmin,min,3,MPIU_REAL,MPIU_MIN,PetscObjectComm((PetscObject)thi));
1100:     MPI_Allreduce(tmax,max,3,MPIU_REAL,MPIU_MAX,PetscObjectComm((PetscObject)thi));
1101:     /* Dimensionalize to meters/year */
1102:     nrm2 *= thi->units->year / thi->units->meter;
1103:     for (j=0; j<3; j++) {
1104:       min[j] *= thi->units->year / thi->units->meter;
1105:       max[j] *= thi->units->year / thi->units->meter;
1106:     }
1107:     PetscPrintf(comm,"|X|_2 %g   u in [%g, %g]   v in [%g, %g]   c in [%g, %g] \n",nrm2,min[0],max[0],min[1],max[1],min[2],max[2]);
1108:     {
1109:       PetscReal umin,umax,umean;
1110:       THISurfaceStatistics(pack,X,&umin,&umax,&umean);
1111:       umin  *= thi->units->year / thi->units->meter;
1112:       umax  *= thi->units->year / thi->units->meter;
1113:       umean *= thi->units->year / thi->units->meter;
1114:       PetscPrintf(comm,"Surface statistics: u in [%12.6e, %12.6e] mean %12.6e\n",umin,umax,umean);
1115:     }
1116:     /* These values stay nondimensional */
1117:     PetscPrintf(comm,"Global eta range   [%g, %g], converged range [%g, %g]\n",thi->eta.min,thi->eta.max,thi->eta.cmin,thi->eta.cmax);
1118:     PetscPrintf(comm,"Global beta2 range [%g, %g], converged range [%g, %g]\n",thi->beta2.min,thi->beta2.max,thi->beta2.cmin,thi->beta2.cmax);
1119:   }
1120:   PetscPrintf(comm,"\n");
1121:   DMCompositeRestoreAccess(pack,X,&X3,&X2);
1122:   return(0);
1123: }

1125: static inline PetscInt DMDALocalIndex3D(DMDALocalInfo *info,PetscInt i,PetscInt j,PetscInt k)
1126: {return ((i-info->gzs)*info->gym + (j-info->gys))*info->gxm + (k-info->gxs);}
1127: static inline PetscInt DMDALocalIndex2D(DMDALocalInfo *info,PetscInt i,PetscInt j)
1128: {return (i-info->gzs)*info->gym + (j-info->gys);}

1132: static PetscErrorCode THIJacobianLocal_Momentum(DMDALocalInfo *info,const Node ***x,const PrmNode **prm,Mat B,Mat Bcpl,THI thi)
1133: {
1134:   PetscInt       xs,ys,xm,ym,zm,i,j,k,q,l,ll;
1135:   PetscReal      hx,hy;

1139:   xs = info->zs;
1140:   ys = info->ys;
1141:   xm = info->zm;
1142:   ym = info->ym;
1143:   zm = info->xm;
1144:   hx = thi->Lx / info->mz;
1145:   hy = thi->Ly / info->my;

1147:   for (i=xs; i<xs+xm; i++) {
1148:     for (j=ys; j<ys+ym; j++) {
1149:       PrmNode pn[4],dpn[4][2];
1150:       QuadExtract(prm,i,j,pn);
1151:       QuadComputeGrad4(QuadQDeriv,hx,hy,pn,dpn);
1152:       for (k=0; k<zm-1; k++) {
1153:         Node        n[8];
1154:         PetscReal   zn[8],etabase = 0;
1155:         PetscScalar Ke[8*NODE_SIZE][8*NODE_SIZE],Kcpl[8*NODE_SIZE][4*PRMNODE_SIZE];
1156:         PetscInt    ls = 0;

1158:         PrmHexGetZ(pn,k,zm,zn);
1159:         HexExtract(x,i,j,k,n);
1160:         PetscMemzero(Ke,sizeof(Ke));
1161:         PetscMemzero(Kcpl,sizeof(Kcpl));
1162:         if (thi->no_slip && k == 0) {
1163:           for (l=0; l<4; l++) n[l].u = n[l].v = 0;
1164:           ls = 4;
1165:         }
1166:         for (q=0; q<8; q++) {
1167:           PetscReal   dz[3],phi[8],dphi[8][3],jw,eta,deta;
1168:           PetscScalar du[3],dv[3],u,v;
1169:           HexGrad(HexQDeriv[q],zn,dz);
1170:           HexComputeGeometry(q,hx,hy,dz,phi,dphi,&jw);
1171:           PointwiseNonlinearity(thi,n,phi,dphi,&u,&v,du,dv,&eta,&deta);
1172:           jw /= thi->rhog;      /* residuals are scaled by this factor */
1173:           if (q == 0) etabase = eta;
1174:           for (l=ls; l<8; l++) { /* test functions */
1175:             const PetscReal pp=phi[l],*restrict dp = dphi[l];
1176:             for (ll=ls; ll<8; ll++) { /* trial functions */
1177:               const PetscReal *restrict dpl = dphi[ll];
1178:               PetscScalar dgdu,dgdv;
1179:               dgdu = 2.*du[0]*dpl[0] + dv[1]*dpl[0] + 0.5*(du[1]+dv[0])*dpl[1] + 0.5*du[2]*dpl[2];
1180:               dgdv = 2.*dv[1]*dpl[1] + du[0]*dpl[1] + 0.5*(du[1]+dv[0])*dpl[0] + 0.5*dv[2]*dpl[2];
1181:               /* Picard part */
1182:               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];
1183:               Ke[l*2+0][ll*2+1] += dp[0]*jw*eta*2.*dpl[1] + dp[1]*jw*eta*dpl[0];
1184:               Ke[l*2+1][ll*2+0] += dp[1]*jw*eta*2.*dpl[0] + dp[0]*jw*eta*dpl[1];
1185:               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];
1186:               /* extra Newton terms */
1187:               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];
1188:               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];
1189:               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];
1190:               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];
1191:               /* inertial part */
1192:               Ke[l*2+0][ll*2+0] += pp*jw*thi->inertia*pp;
1193:               Ke[l*2+1][ll*2+1] += pp*jw*thi->inertia*pp;
1194:             }
1195:             for (ll=0; ll<4; ll++) { /* Trial functions for surface/bed */
1196:               const PetscReal dpl[] = {QuadQDeriv[q%4][ll][0]/hx, QuadQDeriv[q%4][ll][1]/hy}; /* surface = h + b */
1197:               Kcpl[FieldIndex(Node,l,u)][FieldIndex(PrmNode,ll,h)] += pp*jw*thi->rhog*dpl[0];
1198:               Kcpl[FieldIndex(Node,l,u)][FieldIndex(PrmNode,ll,b)] += pp*jw*thi->rhog*dpl[0];
1199:               Kcpl[FieldIndex(Node,l,v)][FieldIndex(PrmNode,ll,h)] += pp*jw*thi->rhog*dpl[1];
1200:               Kcpl[FieldIndex(Node,l,v)][FieldIndex(PrmNode,ll,b)] += pp*jw*thi->rhog*dpl[1];
1201:             }
1202:           }
1203:         }
1204:         if (k == 0) { /* on a bottom face */
1205:           if (thi->no_slip) {
1206:             const PetscReal   hz    = PetscRealPart(pn[0].h)/(zm-1);
1207:             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);
1208:             Ke[0][0] = thi->dirichlet_scale*diagu;
1209:             Ke[0][1] = 0;
1210:             Ke[1][0] = 0;
1211:             Ke[1][1] = thi->dirichlet_scale*diagv;
1212:           } else {
1213:             for (q=0; q<4; q++) { /* We remove the explicit scaling by 1/rhog because beta2 already has that scaling to be O(1) */
1214:               const PetscReal jw = 0.25*hx*hy,*phi = QuadQInterp[q];
1215:               PetscScalar     u  =0,v=0,rbeta2=0;
1216:               PetscReal       beta2,dbeta2;
1217:               for (l=0; l<4; l++) {
1218:                 u      += phi[l]*n[l].u;
1219:                 v      += phi[l]*n[l].v;
1220:                 rbeta2 += phi[l]*pn[l].beta2;
1221:               }
1222:               THIFriction(thi,PetscRealPart(rbeta2),PetscRealPart(u*u+v*v)/2,&beta2,&dbeta2);
1223:               for (l=0; l<4; l++) {
1224:                 const PetscReal pp = phi[l];
1225:                 for (ll=0; ll<4; ll++) {
1226:                   const PetscReal ppl = phi[ll];
1227:                   Ke[l*2+0][ll*2+0] += pp*jw*beta2*ppl + pp*jw*dbeta2*u*u*ppl;
1228:                   Ke[l*2+0][ll*2+1] +=                   pp*jw*dbeta2*u*v*ppl;
1229:                   Ke[l*2+1][ll*2+0] +=                   pp*jw*dbeta2*v*u*ppl;
1230:                   Ke[l*2+1][ll*2+1] += pp*jw*beta2*ppl + pp*jw*dbeta2*v*v*ppl;
1231:                 }
1232:               }
1233:             }
1234:           }
1235:         }
1236:         {
1237:           const PetscInt rc3blocked[8] = {
1238:             DMDALocalIndex3D(info,i+0,j+0,k+0),
1239:             DMDALocalIndex3D(info,i+1,j+0,k+0),
1240:             DMDALocalIndex3D(info,i+1,j+1,k+0),
1241:             DMDALocalIndex3D(info,i+0,j+1,k+0),
1242:             DMDALocalIndex3D(info,i+0,j+0,k+1),
1243:             DMDALocalIndex3D(info,i+1,j+0,k+1),
1244:             DMDALocalIndex3D(info,i+1,j+1,k+1),
1245:             DMDALocalIndex3D(info,i+0,j+1,k+1)
1246:           },col2blocked[PRMNODE_SIZE*4] = {
1247:             DMDALocalIndex2D(info,i+0,j+0),
1248:             DMDALocalIndex2D(info,i+1,j+0),
1249:             DMDALocalIndex2D(info,i+1,j+1),
1250:             DMDALocalIndex2D(info,i+0,j+1)
1251:           };
1252: #if !defined COMPUTE_LOWER_TRIANGULAR /* fill in lower-triangular part, this is really cheap compared to computing the entries */
1253:           for (l=0; l<8; l++) {
1254:             for (ll=l+1; ll<8; ll++) {
1255:               Ke[ll*2+0][l*2+0] = Ke[l*2+0][ll*2+0];
1256:               Ke[ll*2+1][l*2+0] = Ke[l*2+0][ll*2+1];
1257:               Ke[ll*2+0][l*2+1] = Ke[l*2+1][ll*2+0];
1258:               Ke[ll*2+1][l*2+1] = Ke[l*2+1][ll*2+1];
1259:             }
1260:           }
1261: #endif
1262:           MatSetValuesBlockedLocal(B,8,rc3blocked,8,rc3blocked,&Ke[0][0],ADD_VALUES); /* velocity-velocity coupling can use blocked insertion */
1263:           {                     /* The off-diagonal part cannot (yet) */
1264:             PetscInt row3scalar[NODE_SIZE*8],col2scalar[PRMNODE_SIZE*4];
1265:             for (l=0; l<8; l++) for (ll=0; ll<NODE_SIZE; ll++) row3scalar[l*NODE_SIZE+ll] = rc3blocked[l]*NODE_SIZE+ll;
1266:             for (l=0; l<4; l++) for (ll=0; ll<PRMNODE_SIZE; ll++) col2scalar[l*PRMNODE_SIZE+ll] = col2blocked[l]*PRMNODE_SIZE+ll;
1267:             MatSetValuesLocal(Bcpl,8*NODE_SIZE,row3scalar,4*PRMNODE_SIZE,col2scalar,&Kcpl[0][0],ADD_VALUES);
1268:           }
1269:         }
1270:       }
1271:     }
1272:   }
1273:   return(0);
1274: }

1278: static PetscErrorCode THIJacobianLocal_2D(DMDALocalInfo *info,const Node ***x3,const PrmNode **x2,const PrmNode **xdot2,PetscReal a,Mat B22,Mat B21,THI thi)
1279: {
1281:   PetscInt       xs,ys,xm,ym,zm,i,j,k;

1284:   xs = info->zs;
1285:   ys = info->ys;
1286:   xm = info->zm;
1287:   ym = info->ym;
1288:   zm = info->xm;

1290:   if (zm > 1024) SETERRQ(((PetscObject)info->da)->comm,PETSC_ERR_SUP,"Need to allocate more space");
1291:   for (i=xs; i<xs+xm; i++) {
1292:     for (j=ys; j<ys+ym; j++) {
1293:       {                         /* Self-coupling */
1294:         const PetscInt    row[]  = {DMDALocalIndex2D(info,i,j)};
1295:         const PetscInt    col[]  = {DMDALocalIndex2D(info,i,j)};
1296:         const PetscScalar vals[] = {
1297:           a,0,0,
1298:           0,a,0,
1299:           0,0,a
1300:         };
1301:         MatSetValuesBlockedLocal(B22,1,row,1,col,vals,INSERT_VALUES);
1302:       }
1303:       for (k=0; k<zm; k++) {    /* Coupling to velocity problem */
1304:         /* Use a cheaper quadrature than for residual evaluation, because it is much sparser */
1305:         const PetscInt row[]  = {FieldIndex(PrmNode,DMDALocalIndex2D(info,i,j),h)};
1306:         const PetscInt cols[] = {
1307:           FieldIndex(Node,DMDALocalIndex3D(info,i-1,j,k),u),
1308:           FieldIndex(Node,DMDALocalIndex3D(info,i  ,j,k),u),
1309:           FieldIndex(Node,DMDALocalIndex3D(info,i+1,j,k),u),
1310:           FieldIndex(Node,DMDALocalIndex3D(info,i,j-1,k),v),
1311:           FieldIndex(Node,DMDALocalIndex3D(info,i,j  ,k),v),
1312:           FieldIndex(Node,DMDALocalIndex3D(info,i,j+1,k),v)
1313:         };
1314:         const PetscScalar
1315:           w  = (k && k<zm-1) ? 0.5 : 0.25,
1316:           hW = w*(x2[i-1][j  ].h+x2[i  ][j  ].h)/(zm-1.),
1317:           hE = w*(x2[i  ][j  ].h+x2[i+1][j  ].h)/(zm-1.),
1318:           hS = w*(x2[i  ][j-1].h+x2[i  ][j  ].h)/(zm-1.),
1319:           hN = w*(x2[i  ][j  ].h+x2[i  ][j+1].h)/(zm-1.);
1320:         PetscScalar *vals,
1321:                      vals_upwind[] = {((PetscRealPart(x3[i][j][k].u) > 0) ? -hW : 0),
1322:                                       ((PetscRealPart(x3[i][j][k].u) > 0) ? +hE : -hW),
1323:                                       ((PetscRealPart(x3[i][j][k].u) > 0) ?  0  : +hE),
1324:                                       ((PetscRealPart(x3[i][j][k].v) > 0) ? -hS : 0),
1325:                                       ((PetscRealPart(x3[i][j][k].v) > 0) ? +hN : -hS),
1326:                                       ((PetscRealPart(x3[i][j][k].v) > 0) ?  0  : +hN)},
1327:                      vals_centered[] = {-0.5*hW, 0.5*(-hW+hE), 0.5*hE,
1328:                                         -0.5*hS, 0.5*(-hS+hN), 0.5*hN};
1329:         vals = 1 ? vals_upwind : vals_centered;
1330:         if (k == 0) {
1331:           Node derate;
1332:           THIErosion(thi,&x3[i][j][0],NULL,&derate);
1333:           vals[1] -= derate.u;
1334:           vals[4] -= derate.v;
1335:         }
1336:         MatSetValuesLocal(B21,1,row,6,cols,vals,INSERT_VALUES);
1337:       }
1338:     }
1339:   }
1340:   return(0);
1341: }

1345: static PetscErrorCode THIJacobian(TS ts,PetscReal t,Vec X,Vec Xdot,PetscReal a,Mat *A,Mat *B,MatStructure *mstr,void *ctx)
1346: {
1348:   THI            thi = (THI)ctx;
1349:   DM             pack,da3,da2;
1350:   Vec            X3,X2,Xdot2;
1351:   Mat            B11,B12,B21,B22;
1352:   DMDALocalInfo  info3;
1353:   IS             *isloc;
1354:   const Node     ***x3;
1355:   const PrmNode  **x2,**xdot2;

1358:   TSGetDM(ts,&pack);
1359:   DMCompositeGetEntries(pack,&da3,&da2);
1360:   DMDAGetLocalInfo(da3,&info3);
1361:   DMCompositeGetLocalVectors(pack,&X3,&X2);
1362:   DMCompositeGetLocalVectors(pack,NULL,&Xdot2);
1363:   DMCompositeScatter(pack,X,X3,X2);
1364:   THIFixGhosts(thi,da3,da2,X3,X2);
1365:   DMCompositeScatter(pack,Xdot,NULL,Xdot2);

1367:   MatZeroEntries(*B);

1369:   DMCompositeGetLocalISs(pack,&isloc);
1370:   MatGetLocalSubMatrix(*B,isloc[0],isloc[0],&B11);
1371:   MatGetLocalSubMatrix(*B,isloc[0],isloc[1],&B12);
1372:   MatGetLocalSubMatrix(*B,isloc[1],isloc[0],&B21);
1373:   MatGetLocalSubMatrix(*B,isloc[1],isloc[1],&B22);

1375:   DMDAVecGetArray(da3,X3,&x3);
1376:   DMDAVecGetArray(da2,X2,&x2);
1377:   DMDAVecGetArray(da2,Xdot2,&xdot2);

1379:   THIJacobianLocal_Momentum(&info3,x3,x2,B11,B12,thi);

1381:   /* Need to switch from ADD_VALUES to INSERT_VALUES */
1382:   MatAssemblyBegin(*B,MAT_FLUSH_ASSEMBLY);
1383:   MatAssemblyEnd(*B,MAT_FLUSH_ASSEMBLY);

1385:   THIJacobianLocal_2D(&info3,x3,x2,xdot2,a,B22,B21,thi);

1387:   DMDAVecRestoreArray(da3,X3,&x3);
1388:   DMDAVecRestoreArray(da2,X2,&x2);
1389:   DMDAVecRestoreArray(da2,Xdot2,&xdot2);

1391:   MatRestoreLocalSubMatrix(*B,isloc[0],isloc[0],&B11);
1392:   MatRestoreLocalSubMatrix(*B,isloc[0],isloc[1],&B12);
1393:   MatRestoreLocalSubMatrix(*B,isloc[1],isloc[0],&B21);
1394:   MatRestoreLocalSubMatrix(*B,isloc[1],isloc[1],&B22);
1395:   ISDestroy(&isloc[0]);
1396:   ISDestroy(&isloc[1]);
1397:   PetscFree(isloc);

1399:   DMCompositeRestoreLocalVectors(pack,&X3,&X2);
1400:   DMCompositeRestoreLocalVectors(pack,0,&Xdot2);

1402:   MatAssemblyBegin(*B,MAT_FINAL_ASSEMBLY);
1403:   MatAssemblyEnd(*B,MAT_FINAL_ASSEMBLY);
1404:   if (*A != *B) {
1405:     MatAssemblyBegin(*A,MAT_FINAL_ASSEMBLY);
1406:     MatAssemblyEnd(*A,MAT_FINAL_ASSEMBLY);
1407:   }
1408:   *mstr = SAME_NONZERO_PATTERN;
1409:   if (thi->verbose) {THIMatrixStatistics(thi,*B,PETSC_VIEWER_STDOUT_WORLD);}
1410:   return(0);
1411: }

1415: /* VTK's XML formats are so brain-dead that they can't handle multiple grids in the same file.  Since the communication
1416:  * can be shared between the two grids, we write two files at once, one for velocity (living on a 3D grid defined by
1417:  * h=thickness and b=bed) and another for all properties living on the 2D grid.
1418:  */
1419: static PetscErrorCode THIDAVecView_VTK_XML(THI thi,DM pack,Vec X,const char filename[],const char filename2[])
1420: {
1421:   const PetscInt dof   = NODE_SIZE,dof2 = PRMNODE_SIZE;
1422:   Units          units = thi->units;
1423:   MPI_Comm       comm;
1425:   PetscViewer    viewer3,viewer2;
1426:   PetscMPIInt    rank,size,tag,nn,nmax,nn2,nmax2;
1427:   PetscInt       mx,my,mz,r,range[6];
1428:   PetscScalar    *x,*x2;
1429:   DM             da3,da2;
1430:   Vec            X3,X2;

1433:   PetscObjectGetComm((PetscObject)thi,&comm);
1434:   DMCompositeGetEntries(pack,&da3,&da2);
1435:   DMCompositeGetAccess(pack,X,&X3,&X2);
1436:   DMDAGetInfo(da3,0, &mz,&my,&mx, 0,0,0, 0,0,0,0,0,0);
1437:   MPI_Comm_size(comm,&size);
1438:   MPI_Comm_rank(comm,&rank);
1439:   PetscViewerASCIIOpen(comm,filename,&viewer3);
1440:   PetscViewerASCIIOpen(comm,filename2,&viewer2);
1441:   PetscViewerASCIIPrintf(viewer3,"<VTKFile type=\"StructuredGrid\" version=\"0.1\" byte_order=\"LittleEndian\">\n");
1442:   PetscViewerASCIIPrintf(viewer2,"<VTKFile type=\"StructuredGrid\" version=\"0.1\" byte_order=\"LittleEndian\">\n");
1443:   PetscViewerASCIIPrintf(viewer3,"  <StructuredGrid WholeExtent=\"%d %d %d %d %d %d\">\n",0,mz-1,0,my-1,0,mx-1);
1444:   PetscViewerASCIIPrintf(viewer2,"  <StructuredGrid WholeExtent=\"%d %d %d %d %d %d\">\n",0,0,0,my-1,0,mx-1);

1446:   DMDAGetCorners(da3,range,range+1,range+2,range+3,range+4,range+5);
1447:   PetscMPIIntCast(range[3]*range[4]*range[5]*dof,&nn);
1448:   MPI_Reduce(&nn,&nmax,1,MPI_INT,MPI_MAX,0,comm);
1449:   PetscMPIIntCast(range[4]*range[5]*dof2,&nn2);
1450:   MPI_Reduce(&nn2,&nmax2,1,MPI_INT,MPI_MAX,0,comm);
1451:   tag  = ((PetscObject)viewer3)->tag;
1452:   VecGetArray(X3,&x);
1453:   VecGetArray(X2,&x2);
1454:   if (!rank) {
1455:     PetscScalar *array,*array2;
1456:     PetscMalloc2(nmax,PetscScalar,&array,nmax2,PetscScalar,&array2);
1457:     for (r=0; r<size; r++) {
1458:       PetscInt i,j,k,f,xs,xm,ys,ym,zs,zm;
1459:       Node     *y3;
1460:       PetscScalar (*y2)[PRMNODE_SIZE];
1461:       MPI_Status status;
1462:       if (r) {
1463:         MPI_Recv(range,6,MPIU_INT,r,tag,comm,MPI_STATUS_IGNORE);
1464:       }
1465:       zs = range[0];ys = range[1];xs = range[2];zm = range[3];ym = range[4];xm = range[5];
1466:       if (xm*ym*zm*dof > nmax) SETERRQ(PETSC_COMM_SELF,1,"should not happen");
1467:       if (r) {
1468:         MPI_Recv(array,nmax,MPIU_SCALAR,r,tag,comm,&status);
1469:         MPI_Get_count(&status,MPIU_SCALAR,&nn);
1470:         if (nn != xm*ym*zm*dof) SETERRQ(PETSC_COMM_SELF,1,"corrupt da3 send");
1471:         y3   = (Node*)array;
1472:         MPI_Recv(array2,nmax2,MPIU_SCALAR,r,tag,comm,&status);
1473:         MPI_Get_count(&status,MPIU_SCALAR,&nn2);
1474:         if (nn2 != xm*ym*dof2) SETERRQ(PETSC_COMM_SELF,1,"corrupt da2 send");
1475:         y2 = (PetscScalar(*)[PRMNODE_SIZE])array2;
1476:       } else {
1477:         y3 = (Node*)x;
1478:         y2 = (PetscScalar(*)[PRMNODE_SIZE])x2;
1479:       }
1480:       PetscViewerASCIIPrintf(viewer3,"    <Piece Extent=\"%d %d %d %d %d %d\">\n",zs,zs+zm-1,ys,ys+ym-1,xs,xs+xm-1);
1481:       PetscViewerASCIIPrintf(viewer2,"    <Piece Extent=\"%d %d %d %d %d %d\">\n",0,0,ys,ys+ym-1,xs,xs+xm-1);

1483:       PetscViewerASCIIPrintf(viewer3,"      <Points>\n");
1484:       PetscViewerASCIIPrintf(viewer2,"      <Points>\n");
1485:       PetscViewerASCIIPrintf(viewer3,"        <DataArray type=\"Float32\" NumberOfComponents=\"3\" format=\"ascii\">\n");
1486:       PetscViewerASCIIPrintf(viewer2,"        <DataArray type=\"Float32\" NumberOfComponents=\"3\" format=\"ascii\">\n");
1487:       for (i=xs; i<xs+xm; i++) {
1488:         for (j=ys; j<ys+ym; j++) {
1489:           PetscReal
1490:             xx = thi->Lx*i/mx,
1491:             yy = thi->Ly*j/my,
1492:             b  = PetscRealPart(y2[i*ym+j][FieldOffset(PrmNode,b)]),
1493:             h  = PetscRealPart(y2[i*ym+j][FieldOffset(PrmNode,h)]);
1494:           for (k=zs; k<zs+zm; k++) {
1495:             PetscReal zz = b + h*k/(mz-1.);
1496:             PetscViewerASCIIPrintf(viewer3,"%f %f %f\n",xx,yy,zz);
1497:           }
1498:           PetscViewerASCIIPrintf(viewer2,"%f %f %f\n",xx,yy,(double)0.0);
1499:         }
1500:       }
1501:       PetscViewerASCIIPrintf(viewer3,"        </DataArray>\n");
1502:       PetscViewerASCIIPrintf(viewer2,"        </DataArray>\n");
1503:       PetscViewerASCIIPrintf(viewer3,"      </Points>\n");
1504:       PetscViewerASCIIPrintf(viewer2,"      </Points>\n");

1506:       {                         /* Velocity and rank (3D) */
1507:         PetscViewerASCIIPrintf(viewer3,"      <PointData>\n");
1508:         PetscViewerASCIIPrintf(viewer3,"        <DataArray type=\"Float32\" Name=\"velocity\" NumberOfComponents=\"3\" format=\"ascii\">\n");
1509:         for (i=0; i<nn/dof; i++) {
1510:           PetscViewerASCIIPrintf(viewer3,"%f %f %f\n",PetscRealPart(y3[i].u)*units->year/units->meter,PetscRealPart(y3[i].v)*units->year/units->meter,0.0);
1511:         }
1512:         PetscViewerASCIIPrintf(viewer3,"        </DataArray>\n");

1514:         PetscViewerASCIIPrintf(viewer3,"        <DataArray type=\"Int32\" Name=\"rank\" NumberOfComponents=\"1\" format=\"ascii\">\n");
1515:         for (i=0; i<nn; i+=dof) {
1516:           PetscViewerASCIIPrintf(viewer3,"%d\n",r);
1517:         }
1518:         PetscViewerASCIIPrintf(viewer3,"        </DataArray>\n");
1519:         PetscViewerASCIIPrintf(viewer3,"      </PointData>\n");
1520:       }

1522:       {                         /* 2D */
1523:         PetscViewerASCIIPrintf(viewer2,"      <PointData>\n");
1524:         for (f=0; f<PRMNODE_SIZE; f++) {
1525:           const char *fieldname;
1526:           DMDAGetFieldName(da2,f,&fieldname);
1527:           PetscViewerASCIIPrintf(viewer2,"        <DataArray type=\"Float32\" Name=\"%s\" format=\"ascii\">\n",fieldname);
1528:           for (i=0; i<nn2/PRMNODE_SIZE; i++) {
1529:             PetscViewerASCIIPrintf(viewer2,"%g\n",y2[i][f]);
1530:           }
1531:           PetscViewerASCIIPrintf(viewer2,"        </DataArray>\n");
1532:         }
1533:         PetscViewerASCIIPrintf(viewer2,"      </PointData>\n");
1534:       }

1536:       PetscViewerASCIIPrintf(viewer3,"    </Piece>\n");
1537:       PetscViewerASCIIPrintf(viewer2,"    </Piece>\n");
1538:     }
1539:     PetscFree2(array,array2);
1540:   } else {
1541:     MPI_Send(range,6,MPIU_INT,0,tag,comm);
1542:     MPI_Send(x,nn,MPIU_SCALAR,0,tag,comm);
1543:     MPI_Send(x2,nn2,MPIU_SCALAR,0,tag,comm);
1544:   }
1545:   VecRestoreArray(X3,&x);
1546:   VecRestoreArray(X2,&x2);
1547:   PetscViewerASCIIPrintf(viewer3,"  </StructuredGrid>\n");
1548:   PetscViewerASCIIPrintf(viewer2,"  </StructuredGrid>\n");

1550:   DMCompositeRestoreAccess(pack,X,&X3,&X2);
1551:   PetscViewerASCIIPrintf(viewer3,"</VTKFile>\n");
1552:   PetscViewerASCIIPrintf(viewer2,"</VTKFile>\n");
1553:   PetscViewerDestroy(&viewer3);
1554:   PetscViewerDestroy(&viewer2);
1555:   return(0);
1556: }

1560: static PetscErrorCode THITSMonitor(TS ts,PetscInt step,PetscReal t,Vec X,void *ctx)
1561: {
1563:   THI            thi = (THI)ctx;
1564:   DM             pack;
1565:   char           filename3[PETSC_MAX_PATH_LEN],filename2[PETSC_MAX_PATH_LEN];

1568:   PetscPrintf(PetscObjectComm((PetscObject)ts),"%3D: t=%G\n",step,t);
1569:   if (thi->monitor_interval && step % thi->monitor_interval) return(0);
1570:   TSGetDM(ts,&pack);
1571:   PetscSNPrintf(filename3,sizeof(filename3),"%s-3d-%03d.vts",thi->monitor_basename,step);
1572:   PetscSNPrintf(filename2,sizeof(filename2),"%s-2d-%03d.vts",thi->monitor_basename,step);
1573:   THIDAVecView_VTK_XML(thi,pack,X,filename3,filename2);
1574:   return(0);
1575: }


1580: static PetscErrorCode THICreateDM3d(THI thi,DM *dm3d)
1581: {
1582:   MPI_Comm       comm;
1583:   PetscInt       M    = 3,N = 3,P = 2;
1584:   DM             da;

1588:   PetscObjectGetComm((PetscObject)thi,&comm);
1589:   PetscOptionsBegin(comm,NULL,"Grid resolution options","");
1590:   {
1591:     PetscOptionsInt("-M","Number of elements in x-direction on coarse level","",M,&M,NULL);
1592:     N    = M;
1593:     PetscOptionsInt("-N","Number of elements in y-direction on coarse level (if different from M)","",N,&N,NULL);
1594:     PetscOptionsInt("-P","Number of elements in z-direction on coarse level","",P,&P,NULL);
1595:   }
1596:   PetscOptionsEnd();
1597:   DMDACreate3d(comm,DMDA_BOUNDARY_NONE,DMDA_BOUNDARY_PERIODIC,DMDA_BOUNDARY_PERIODIC,DMDA_STENCIL_BOX,P,N,M,1,PETSC_DETERMINE,PETSC_DETERMINE,sizeof(Node)/sizeof(PetscScalar),1,0,0,0,&da);
1598:   DMDASetFieldName(da,0,"x-velocity");
1599:   DMDASetFieldName(da,1,"y-velocity");
1600:   *dm3d = da;
1601:   return(0);
1602: }

1606: int main(int argc,char *argv[])
1607: {
1608:   MPI_Comm       comm;
1609:   DM             pack,da3,da2;
1610:   TS             ts;
1611:   THI            thi;
1612:   Vec            X;
1613:   Mat            B;
1614:   PetscInt       i,steps;
1615:   PetscReal      ftime;

1618:   PetscInitialize(&argc,&argv,0,help);
1619:   comm = PETSC_COMM_WORLD;

1621:   THICreate(comm,&thi);
1622:   THICreateDM3d(thi,&da3);
1623:   {
1624:     PetscInt        Mx,My,mx,my,s;
1625:     DMDAStencilType st;
1626:     DMDAGetInfo(da3,0, 0,&My,&Mx, 0,&my,&mx, 0,&s,0,0,0,&st);
1627:     DMDACreate2d(PetscObjectComm((PetscObject)thi),DMDA_BOUNDARY_PERIODIC,DMDA_BOUNDARY_PERIODIC,st,My,Mx,my,mx,sizeof(PrmNode)/sizeof(PetscScalar),s,0,0,&da2);
1628:   }

1630:   PetscObjectSetName((PetscObject)da3,"3D_Velocity");
1631:   DMSetOptionsPrefix(da3,"f3d_");
1632:   DMDASetFieldName(da3,0,"u");
1633:   DMDASetFieldName(da3,1,"v");
1634:   PetscObjectSetName((PetscObject)da2,"2D_Fields");
1635:   DMSetOptionsPrefix(da2,"f2d_");
1636:   DMDASetFieldName(da2,0,"b");
1637:   DMDASetFieldName(da2,1,"h");
1638:   DMDASetFieldName(da2,2,"beta2");
1639:   DMCompositeCreate(comm,&pack);
1640:   DMCompositeAddDM(pack,da3);
1641:   DMCompositeAddDM(pack,da2);
1642:   DMDestroy(&da3);
1643:   DMDestroy(&da2);
1644:   DMSetUp(pack);
1645:   DMCreateMatrix(pack,NULL,&B);
1646:   MatSetOption(B,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_FALSE);
1647:   MatSetOptionsPrefix(B,"thi_");

1649:   for (i=0; i<thi->nlevels; i++) {
1650:     PetscReal Lx = thi->Lx / thi->units->meter,Ly = thi->Ly / thi->units->meter,Lz = thi->Lz / thi->units->meter;
1651:     PetscInt  Mx,My,Mz;
1652:     DMCompositeGetEntries(pack,&da3,&da2);
1653:     DMDAGetInfo(da3,0, &Mz,&My,&Mx, 0,0,0, 0,0,0,0,0,0);
1654:     PetscPrintf(PetscObjectComm((PetscObject)thi),"Level %d domain size (m) %8.2g x %8.2g x %8.2g, num elements %3d x %3d x %3d (%8d), size (m) %g x %g x %g\n",i,Lx,Ly,Lz,Mx,My,Mz,Mx*My*Mz,Lx/Mx,Ly/My,1000./(Mz-1));
1655:   }

1657:   DMCreateGlobalVector(pack,&X);
1658:   THIInitial(thi,pack,X);

1660:   TSCreate(comm,&ts);
1661:   TSSetDM(ts,pack);
1662:   TSSetProblemType(ts,TS_NONLINEAR);
1663:   TSMonitorSet(ts,THITSMonitor,thi,NULL);
1664:   TSSetType(ts,TSTHETA);
1665:   TSSetIFunction(ts,NULL,THIFunction,thi);
1666:   TSSetIJacobian(ts,B,B,THIJacobian,thi);
1667:   TSSetDuration(ts,100,10.0);
1668:   TSSetSolution(ts,X);
1669:   TSSetInitialTimeStep(ts,0.,1e-3);
1670:   TSSetFromOptions(ts);

1672:   TSSolve(ts,X);
1673:   TSGetSolveTime(ts,&ftime);
1674:   TSGetTimeStepNumber(ts,&steps);
1675:   PetscPrintf(PETSC_COMM_WORLD,"Steps %D  final time %G\n",steps,ftime);

1677:   if (0) {THISolveStatistics(thi,ts,0,"Full");}

1679:   {
1680:     PetscBool flg;
1681:     char      filename[PETSC_MAX_PATH_LEN] = "";
1682:     PetscOptionsGetString(NULL,"-o",filename,sizeof(filename),&flg);
1683:     if (flg) {
1684:       THIDAVecView_VTK_XML(thi,pack,X,filename,NULL);
1685:     }
1686:   }

1688:   VecDestroy(&X);
1689:   MatDestroy(&B);
1690:   DMDestroy(&pack);
1691:   TSDestroy(&ts);
1692:   THIDestroy(&thi);
1693:   PetscFinalize();
1694:   return 0;
1695: }