Actual source code: ex14.c
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 <petscdm.h>
48: #include <petscdmda.h>
49: #include <petscdmcomposite.h>
50: #include <ctype.h> /* toupper() */
51: #include <petsc/private/petscimpl.h>
53: #if defined __SSE2__
54: # include <emmintrin.h>
55: #endif
57: /* The SSE2 kernels are only for PetscScalar=double on architectures that support it */
58: #define USE_SSE2_KERNELS (!defined NO_SSE2 \
59: && !defined PETSC_USE_COMPLEX \
60: && !defined PETSC_USE_REAL_SINGLE \
61: && defined __SSE2__)
63: #if !defined __STDC_VERSION__ || __STDC_VERSION__ < 199901L
64: # if defined __cplusplus /* C++ restrict is nonstandard and compilers have inconsistent rules about where it can be used */
65: # define restrict
66: # else
67: # define restrict PETSC_RESTRICT
68: # endif
69: #endif
71: static PetscClassId THI_CLASSID;
73: typedef enum {QUAD_GAUSS,QUAD_LOBATTO} QuadratureType;
74: static const char *QuadratureTypes[] = {"gauss","lobatto","QuadratureType","QUAD_",0};
75: static const PetscReal HexQWeights[8] = {1,1,1,1,1,1,1,1};
76: static const PetscReal HexQNodes[] = {-0.57735026918962573, 0.57735026918962573};
77: #define G 0.57735026918962573
78: #define H (0.5*(1.+G))
79: #define L (0.5*(1.-G))
80: #define M (-0.5)
81: #define P (0.5)
82: /* Special quadrature: Lobatto in horizontal, Gauss in vertical */
83: static const PetscReal HexQInterp_Lobatto[8][8] = {{H,0,0,0,L,0,0,0},
84: {0,H,0,0,0,L,0,0},
85: {0,0,H,0,0,0,L,0},
86: {0,0,0,H,0,0,0,L},
87: {L,0,0,0,H,0,0,0},
88: {0,L,0,0,0,H,0,0},
89: {0,0,L,0,0,0,H,0},
90: {0,0,0,L,0,0,0,H}};
91: static const PetscReal HexQDeriv_Lobatto[8][8][3] = {
92: {{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} },
93: {{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} },
94: {{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} },
95: {{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}},
96: {{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} },
97: {{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} },
98: {{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} },
99: {{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}}};
100: /* Stanndard Gauss */
101: 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},
102: {L*H*H,H*H*H,H*L*H,L*L*H, L*H*L,H*H*L,H*L*L,L*L*L},
103: {L*L*H,H*L*H,H*H*H,L*H*H, L*L*L,H*L*L,H*H*L,L*H*L},
104: {H*L*H,L*L*H,L*H*H,H*H*H, H*L*L,L*L*L,L*H*L,H*H*L},
105: {H*H*L,L*H*L,L*L*L,H*L*L, H*H*H,L*H*H,L*L*H,H*L*H},
106: {L*H*L,H*H*L,H*L*L,L*L*L, L*H*H,H*H*H,H*L*H,L*L*H},
107: {L*L*L,H*L*L,H*H*L,L*H*L, L*L*H,H*L*H,H*H*H,L*H*H},
108: {H*L*L,L*L*L,L*H*L,H*H*L, H*L*H,L*L*H,L*H*H,H*H*H}};
109: static const PetscReal HexQDeriv_Gauss[8][8][3] = {
110: {{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}},
111: {{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}},
112: {{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}},
113: {{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}},
114: {{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}},
115: {{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}},
116: {{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}},
117: {{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}}};
118: static const PetscReal (*HexQInterp)[8],(*HexQDeriv)[8][3];
119: /* Standard 2x2 Gauss quadrature for the bottom layer. */
120: static const PetscReal QuadQInterp[4][4] = {{H*H,L*H,L*L,H*L},
121: {L*H,H*H,H*L,L*L},
122: {L*L,H*L,H*H,L*H},
123: {H*L,L*L,L*H,H*H}};
124: static const PetscReal QuadQDeriv[4][4][2] = {
125: {{M*H,M*H},{P*H,M*L},{P*L,P*L},{M*L,P*H}},
126: {{M*H,M*L},{P*H,M*H},{P*L,P*H},{M*L,P*L}},
127: {{M*L,M*L},{P*L,M*H},{P*H,P*H},{M*H,P*L}},
128: {{M*L,M*H},{P*L,M*L},{P*H,P*L},{M*H,P*H}}};
129: #undef G
130: #undef H
131: #undef L
132: #undef M
133: #undef P
135: #define HexExtract(x,i,j,k,n) do { \
136: (n)[0] = (x)[i][j][k]; \
137: (n)[1] = (x)[i+1][j][k]; \
138: (n)[2] = (x)[i+1][j+1][k]; \
139: (n)[3] = (x)[i][j+1][k]; \
140: (n)[4] = (x)[i][j][k+1]; \
141: (n)[5] = (x)[i+1][j][k+1]; \
142: (n)[6] = (x)[i+1][j+1][k+1]; \
143: (n)[7] = (x)[i][j+1][k+1]; \
144: } while (0)
146: #define HexExtractRef(x,i,j,k,n) do { \
147: (n)[0] = &(x)[i][j][k]; \
148: (n)[1] = &(x)[i+1][j][k]; \
149: (n)[2] = &(x)[i+1][j+1][k]; \
150: (n)[3] = &(x)[i][j+1][k]; \
151: (n)[4] = &(x)[i][j][k+1]; \
152: (n)[5] = &(x)[i+1][j][k+1]; \
153: (n)[6] = &(x)[i+1][j+1][k+1]; \
154: (n)[7] = &(x)[i][j+1][k+1]; \
155: } while (0)
157: #define QuadExtract(x,i,j,n) do { \
158: (n)[0] = (x)[i][j]; \
159: (n)[1] = (x)[i+1][j]; \
160: (n)[2] = (x)[i+1][j+1]; \
161: (n)[3] = (x)[i][j+1]; \
162: } while (0)
164: static PetscScalar Sqr(PetscScalar a) {return a*a;}
166: static void HexGrad(const PetscReal dphi[][3],const PetscReal zn[],PetscReal dz[])
167: {
168: PetscInt i;
169: dz[0] = dz[1] = dz[2] = 0;
170: for (i=0; i<8; i++) {
171: dz[0] += dphi[i][0] * zn[i];
172: dz[1] += dphi[i][1] * zn[i];
173: dz[2] += dphi[i][2] * zn[i];
174: }
175: }
177: static void HexComputeGeometry(PetscInt q,PetscReal hx,PetscReal hy,const PetscReal dz[restrict],PetscReal phi[restrict],PetscReal dphi[restrict][3],PetscReal *restrict jw)
178: {
179: const PetscReal
180: jac[3][3] = {{hx/2,0,0}, {0,hy/2,0}, {dz[0],dz[1],dz[2]}}
181: ,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]}}
182: ,jdet = jac[0][0]*jac[1][1]*jac[2][2];
183: PetscInt i;
185: for (i=0; i<8; i++) {
186: const PetscReal *dphir = HexQDeriv[q][i];
187: phi[i] = HexQInterp[q][i];
188: dphi[i][0] = dphir[0]*ijac[0][0] + dphir[1]*ijac[1][0] + dphir[2]*ijac[2][0];
189: dphi[i][1] = dphir[0]*ijac[0][1] + dphir[1]*ijac[1][1] + dphir[2]*ijac[2][1];
190: dphi[i][2] = dphir[0]*ijac[0][2] + dphir[1]*ijac[1][2] + dphir[2]*ijac[2][2];
191: }
192: *jw = 1.0 * jdet;
193: }
195: typedef struct _p_THI *THI;
196: typedef struct _n_Units *Units;
198: typedef struct {
199: PetscScalar u,v;
200: } Node;
202: typedef struct {
203: PetscScalar b; /* bed */
204: PetscScalar h; /* thickness */
205: PetscScalar beta2; /* friction */
206: } PrmNode;
208: #define FieldSize(ntype) ((PetscInt)(sizeof(ntype)/sizeof(PetscScalar)))
209: #define FieldOffset(ntype,member) ((PetscInt)(offsetof(ntype,member)/sizeof(PetscScalar)))
210: #define FieldIndex(ntype,i,member) ((PetscInt)((i)*FieldSize(ntype) + FieldOffset(ntype,member)))
211: #define NODE_SIZE FieldSize(Node)
212: #define PRMNODE_SIZE FieldSize(PrmNode)
214: typedef struct {
215: PetscReal min,max,cmin,cmax;
216: } PRange;
218: struct _p_THI {
219: PETSCHEADER(int);
220: void (*initialize)(THI,PetscReal x,PetscReal y,PrmNode *p);
221: PetscInt nlevels;
222: PetscInt zlevels;
223: PetscReal Lx,Ly,Lz; /* Model domain */
224: PetscReal alpha; /* Bed angle */
225: Units units;
226: PetscReal dirichlet_scale;
227: PetscReal ssa_friction_scale;
228: PetscReal inertia;
229: PRange eta;
230: PRange beta2;
231: struct {
232: PetscReal Bd2,eps,exponent,glen_n;
233: } viscosity;
234: struct {
235: PetscReal irefgam,eps2,exponent;
236: } friction;
237: struct {
238: PetscReal rate,exponent,refvel;
239: } erosion;
240: PetscReal rhog;
241: PetscBool no_slip;
242: PetscBool verbose;
243: char *mattype;
244: char *monitor_basename;
245: PetscInt monitor_interval;
246: };
248: struct _n_Units {
249: /* fundamental */
250: PetscReal meter;
251: PetscReal kilogram;
252: PetscReal second;
253: /* derived */
254: PetscReal Pascal;
255: PetscReal year;
256: };
258: static void PrmHexGetZ(const PrmNode pn[],PetscInt k,PetscInt zm,PetscReal zn[])
259: {
260: const PetscScalar zm1 = zm-1,
261: znl[8] = {pn[0].b + pn[0].h*(PetscScalar)k/zm1,
262: pn[1].b + pn[1].h*(PetscScalar)k/zm1,
263: pn[2].b + pn[2].h*(PetscScalar)k/zm1,
264: pn[3].b + pn[3].h*(PetscScalar)k/zm1,
265: pn[0].b + pn[0].h*(PetscScalar)(k+1)/zm1,
266: pn[1].b + pn[1].h*(PetscScalar)(k+1)/zm1,
267: pn[2].b + pn[2].h*(PetscScalar)(k+1)/zm1,
268: pn[3].b + pn[3].h*(PetscScalar)(k+1)/zm1};
269: PetscInt i;
270: for (i=0; i<8; i++) zn[i] = PetscRealPart(znl[i]);
271: }
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: PetscArrayzero(dpg,4);
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*PetscSinReal(thi->alpha);
329: p->b = s - 1000*units->meter + 500*units->meter * PetscSinReal(x*2*PETSC_PI/thi->Lx) * PetscSinReal(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*PetscSinReal(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 + PetscSinReal(x*2*PETSC_PI/thi->Lx)*PetscSinReal(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*PetscSinReal(thi->alpha);
352: p->b = s - 1000*units->meter + 100*units->meter * PetscSinReal(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*PetscSinReal(thi->alpha);
366: p->b = s - 1000*units->meter + 500*units->meter * PetscSinReal(x + PETSC_PI) * PetscSinReal(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*PetscSinReal(thi->alpha);
377: p->b = s - 1000*units->meter + 500*units->meter * PetscSinReal(x + PETSC_PI) * PetscSinReal(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. + PetscSinReal(PetscSqrtReal(16*r))/PetscSqrtReal(1e-2 + 16*r)*PetscCosReal(x*3/2)*PetscCosReal(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*PetscSinReal(thi->alpha);
389: p->b = s - 1000*units->meter + 500*units->meter * PetscSinReal(x + PETSC_PI) * PetscSinReal(y + PETSC_PI);
390: p->h = s - p->b;
391: 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 / 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 * PetscPowReal(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 * PetscPowReal(units->Pascal,-n) / units->year, /* softness parameter (Pa^{-n}/s) */
419: B = PetscPowReal(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 * PetscPowReal(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: }
459: static PetscErrorCode PRangeMinMax(PRange *p,PetscReal min,PetscReal max)
460: {
463: p->cmin = min;
464: p->cmax = max;
465: if (min < p->min) p->min = min;
466: if (max > p->max) p->max = max;
467: return(0);
468: }
470: static PetscErrorCode THIDestroy(THI *thi)
471: {
475: if (--((PetscObject)(*thi))->refct > 0) return(0);
476: PetscFree((*thi)->units);
477: PetscFree((*thi)->mattype);
478: PetscFree((*thi)->monitor_basename);
479: PetscHeaderDestroy(thi);
480: return(0);
481: }
483: static PetscErrorCode THICreate(MPI_Comm comm,THI *inthi)
484: {
485: static PetscBool registered = PETSC_FALSE;
486: THI thi;
487: Units units;
488: char monitor_basename[PETSC_MAX_PATH_LEN] = "thi-";
489: PetscErrorCode ierr;
492: *inthi = 0;
493: if (!registered) {
494: PetscClassIdRegister("Toy Hydrostatic Ice",&THI_CLASSID);
495: registered = PETSC_TRUE;
496: }
497: PetscHeaderCreate(thi,THI_CLASSID,"THI","Toy Hydrostatic Ice","THI",comm,THIDestroy,0);
499: PetscNew(&thi->units);
501: units = thi->units;
502: units->meter = 1e-2;
503: units->second = 1e-7;
504: units->kilogram = 1e-12;
506: PetscOptionsBegin(comm,NULL,"Scaled units options","");
507: {
508: PetscOptionsReal("-units_meter","1 meter in scaled length units","",units->meter,&units->meter,NULL);
509: PetscOptionsReal("-units_second","1 second in scaled time units","",units->second,&units->second,NULL);
510: PetscOptionsReal("-units_kilogram","1 kilogram in scaled mass units","",units->kilogram,&units->kilogram,NULL);
511: }
512: PetscOptionsEnd();
513: units->Pascal = units->kilogram / (units->meter * PetscSqr(units->second));
514: units->year = 31556926. * units->second, /* seconds per year */
516: thi->Lx = 10.e3;
517: thi->Ly = 10.e3;
518: thi->Lz = 1000;
519: thi->nlevels = 1;
520: thi->dirichlet_scale = 1;
521: thi->verbose = PETSC_FALSE;
523: thi->viscosity.glen_n = 3.;
524: thi->erosion.rate = 1e-3; /* m/a */
525: thi->erosion.exponent = 1.;
526: thi->erosion.refvel = 1.; /* m/a */
528: PetscOptionsBegin(comm,NULL,"Toy Hydrostatic Ice options","");
529: {
530: QuadratureType quad = QUAD_GAUSS;
531: char homexp[] = "A";
532: char mtype[256] = MATSBAIJ;
533: PetscReal L,m = 1.0;
534: PetscBool flg;
535: L = thi->Lx;
536: PetscOptionsReal("-thi_L","Domain size (m)","",L,&L,&flg);
537: if (flg) thi->Lx = thi->Ly = L;
538: PetscOptionsReal("-thi_Lx","X Domain size (m)","",thi->Lx,&thi->Lx,NULL);
539: PetscOptionsReal("-thi_Ly","Y Domain size (m)","",thi->Ly,&thi->Ly,NULL);
540: PetscOptionsReal("-thi_Lz","Z Domain size (m)","",thi->Lz,&thi->Lz,NULL);
541: PetscOptionsString("-thi_hom","ISMIP-HOM experiment (A or C)","",homexp,homexp,sizeof(homexp),NULL);
542: switch (homexp[0] = toupper(homexp[0])) {
543: case 'A':
544: thi->initialize = THIInitialize_HOM_A;
545: thi->no_slip = PETSC_TRUE;
546: thi->alpha = 0.5;
547: break;
548: case 'C':
549: thi->initialize = THIInitialize_HOM_C;
550: thi->no_slip = PETSC_FALSE;
551: thi->alpha = 0.1;
552: break;
553: case 'F':
554: thi->initialize = THIInitialize_HOM_F;
555: thi->no_slip = PETSC_FALSE;
556: thi->alpha = 0.5;
557: break;
558: case 'X':
559: thi->initialize = THIInitialize_HOM_X;
560: thi->no_slip = PETSC_FALSE;
561: thi->alpha = 0.3;
562: break;
563: case 'Y':
564: thi->initialize = THIInitialize_HOM_Y;
565: thi->no_slip = PETSC_FALSE;
566: thi->alpha = 0.5;
567: break;
568: case 'Z':
569: thi->initialize = THIInitialize_HOM_Z;
570: thi->no_slip = PETSC_FALSE;
571: thi->alpha = 0.5;
572: break;
573: default:
574: SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"HOM experiment '%c' not implemented",homexp[0]);
575: }
576: PetscOptionsEnum("-thi_quadrature","Quadrature to use for 3D elements","",QuadratureTypes,(PetscEnum)quad,(PetscEnum*)&quad,NULL);
577: switch (quad) {
578: case QUAD_GAUSS:
579: HexQInterp = HexQInterp_Gauss;
580: HexQDeriv = HexQDeriv_Gauss;
581: break;
582: case QUAD_LOBATTO:
583: HexQInterp = HexQInterp_Lobatto;
584: HexQDeriv = HexQDeriv_Lobatto;
585: break;
586: }
587: PetscOptionsReal("-thi_alpha","Bed angle (degrees)","",thi->alpha,&thi->alpha,NULL);
588: 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);
589: PetscOptionsReal("-thi_friction_m","Friction exponent, 0=Coulomb, 1=Navier","",m,&m,NULL);
590: thi->friction.exponent = (m-1)/2;
591: PetscOptionsReal("-thi_erosion_rate","Rate of erosion relative to sliding velocity at reference velocity (m/a)",NULL,thi->erosion.rate,&thi->erosion.rate,NULL);
592: PetscOptionsReal("-thi_erosion_exponent","Power of sliding velocity appearing in erosion relation",NULL,thi->erosion.exponent,&thi->erosion.exponent,NULL);
593: PetscOptionsReal("-thi_erosion_refvel","Reference sliding velocity for erosion (m/a)",NULL,thi->erosion.refvel,&thi->erosion.refvel,NULL);
594: thi->erosion.rate *= units->meter / units->year;
595: thi->erosion.refvel *= units->meter / units->year;
596: PetscOptionsReal("-thi_dirichlet_scale","Scale Dirichlet boundary conditions by this factor","",thi->dirichlet_scale,&thi->dirichlet_scale,NULL);
597: 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);
598: PetscOptionsReal("-thi_inertia","Coefficient of accelaration term in velocity system, physical is almost zero",NULL,thi->inertia,&thi->inertia,NULL);
599: PetscOptionsInt("-thi_nlevels","Number of levels of refinement","",thi->nlevels,&thi->nlevels,NULL);
600: PetscOptionsFList("-thi_mat_type","Matrix type","MatSetType",MatList,mtype,(char*)mtype,sizeof(mtype),NULL);
601: PetscStrallocpy(mtype,&thi->mattype);
602: PetscOptionsBool("-thi_verbose","Enable verbose output (like matrix sizes and statistics)","",thi->verbose,&thi->verbose,NULL);
603: PetscOptionsString("-thi_monitor","Basename to write state files to",NULL,monitor_basename,monitor_basename,sizeof(monitor_basename),&flg);
604: if (flg) {
605: PetscStrallocpy(monitor_basename,&thi->monitor_basename);
606: thi->monitor_interval = 1;
607: PetscOptionsInt("-thi_monitor_interval","Frequency at which to write state files",NULL,thi->monitor_interval,&thi->monitor_interval,NULL);
608: }
609: }
610: PetscOptionsEnd();
612: /* dimensionalize */
613: thi->Lx *= units->meter;
614: thi->Ly *= units->meter;
615: thi->Lz *= units->meter;
616: thi->alpha *= PETSC_PI / 180;
618: PRangeClear(&thi->eta);
619: PRangeClear(&thi->beta2);
621: {
622: PetscReal u = 1000*units->meter/(3e7*units->second),
623: gradu = u / (100*units->meter),eta,deta,
624: rho = 910 * units->kilogram/PetscPowRealInt(units->meter,3),
625: grav = 9.81 * units->meter/PetscSqr(units->second),
626: driving = rho * grav * PetscSinReal(thi->alpha) * 1000*units->meter;
627: THIViscosity(thi,0.5*gradu*gradu,&eta,&deta);
628: thi->rhog = rho * grav;
629: if (thi->verbose) {
630: 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);
631: 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);
632: 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);
633: THIViscosity(thi,0.5*PetscSqr(1e-3*gradu),&eta,&deta);
634: 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);
635: }
636: }
638: *inthi = thi;
639: return(0);
640: }
642: /* Our problem is periodic, but the domain has a mean slope of alpha so the bed does not line up between the upstream
643: * and downstream ends of the domain. This function fixes the ghost values so that the domain appears truly periodic in
644: * the horizontal. */
645: static PetscErrorCode THIFixGhosts(THI thi,DM da3,DM da2,Vec X3,Vec X2)
646: {
648: DMDALocalInfo info;
649: PrmNode **x2;
650: PetscInt i,j;
653: DMDAGetLocalInfo(da3,&info);
654: /* VecView(X2,PETSC_VIEWER_STDOUT_WORLD); */
655: DMDAVecGetArray(da2,X2,&x2);
656: for (i=info.gzs; i<info.gzs+info.gzm; i++) {
657: if (i > -1 && i < info.mz) continue;
658: for (j=info.gys; j<info.gys+info.gym; j++) {
659: x2[i][j].b += PetscSinReal(thi->alpha) * thi->Lx * (i<0 ? 1.0 : -1.0);
660: }
661: }
662: DMDAVecRestoreArray(da2,X2,&x2);
663: /* VecView(X2,PETSC_VIEWER_STDOUT_WORLD); */
664: return(0);
665: }
667: static PetscErrorCode THIInitializePrm(THI thi,DM da2prm,PrmNode **p)
668: {
669: PetscInt i,j,xs,xm,ys,ym,mx,my;
673: DMDAGetGhostCorners(da2prm,&ys,&xs,0,&ym,&xm,0);
674: DMDAGetInfo(da2prm,0, &my,&mx,0, 0,0,0, 0,0,0,0,0,0);
675: for (i=xs; i<xs+xm; i++) {
676: for (j=ys; j<ys+ym; j++) {
677: PetscReal xx = thi->Lx*i/mx,yy = thi->Ly*j/my;
678: thi->initialize(thi,xx,yy,&p[i][j]);
679: }
680: }
681: return(0);
682: }
684: static PetscErrorCode THIInitial(THI thi,DM pack,Vec X)
685: {
686: DM da3,da2;
687: PetscInt i,j,k,xs,xm,ys,ym,zs,zm,mx,my;
688: PetscReal hx,hy;
689: PrmNode **prm;
690: Node ***x;
691: Vec X3g,X2g,X2;
695: DMCompositeGetEntries(pack,&da3,&da2);
696: DMCompositeGetAccess(pack,X,&X3g,&X2g);
697: DMGetLocalVector(da2,&X2);
699: DMDAGetInfo(da3,0, 0,&my,&mx, 0,0,0, 0,0,0,0,0,0);
700: DMDAGetCorners(da3,&zs,&ys,&xs,&zm,&ym,&xm);
701: DMDAVecGetArray(da3,X3g,&x);
702: DMDAVecGetArray(da2,X2,&prm);
704: THIInitializePrm(thi,da2,prm);
706: hx = thi->Lx / mx;
707: hy = thi->Ly / my;
708: for (i=xs; i<xs+xm; i++) {
709: for (j=ys; j<ys+ym; j++) {
710: for (k=zs; k<zs+zm; k++) {
711: const PetscScalar zm1 = zm-1,
712: 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),
713: 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);
714: x[i][j][k].u = 0. * drivingx * prm[i][j].h*(PetscScalar)k/zm1;
715: x[i][j][k].v = 0. * drivingy * prm[i][j].h*(PetscScalar)k/zm1;
716: }
717: }
718: }
720: DMDAVecRestoreArray(da3,X3g,&x);
721: DMDAVecRestoreArray(da2,X2,&prm);
723: DMLocalToGlobalBegin(da2,X2,INSERT_VALUES,X2g);
724: DMLocalToGlobalEnd (da2,X2,INSERT_VALUES,X2g);
725: DMRestoreLocalVector(da2,&X2);
727: DMCompositeRestoreAccess(pack,X,&X3g,&X2g);
728: return(0);
729: }
731: 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)
732: {
733: PetscInt l,ll;
734: PetscScalar gam;
736: du[0] = du[1] = du[2] = 0;
737: dv[0] = dv[1] = dv[2] = 0;
738: *u = 0;
739: *v = 0;
740: for (l=0; l<8; l++) {
741: *u += phi[l] * n[l].u;
742: *v += phi[l] * n[l].v;
743: for (ll=0; ll<3; ll++) {
744: du[ll] += dphi[l][ll] * n[l].u;
745: dv[ll] += dphi[l][ll] * n[l].v;
746: }
747: }
748: 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]);
749: THIViscosity(thi,PetscRealPart(gam),eta,deta);
750: }
752: static PetscErrorCode THIFunctionLocal_3D(DMDALocalInfo *info,const Node ***x,const PrmNode **prm,const Node ***xdot,Node ***f,THI thi)
753: {
754: PetscInt xs,ys,xm,ym,zm,i,j,k,q,l;
755: PetscReal hx,hy,etamin,etamax,beta2min,beta2max;
759: xs = info->zs;
760: ys = info->ys;
761: xm = info->zm;
762: ym = info->ym;
763: zm = info->xm;
764: hx = thi->Lx / info->mz;
765: hy = thi->Ly / info->my;
767: etamin = 1e100;
768: etamax = 0;
769: beta2min = 1e100;
770: beta2max = 0;
772: for (i=xs; i<xs+xm; i++) {
773: for (j=ys; j<ys+ym; j++) {
774: PrmNode pn[4],dpn[4][2];
775: QuadExtract(prm,i,j,pn);
776: QuadComputeGrad4(QuadQDeriv,hx,hy,pn,dpn);
777: for (k=0; k<zm-1; k++) {
778: PetscInt ls = 0;
779: Node n[8],ndot[8],*fn[8];
780: PetscReal zn[8],etabase = 0;
781: PrmHexGetZ(pn,k,zm,zn);
782: HexExtract(x,i,j,k,n);
783: HexExtract(xdot,i,j,k,ndot);
784: HexExtractRef(f,i,j,k,fn);
785: if (thi->no_slip && k == 0) {
786: for (l=0; l<4; l++) n[l].u = n[l].v = 0;
787: /* The first 4 basis functions lie on the bottom layer, so their contribution is exactly 0, hence we can skip them */
788: ls = 4;
789: }
790: for (q=0; q<8; q++) {
791: PetscReal dz[3],phi[8],dphi[8][3],jw,eta,deta;
792: PetscScalar du[3],dv[3],u,v,udot=0,vdot=0;
793: for (l=ls; l<8; l++) {
794: udot += HexQInterp[q][l]*ndot[l].u;
795: vdot += HexQInterp[q][l]*ndot[l].v;
796: }
797: HexGrad(HexQDeriv[q],zn,dz);
798: HexComputeGeometry(q,hx,hy,dz,phi,dphi,&jw);
799: PointwiseNonlinearity(thi,n,phi,dphi,&u,&v,du,dv,&eta,&deta);
800: jw /= thi->rhog; /* scales residuals to be O(1) */
801: if (q == 0) etabase = eta;
802: RangeUpdate(&etamin,&etamax,eta);
803: for (l=ls; l<8; l++) { /* test functions */
804: const PetscScalar ds[2] = {dpn[q%4][0].h+dpn[q%4][0].b, dpn[q%4][1].h+dpn[q%4][1].b};
805: const PetscReal pp = phi[l],*dp = dphi[l];
806: 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];
807: 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];
808: fn[l]->u += pp*jw*udot*thi->inertia*pp;
809: fn[l]->v += pp*jw*vdot*thi->inertia*pp;
810: }
811: }
812: if (k == 0) { /* we are on a bottom face */
813: if (thi->no_slip) {
814: /* Note: Non-Galerkin coarse grid operators are very sensitive to the scaling of Dirichlet boundary
815: * conditions. After shenanigans above, etabase contains the effective viscosity at the closest quadrature
816: * point to the bed. We want the diagonal entry in the Dirichlet condition to have similar magnitude to the
817: * diagonal entry corresponding to the adjacent node. The fundamental scaling of the viscous part is in
818: * diagu, diagv below. This scaling is easy to recognize by considering the finite difference operator after
819: * scaling by element size. The no-slip Dirichlet condition is scaled by this factor, and also in the
820: * assembled matrix (see the similar block in THIJacobianLocal).
821: *
822: * Note that the residual at this Dirichlet node is linear in the state at this node, but also depends
823: * (nonlinearly in general) on the neighboring interior nodes through the local viscosity. This will make
824: * a matrix-free Jacobian have extra entries in the corresponding row. We assemble only the diagonal part,
825: * so the solution will exactly satisfy the boundary condition after the first linear iteration.
826: */
827: const PetscReal hz = PetscRealPart(pn[0].h)/(zm-1.);
828: 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);
829: fn[0]->u = thi->dirichlet_scale*diagu*x[i][j][k].u;
830: fn[0]->v = thi->dirichlet_scale*diagv*x[i][j][k].v;
831: } else { /* Integrate over bottom face to apply boundary condition */
832: 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) */
833: const PetscReal jw = 0.25*hx*hy,*phi = QuadQInterp[q];
834: PetscScalar u =0,v=0,rbeta2=0;
835: PetscReal beta2,dbeta2;
836: for (l=0; l<4; l++) {
837: u += phi[l]*n[l].u;
838: v += phi[l]*n[l].v;
839: rbeta2 += phi[l]*pn[l].beta2;
840: }
841: THIFriction(thi,PetscRealPart(rbeta2),PetscRealPart(u*u+v*v)/2,&beta2,&dbeta2);
842: RangeUpdate(&beta2min,&beta2max,beta2);
843: for (l=0; l<4; l++) {
844: const PetscReal pp = phi[l];
845: fn[ls+l]->u += pp*jw*beta2*u;
846: fn[ls+l]->v += pp*jw*beta2*v;
847: }
848: }
849: }
850: }
851: }
852: }
853: }
855: PRangeMinMax(&thi->eta,etamin,etamax);
856: PRangeMinMax(&thi->beta2,beta2min,beta2max);
857: return(0);
858: }
860: static PetscErrorCode THIFunctionLocal_2D(DMDALocalInfo *info,const Node ***x,const PrmNode **prm,const PrmNode **prmdot,PrmNode **f,THI thi)
861: {
862: PetscInt xs,ys,xm,ym,zm,i,j,k;
865: xs = info->zs;
866: ys = info->ys;
867: xm = info->zm;
868: ym = info->ym;
869: zm = info->xm;
871: for (i=xs; i<xs+xm; i++) {
872: for (j=ys; j<ys+ym; j++) {
873: PetscScalar div = 0,erate,h[8];
874: PrmNodeGetFaceMeasure(prm,i,j,h);
875: for (k=0; k<zm; k++) {
876: PetscScalar weight = (k==0 || k == zm-1) ? 0.5/(zm-1) : 1.0/(zm-1);
877: if (0) { /* centered flux */
878: 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)
879: - 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)
880: + 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)
881: + 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)
882: - 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)
883: - 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)
884: + 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)
885: + 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));
886: } else { /* Upwind flux */
887: div += weight*(-UpwindFluxXW(x,prm,h,i,j,k, 1)
888: -UpwindFluxXW(x,prm,h,i,j,k,-1)
889: +UpwindFluxXE(x,prm,h,i,j,k, 1)
890: +UpwindFluxXE(x,prm,h,i,j,k,-1)
891: -UpwindFluxYS(x,prm,h,i,j,k, 1)
892: -UpwindFluxYS(x,prm,h,i,j,k,-1)
893: +UpwindFluxYN(x,prm,h,i,j,k, 1)
894: +UpwindFluxYN(x,prm,h,i,j,k,-1));
895: }
896: }
897: /* printf("div[%d][%d] %g\n",i,j,div); */
898: THIErosion(thi,&x[i][j][0],&erate,NULL);
899: f[i][j].b = prmdot[i][j].b - erate;
900: f[i][j].h = prmdot[i][j].h + div;
901: f[i][j].beta2 = prmdot[i][j].beta2;
902: }
903: }
904: return(0);
905: }
907: static PetscErrorCode THIFunction(TS ts,PetscReal t,Vec X,Vec Xdot,Vec F,void *ctx)
908: {
910: THI thi = (THI)ctx;
911: DM pack,da3,da2;
912: Vec X3,X2,Xdot3,Xdot2,F3,F2,F3g,F2g;
913: const Node ***x3,***xdot3;
914: const PrmNode **x2,**xdot2;
915: Node ***f3;
916: PrmNode **f2;
917: DMDALocalInfo info3;
920: TSGetDM(ts,&pack);
921: DMCompositeGetEntries(pack,&da3,&da2);
922: DMDAGetLocalInfo(da3,&info3);
923: DMCompositeGetLocalVectors(pack,&X3,&X2);
924: DMCompositeGetLocalVectors(pack,&Xdot3,&Xdot2);
925: DMCompositeScatter(pack,X,X3,X2);
926: THIFixGhosts(thi,da3,da2,X3,X2);
927: DMCompositeScatter(pack,Xdot,Xdot3,Xdot2);
929: DMGetLocalVector(da3,&F3);
930: DMGetLocalVector(da2,&F2);
931: VecZeroEntries(F3);
933: DMDAVecGetArray(da3,X3,&x3);
934: DMDAVecGetArray(da2,X2,&x2);
935: DMDAVecGetArray(da3,Xdot3,&xdot3);
936: DMDAVecGetArray(da2,Xdot2,&xdot2);
937: DMDAVecGetArray(da3,F3,&f3);
938: DMDAVecGetArray(da2,F2,&f2);
940: THIFunctionLocal_3D(&info3,x3,x2,xdot3,f3,thi);
941: THIFunctionLocal_2D(&info3,x3,x2,xdot2,f2,thi);
943: DMDAVecRestoreArray(da3,X3,&x3);
944: DMDAVecRestoreArray(da2,X2,&x2);
945: DMDAVecRestoreArray(da3,Xdot3,&xdot3);
946: DMDAVecRestoreArray(da2,Xdot2,&xdot2);
947: DMDAVecRestoreArray(da3,F3,&f3);
948: DMDAVecRestoreArray(da2,F2,&f2);
950: DMCompositeRestoreLocalVectors(pack,&X3,&X2);
951: DMCompositeRestoreLocalVectors(pack,&Xdot3,&Xdot2);
953: VecZeroEntries(F);
954: DMCompositeGetAccess(pack,F,&F3g,&F2g);
955: DMLocalToGlobalBegin(da3,F3,ADD_VALUES,F3g);
956: DMLocalToGlobalEnd (da3,F3,ADD_VALUES,F3g);
957: DMLocalToGlobalBegin(da2,F2,INSERT_VALUES,F2g);
958: DMLocalToGlobalEnd (da2,F2,INSERT_VALUES,F2g);
960: if (thi->verbose) {
961: PetscViewer viewer;
962: PetscViewerASCIIGetStdout(PetscObjectComm((PetscObject)thi),&viewer);
963: PetscViewerASCIIPrintf(viewer,"3D_Velocity residual (bs=2):\n");
964: PetscViewerASCIIPushTab(viewer);
965: VecView(F3,viewer);
966: PetscViewerASCIIPopTab(viewer);
967: PetscViewerASCIIPrintf(viewer,"2D_Fields residual (bs=3):\n");
968: PetscViewerASCIIPushTab(viewer);
969: VecView(F2,viewer);
970: PetscViewerASCIIPopTab(viewer);
971: }
973: DMCompositeRestoreAccess(pack,F,&F3g,&F2g);
975: DMRestoreLocalVector(da3,&F3);
976: DMRestoreLocalVector(da2,&F2);
977: return(0);
978: }
980: static PetscErrorCode THIMatrixStatistics(THI thi,Mat B,PetscViewer viewer)
981: {
983: PetscReal nrm;
984: PetscInt m;
985: PetscMPIInt rank;
988: MatNorm(B,NORM_FROBENIUS,&nrm);
989: MatGetSize(B,&m,0);
990: MPI_Comm_rank(PetscObjectComm((PetscObject)B),&rank);
991: if (rank == 0) {
992: PetscScalar val0,val2;
993: MatGetValue(B,0,0,&val0);
994: MatGetValue(B,2,2,&val2);
995: 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);
996: }
997: return(0);
998: }
1000: static PetscErrorCode THISurfaceStatistics(DM pack,Vec X,PetscReal *min,PetscReal *max,PetscReal *mean)
1001: {
1003: DM da3,da2;
1004: Vec X3,X2;
1005: Node ***x;
1006: PetscInt i,j,xs,ys,zs,xm,ym,zm,mx,my,mz;
1007: PetscReal umin = 1e100,umax=-1e100;
1008: PetscScalar usum =0.0,gusum;
1011: DMCompositeGetEntries(pack,&da3,&da2);
1012: DMCompositeGetAccess(pack,X,&X3,&X2);
1013: *min = *max = *mean = 0;
1014: DMDAGetInfo(da3,0, &mz,&my,&mx, 0,0,0, 0,0,0,0,0,0);
1015: DMDAGetCorners(da3,&zs,&ys,&xs,&zm,&ym,&xm);
1016: if (zs != 0 || zm != mz) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_PLIB,"Unexpected decomposition");
1017: DMDAVecGetArray(da3,X3,&x);
1018: for (i=xs; i<xs+xm; i++) {
1019: for (j=ys; j<ys+ym; j++) {
1020: PetscReal u = PetscRealPart(x[i][j][zm-1].u);
1021: RangeUpdate(&umin,&umax,u);
1022: usum += u;
1023: }
1024: }
1025: DMDAVecRestoreArray(da3,X3,&x);
1026: DMCompositeRestoreAccess(pack,X,&X3,&X2);
1028: MPI_Allreduce(&umin,min,1,MPIU_REAL,MPIU_MIN,PetscObjectComm((PetscObject)da3));
1029: MPI_Allreduce(&umax,max,1,MPIU_REAL,MPIU_MAX,PetscObjectComm((PetscObject)da3));
1030: MPI_Allreduce(&usum,&gusum,1,MPIU_SCALAR,MPIU_SUM,PetscObjectComm((PetscObject)da3));
1031: *mean = PetscRealPart(gusum) / (mx*my);
1032: return(0);
1033: }
1035: static PetscErrorCode THISolveStatistics(THI thi,TS ts,PetscInt coarsened,const char name[])
1036: {
1037: MPI_Comm comm;
1038: DM pack;
1039: Vec X,X3,X2;
1043: PetscObjectGetComm((PetscObject)thi,&comm);
1044: TSGetDM(ts,&pack);
1045: TSGetSolution(ts,&X);
1046: DMCompositeGetAccess(pack,X,&X3,&X2);
1047: PetscPrintf(comm,"Solution statistics after solve: %s\n",name);
1048: {
1049: PetscInt its,lits;
1050: SNESConvergedReason reason;
1051: SNES snes;
1052: TSGetSNES(ts,&snes);
1053: SNESGetIterationNumber(snes,&its);
1054: SNESGetConvergedReason(snes,&reason);
1055: SNESGetLinearSolveIterations(snes,&lits);
1056: PetscPrintf(comm,"%s: Number of SNES iterations = %d, total linear iterations = %d\n",SNESConvergedReasons[reason],its,lits);
1057: }
1058: {
1059: PetscReal nrm2,tmin[3]={1e100,1e100,1e100},tmax[3]={-1e100,-1e100,-1e100},min[3],max[3];
1060: PetscInt i,j,m;
1061: PetscScalar *x;
1062: VecNorm(X3,NORM_2,&nrm2);
1063: VecGetLocalSize(X3,&m);
1064: VecGetArray(X3,&x);
1065: for (i=0; i<m; i+=2) {
1066: PetscReal u = PetscRealPart(x[i]),v = PetscRealPart(x[i+1]),c = PetscSqrtReal(u*u+v*v);
1067: tmin[0] = PetscMin(u,tmin[0]);
1068: tmin[1] = PetscMin(v,tmin[1]);
1069: tmin[2] = PetscMin(c,tmin[2]);
1070: tmax[0] = PetscMax(u,tmax[0]);
1071: tmax[1] = PetscMax(v,tmax[1]);
1072: tmax[2] = PetscMax(c,tmax[2]);
1073: }
1074: VecRestoreArray(X,&x);
1075: MPI_Allreduce(tmin,min,3,MPIU_REAL,MPIU_MIN,PetscObjectComm((PetscObject)thi));
1076: MPI_Allreduce(tmax,max,3,MPIU_REAL,MPIU_MAX,PetscObjectComm((PetscObject)thi));
1077: /* Dimensionalize to meters/year */
1078: nrm2 *= thi->units->year / thi->units->meter;
1079: for (j=0; j<3; j++) {
1080: min[j] *= thi->units->year / thi->units->meter;
1081: max[j] *= thi->units->year / thi->units->meter;
1082: }
1083: 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]);
1084: {
1085: PetscReal umin,umax,umean;
1086: THISurfaceStatistics(pack,X,&umin,&umax,&umean);
1087: umin *= thi->units->year / thi->units->meter;
1088: umax *= thi->units->year / thi->units->meter;
1089: umean *= thi->units->year / thi->units->meter;
1090: PetscPrintf(comm,"Surface statistics: u in [%12.6e, %12.6e] mean %12.6e\n",umin,umax,umean);
1091: }
1092: /* These values stay nondimensional */
1093: PetscPrintf(comm,"Global eta range [%g, %g], converged range [%g, %g]\n",thi->eta.min,thi->eta.max,thi->eta.cmin,thi->eta.cmax);
1094: PetscPrintf(comm,"Global beta2 range [%g, %g], converged range [%g, %g]\n",thi->beta2.min,thi->beta2.max,thi->beta2.cmin,thi->beta2.cmax);
1095: }
1096: PetscPrintf(comm,"\n");
1097: DMCompositeRestoreAccess(pack,X,&X3,&X2);
1098: return(0);
1099: }
1101: static inline PetscInt DMDALocalIndex3D(DMDALocalInfo *info,PetscInt i,PetscInt j,PetscInt k)
1102: {return ((i-info->gzs)*info->gym + (j-info->gys))*info->gxm + (k-info->gxs);}
1103: static inline PetscInt DMDALocalIndex2D(DMDALocalInfo *info,PetscInt i,PetscInt j)
1104: {return (i-info->gzs)*info->gym + (j-info->gys);}
1106: static PetscErrorCode THIJacobianLocal_Momentum(DMDALocalInfo *info,const Node ***x,const PrmNode **prm,Mat B,Mat Bcpl,THI thi)
1107: {
1108: PetscInt xs,ys,xm,ym,zm,i,j,k,q,l,ll;
1109: PetscReal hx,hy;
1113: xs = info->zs;
1114: ys = info->ys;
1115: xm = info->zm;
1116: ym = info->ym;
1117: zm = info->xm;
1118: hx = thi->Lx / info->mz;
1119: hy = thi->Ly / info->my;
1121: for (i=xs; i<xs+xm; i++) {
1122: for (j=ys; j<ys+ym; j++) {
1123: PrmNode pn[4],dpn[4][2];
1124: QuadExtract(prm,i,j,pn);
1125: QuadComputeGrad4(QuadQDeriv,hx,hy,pn,dpn);
1126: for (k=0; k<zm-1; k++) {
1127: Node n[8];
1128: PetscReal zn[8],etabase = 0;
1129: PetscScalar Ke[8*NODE_SIZE][8*NODE_SIZE],Kcpl[8*NODE_SIZE][4*PRMNODE_SIZE];
1130: PetscInt ls = 0;
1132: PrmHexGetZ(pn,k,zm,zn);
1133: HexExtract(x,i,j,k,n);
1134: PetscMemzero(Ke,sizeof(Ke));
1135: PetscMemzero(Kcpl,sizeof(Kcpl));
1136: if (thi->no_slip && k == 0) {
1137: for (l=0; l<4; l++) n[l].u = n[l].v = 0;
1138: ls = 4;
1139: }
1140: for (q=0; q<8; q++) {
1141: PetscReal dz[3],phi[8],dphi[8][3],jw,eta,deta;
1142: PetscScalar du[3],dv[3],u,v;
1143: HexGrad(HexQDeriv[q],zn,dz);
1144: HexComputeGeometry(q,hx,hy,dz,phi,dphi,&jw);
1145: PointwiseNonlinearity(thi,n,phi,dphi,&u,&v,du,dv,&eta,&deta);
1146: jw /= thi->rhog; /* residuals are scaled by this factor */
1147: if (q == 0) etabase = eta;
1148: for (l=ls; l<8; l++) { /* test functions */
1149: const PetscReal pp=phi[l],*restrict dp = dphi[l];
1150: for (ll=ls; ll<8; ll++) { /* trial functions */
1151: const PetscReal *restrict dpl = dphi[ll];
1152: PetscScalar dgdu,dgdv;
1153: dgdu = 2.*du[0]*dpl[0] + dv[1]*dpl[0] + 0.5*(du[1]+dv[0])*dpl[1] + 0.5*du[2]*dpl[2];
1154: dgdv = 2.*dv[1]*dpl[1] + du[0]*dpl[1] + 0.5*(du[1]+dv[0])*dpl[0] + 0.5*dv[2]*dpl[2];
1155: /* Picard part */
1156: 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];
1157: Ke[l*2+0][ll*2+1] += dp[0]*jw*eta*2.*dpl[1] + dp[1]*jw*eta*dpl[0];
1158: Ke[l*2+1][ll*2+0] += dp[1]*jw*eta*2.*dpl[0] + dp[0]*jw*eta*dpl[1];
1159: 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];
1160: /* extra Newton terms */
1161: 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];
1162: 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];
1163: 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];
1164: 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];
1165: /* inertial part */
1166: Ke[l*2+0][ll*2+0] += pp*jw*thi->inertia*pp;
1167: Ke[l*2+1][ll*2+1] += pp*jw*thi->inertia*pp;
1168: }
1169: for (ll=0; ll<4; ll++) { /* Trial functions for surface/bed */
1170: const PetscReal dpl[] = {QuadQDeriv[q%4][ll][0]/hx, QuadQDeriv[q%4][ll][1]/hy}; /* surface = h + b */
1171: Kcpl[FieldIndex(Node,l,u)][FieldIndex(PrmNode,ll,h)] += pp*jw*thi->rhog*dpl[0];
1172: Kcpl[FieldIndex(Node,l,u)][FieldIndex(PrmNode,ll,b)] += pp*jw*thi->rhog*dpl[0];
1173: Kcpl[FieldIndex(Node,l,v)][FieldIndex(PrmNode,ll,h)] += pp*jw*thi->rhog*dpl[1];
1174: Kcpl[FieldIndex(Node,l,v)][FieldIndex(PrmNode,ll,b)] += pp*jw*thi->rhog*dpl[1];
1175: }
1176: }
1177: }
1178: if (k == 0) { /* on a bottom face */
1179: if (thi->no_slip) {
1180: const PetscReal hz = PetscRealPart(pn[0].h)/(zm-1);
1181: 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);
1182: Ke[0][0] = thi->dirichlet_scale*diagu;
1183: Ke[0][1] = 0;
1184: Ke[1][0] = 0;
1185: Ke[1][1] = thi->dirichlet_scale*diagv;
1186: } else {
1187: for (q=0; q<4; q++) { /* We remove the explicit scaling by 1/rhog because beta2 already has that scaling to be O(1) */
1188: const PetscReal jw = 0.25*hx*hy,*phi = QuadQInterp[q];
1189: PetscScalar u =0,v=0,rbeta2=0;
1190: PetscReal beta2,dbeta2;
1191: for (l=0; l<4; l++) {
1192: u += phi[l]*n[l].u;
1193: v += phi[l]*n[l].v;
1194: rbeta2 += phi[l]*pn[l].beta2;
1195: }
1196: THIFriction(thi,PetscRealPart(rbeta2),PetscRealPart(u*u+v*v)/2,&beta2,&dbeta2);
1197: for (l=0; l<4; l++) {
1198: const PetscReal pp = phi[l];
1199: for (ll=0; ll<4; ll++) {
1200: const PetscReal ppl = phi[ll];
1201: Ke[l*2+0][ll*2+0] += pp*jw*beta2*ppl + pp*jw*dbeta2*u*u*ppl;
1202: Ke[l*2+0][ll*2+1] += pp*jw*dbeta2*u*v*ppl;
1203: Ke[l*2+1][ll*2+0] += pp*jw*dbeta2*v*u*ppl;
1204: Ke[l*2+1][ll*2+1] += pp*jw*beta2*ppl + pp*jw*dbeta2*v*v*ppl;
1205: }
1206: }
1207: }
1208: }
1209: }
1210: {
1211: const PetscInt rc3blocked[8] = {
1212: DMDALocalIndex3D(info,i+0,j+0,k+0),
1213: DMDALocalIndex3D(info,i+1,j+0,k+0),
1214: DMDALocalIndex3D(info,i+1,j+1,k+0),
1215: DMDALocalIndex3D(info,i+0,j+1,k+0),
1216: DMDALocalIndex3D(info,i+0,j+0,k+1),
1217: DMDALocalIndex3D(info,i+1,j+0,k+1),
1218: DMDALocalIndex3D(info,i+1,j+1,k+1),
1219: DMDALocalIndex3D(info,i+0,j+1,k+1)
1220: },col2blocked[PRMNODE_SIZE*4] = {
1221: DMDALocalIndex2D(info,i+0,j+0),
1222: DMDALocalIndex2D(info,i+1,j+0),
1223: DMDALocalIndex2D(info,i+1,j+1),
1224: DMDALocalIndex2D(info,i+0,j+1)
1225: };
1226: #if !defined COMPUTE_LOWER_TRIANGULAR /* fill in lower-triangular part, this is really cheap compared to computing the entries */
1227: for (l=0; l<8; l++) {
1228: for (ll=l+1; ll<8; ll++) {
1229: Ke[ll*2+0][l*2+0] = Ke[l*2+0][ll*2+0];
1230: Ke[ll*2+1][l*2+0] = Ke[l*2+0][ll*2+1];
1231: Ke[ll*2+0][l*2+1] = Ke[l*2+1][ll*2+0];
1232: Ke[ll*2+1][l*2+1] = Ke[l*2+1][ll*2+1];
1233: }
1234: }
1235: #endif
1236: MatSetValuesBlockedLocal(B,8,rc3blocked,8,rc3blocked,&Ke[0][0],ADD_VALUES); /* velocity-velocity coupling can use blocked insertion */
1237: { /* The off-diagonal part cannot (yet) */
1238: PetscInt row3scalar[NODE_SIZE*8],col2scalar[PRMNODE_SIZE*4];
1239: for (l=0; l<8; l++) for (ll=0; ll<NODE_SIZE; ll++) row3scalar[l*NODE_SIZE+ll] = rc3blocked[l]*NODE_SIZE+ll;
1240: for (l=0; l<4; l++) for (ll=0; ll<PRMNODE_SIZE; ll++) col2scalar[l*PRMNODE_SIZE+ll] = col2blocked[l]*PRMNODE_SIZE+ll;
1241: MatSetValuesLocal(Bcpl,8*NODE_SIZE,row3scalar,4*PRMNODE_SIZE,col2scalar,&Kcpl[0][0],ADD_VALUES);
1242: }
1243: }
1244: }
1245: }
1246: }
1247: return(0);
1248: }
1250: static PetscErrorCode THIJacobianLocal_2D(DMDALocalInfo *info,const Node ***x3,const PrmNode **x2,const PrmNode **xdot2,PetscReal a,Mat B22,Mat B21,THI thi)
1251: {
1253: PetscInt xs,ys,xm,ym,zm,i,j,k;
1256: xs = info->zs;
1257: ys = info->ys;
1258: xm = info->zm;
1259: ym = info->ym;
1260: zm = info->xm;
1262: if (zm > 1024) SETERRQ(((PetscObject)info->da)->comm,PETSC_ERR_SUP,"Need to allocate more space");
1263: for (i=xs; i<xs+xm; i++) {
1264: for (j=ys; j<ys+ym; j++) {
1265: { /* Self-coupling */
1266: const PetscInt row[] = {DMDALocalIndex2D(info,i,j)};
1267: const PetscInt col[] = {DMDALocalIndex2D(info,i,j)};
1268: const PetscScalar vals[] = {
1269: a,0,0,
1270: 0,a,0,
1271: 0,0,a
1272: };
1273: MatSetValuesBlockedLocal(B22,1,row,1,col,vals,INSERT_VALUES);
1274: }
1275: for (k=0; k<zm; k++) { /* Coupling to velocity problem */
1276: /* Use a cheaper quadrature than for residual evaluation, because it is much sparser */
1277: const PetscInt row[] = {FieldIndex(PrmNode,DMDALocalIndex2D(info,i,j),h)};
1278: const PetscInt cols[] = {
1279: FieldIndex(Node,DMDALocalIndex3D(info,i-1,j,k),u),
1280: FieldIndex(Node,DMDALocalIndex3D(info,i ,j,k),u),
1281: FieldIndex(Node,DMDALocalIndex3D(info,i+1,j,k),u),
1282: FieldIndex(Node,DMDALocalIndex3D(info,i,j-1,k),v),
1283: FieldIndex(Node,DMDALocalIndex3D(info,i,j ,k),v),
1284: FieldIndex(Node,DMDALocalIndex3D(info,i,j+1,k),v)
1285: };
1286: const PetscScalar
1287: w = (k && k<zm-1) ? 0.5 : 0.25,
1288: hW = w*(x2[i-1][j ].h+x2[i ][j ].h)/(zm-1.),
1289: hE = w*(x2[i ][j ].h+x2[i+1][j ].h)/(zm-1.),
1290: hS = w*(x2[i ][j-1].h+x2[i ][j ].h)/(zm-1.),
1291: hN = w*(x2[i ][j ].h+x2[i ][j+1].h)/(zm-1.);
1292: PetscScalar *vals,
1293: vals_upwind[] = {((PetscRealPart(x3[i][j][k].u) > 0) ? -hW : 0),
1294: ((PetscRealPart(x3[i][j][k].u) > 0) ? +hE : -hW),
1295: ((PetscRealPart(x3[i][j][k].u) > 0) ? 0 : +hE),
1296: ((PetscRealPart(x3[i][j][k].v) > 0) ? -hS : 0),
1297: ((PetscRealPart(x3[i][j][k].v) > 0) ? +hN : -hS),
1298: ((PetscRealPart(x3[i][j][k].v) > 0) ? 0 : +hN)},
1299: vals_centered[] = {-0.5*hW, 0.5*(-hW+hE), 0.5*hE,
1300: -0.5*hS, 0.5*(-hS+hN), 0.5*hN};
1301: vals = 1 ? vals_upwind : vals_centered;
1302: if (k == 0) {
1303: Node derate;
1304: THIErosion(thi,&x3[i][j][0],NULL,&derate);
1305: vals[1] -= derate.u;
1306: vals[4] -= derate.v;
1307: }
1308: MatSetValuesLocal(B21,1,row,6,cols,vals,INSERT_VALUES);
1309: }
1310: }
1311: }
1312: return(0);
1313: }
1315: static PetscErrorCode THIJacobian(TS ts,PetscReal t,Vec X,Vec Xdot,PetscReal a,Mat A,Mat B,void *ctx)
1316: {
1318: THI thi = (THI)ctx;
1319: DM pack,da3,da2;
1320: Vec X3,X2,Xdot2;
1321: Mat B11,B12,B21,B22;
1322: DMDALocalInfo info3;
1323: IS *isloc;
1324: const Node ***x3;
1325: const PrmNode **x2,**xdot2;
1328: TSGetDM(ts,&pack);
1329: DMCompositeGetEntries(pack,&da3,&da2);
1330: DMDAGetLocalInfo(da3,&info3);
1331: DMCompositeGetLocalVectors(pack,&X3,&X2);
1332: DMCompositeGetLocalVectors(pack,NULL,&Xdot2);
1333: DMCompositeScatter(pack,X,X3,X2);
1334: THIFixGhosts(thi,da3,da2,X3,X2);
1335: DMCompositeScatter(pack,Xdot,NULL,Xdot2);
1337: MatZeroEntries(B);
1339: DMCompositeGetLocalISs(pack,&isloc);
1340: MatGetLocalSubMatrix(B,isloc[0],isloc[0],&B11);
1341: MatGetLocalSubMatrix(B,isloc[0],isloc[1],&B12);
1342: MatGetLocalSubMatrix(B,isloc[1],isloc[0],&B21);
1343: MatGetLocalSubMatrix(B,isloc[1],isloc[1],&B22);
1345: DMDAVecGetArray(da3,X3,&x3);
1346: DMDAVecGetArray(da2,X2,&x2);
1347: DMDAVecGetArray(da2,Xdot2,&xdot2);
1349: THIJacobianLocal_Momentum(&info3,x3,x2,B11,B12,thi);
1351: /* Need to switch from ADD_VALUES to INSERT_VALUES */
1352: MatAssemblyBegin(B,MAT_FLUSH_ASSEMBLY);
1353: MatAssemblyEnd(B,MAT_FLUSH_ASSEMBLY);
1355: THIJacobianLocal_2D(&info3,x3,x2,xdot2,a,B22,B21,thi);
1357: DMDAVecRestoreArray(da3,X3,&x3);
1358: DMDAVecRestoreArray(da2,X2,&x2);
1359: DMDAVecRestoreArray(da2,Xdot2,&xdot2);
1361: MatRestoreLocalSubMatrix(B,isloc[0],isloc[0],&B11);
1362: MatRestoreLocalSubMatrix(B,isloc[0],isloc[1],&B12);
1363: MatRestoreLocalSubMatrix(B,isloc[1],isloc[0],&B21);
1364: MatRestoreLocalSubMatrix(B,isloc[1],isloc[1],&B22);
1365: ISDestroy(&isloc[0]);
1366: ISDestroy(&isloc[1]);
1367: PetscFree(isloc);
1369: DMCompositeRestoreLocalVectors(pack,&X3,&X2);
1370: DMCompositeRestoreLocalVectors(pack,0,&Xdot2);
1372: MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
1373: MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
1374: if (A != B) {
1375: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
1376: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
1377: }
1378: if (thi->verbose) {THIMatrixStatistics(thi,B,PETSC_VIEWER_STDOUT_WORLD);}
1379: return(0);
1380: }
1382: /* VTK's XML formats are so brain-dead that they can't handle multiple grids in the same file. Since the communication
1383: * can be shared between the two grids, we write two files at once, one for velocity (living on a 3D grid defined by
1384: * h=thickness and b=bed) and another for all properties living on the 2D grid.
1385: */
1386: static PetscErrorCode THIDAVecView_VTK_XML(THI thi,DM pack,Vec X,const char filename[],const char filename2[])
1387: {
1388: const PetscInt dof = NODE_SIZE,dof2 = PRMNODE_SIZE;
1389: Units units = thi->units;
1390: MPI_Comm comm;
1392: PetscViewer viewer3,viewer2;
1393: PetscMPIInt rank,size,tag,nn,nmax,nn2,nmax2;
1394: PetscInt mx,my,mz,r,range[6];
1395: PetscScalar *x,*x2;
1396: DM da3,da2;
1397: Vec X3,X2;
1400: PetscObjectGetComm((PetscObject)thi,&comm);
1401: DMCompositeGetEntries(pack,&da3,&da2);
1402: DMCompositeGetAccess(pack,X,&X3,&X2);
1403: DMDAGetInfo(da3,0, &mz,&my,&mx, 0,0,0, 0,0,0,0,0,0);
1404: MPI_Comm_size(comm,&size);
1405: MPI_Comm_rank(comm,&rank);
1406: PetscViewerASCIIOpen(comm,filename,&viewer3);
1407: PetscViewerASCIIOpen(comm,filename2,&viewer2);
1408: PetscViewerASCIIPrintf(viewer3,"<VTKFile type=\"StructuredGrid\" version=\"0.1\" byte_order=\"LittleEndian\">\n");
1409: PetscViewerASCIIPrintf(viewer2,"<VTKFile type=\"StructuredGrid\" version=\"0.1\" byte_order=\"LittleEndian\">\n");
1410: PetscViewerASCIIPrintf(viewer3," <StructuredGrid WholeExtent=\"%d %d %d %d %d %d\">\n",0,mz-1,0,my-1,0,mx-1);
1411: PetscViewerASCIIPrintf(viewer2," <StructuredGrid WholeExtent=\"%d %d %d %d %d %d\">\n",0,0,0,my-1,0,mx-1);
1413: DMDAGetCorners(da3,range,range+1,range+2,range+3,range+4,range+5);
1414: PetscMPIIntCast(range[3]*range[4]*range[5]*dof,&nn);
1415: MPI_Reduce(&nn,&nmax,1,MPI_INT,MPI_MAX,0,comm);
1416: PetscMPIIntCast(range[4]*range[5]*dof2,&nn2);
1417: MPI_Reduce(&nn2,&nmax2,1,MPI_INT,MPI_MAX,0,comm);
1418: tag = ((PetscObject)viewer3)->tag;
1419: VecGetArrayRead(X3,(const PetscScalar**)&x);
1420: VecGetArrayRead(X2,(const PetscScalar**)&x2);
1421: if (rank == 0) {
1422: PetscScalar *array,*array2;
1423: PetscMalloc2(nmax,&array,nmax2,&array2);
1424: for (r=0; r<size; r++) {
1425: PetscInt i,j,k,f,xs,xm,ys,ym,zs,zm;
1426: Node *y3;
1427: PetscScalar (*y2)[PRMNODE_SIZE];
1428: MPI_Status status;
1430: if (r) {
1431: MPI_Recv(range,6,MPIU_INT,r,tag,comm,MPI_STATUS_IGNORE);
1432: }
1433: zs = range[0];ys = range[1];xs = range[2];zm = range[3];ym = range[4];xm = range[5];
1434: if (xm*ym*zm*dof > nmax) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"should not happen");
1435: if (r) {
1436: MPI_Recv(array,nmax,MPIU_SCALAR,r,tag,comm,&status);
1437: MPI_Get_count(&status,MPIU_SCALAR,&nn);
1438: if (nn != xm*ym*zm*dof) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"corrupt da3 send");
1439: y3 = (Node*)array;
1440: MPI_Recv(array2,nmax2,MPIU_SCALAR,r,tag,comm,&status);
1441: MPI_Get_count(&status,MPIU_SCALAR,&nn2);
1442: if (nn2 != xm*ym*dof2) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"corrupt da2 send");
1443: y2 = (PetscScalar(*)[PRMNODE_SIZE])array2;
1444: } else {
1445: y3 = (Node*)x;
1446: y2 = (PetscScalar(*)[PRMNODE_SIZE])x2;
1447: }
1448: PetscViewerASCIIPrintf(viewer3," <Piece Extent=\"%D %D %D %D %D %D\">\n",zs,zs+zm-1,ys,ys+ym-1,xs,xs+xm-1);
1449: PetscViewerASCIIPrintf(viewer2," <Piece Extent=\"%d %d %D %D %D %D\">\n",0,0,ys,ys+ym-1,xs,xs+xm-1);
1451: PetscViewerASCIIPrintf(viewer3," <Points>\n");
1452: PetscViewerASCIIPrintf(viewer2," <Points>\n");
1453: PetscViewerASCIIPrintf(viewer3," <DataArray type=\"Float32\" NumberOfComponents=\"3\" format=\"ascii\">\n");
1454: PetscViewerASCIIPrintf(viewer2," <DataArray type=\"Float32\" NumberOfComponents=\"3\" format=\"ascii\">\n");
1455: for (i=xs; i<xs+xm; i++) {
1456: for (j=ys; j<ys+ym; j++) {
1457: PetscReal
1458: xx = thi->Lx*i/mx,
1459: yy = thi->Ly*j/my,
1460: b = PetscRealPart(y2[i*ym+j][FieldOffset(PrmNode,b)]),
1461: h = PetscRealPart(y2[i*ym+j][FieldOffset(PrmNode,h)]);
1462: for (k=zs; k<zs+zm; k++) {
1463: PetscReal zz = b + h*k/(mz-1.);
1464: PetscViewerASCIIPrintf(viewer3,"%f %f %f\n",xx,yy,zz);
1465: }
1466: PetscViewerASCIIPrintf(viewer2,"%f %f %f\n",xx,yy,(double)0.0);
1467: }
1468: }
1469: PetscViewerASCIIPrintf(viewer3," </DataArray>\n");
1470: PetscViewerASCIIPrintf(viewer2," </DataArray>\n");
1471: PetscViewerASCIIPrintf(viewer3," </Points>\n");
1472: PetscViewerASCIIPrintf(viewer2," </Points>\n");
1474: { /* Velocity and rank (3D) */
1475: PetscViewerASCIIPrintf(viewer3," <PointData>\n");
1476: PetscViewerASCIIPrintf(viewer3," <DataArray type=\"Float32\" Name=\"velocity\" NumberOfComponents=\"3\" format=\"ascii\">\n");
1477: for (i=0; i<nn/dof; i++) {
1478: PetscViewerASCIIPrintf(viewer3,"%f %f %f\n",PetscRealPart(y3[i].u)*units->year/units->meter,PetscRealPart(y3[i].v)*units->year/units->meter,0.0);
1479: }
1480: PetscViewerASCIIPrintf(viewer3," </DataArray>\n");
1482: PetscViewerASCIIPrintf(viewer3," <DataArray type=\"Int32\" Name=\"rank\" NumberOfComponents=\"1\" format=\"ascii\">\n");
1483: for (i=0; i<nn; i+=dof) {
1484: PetscViewerASCIIPrintf(viewer3,"%D\n",r);
1485: }
1486: PetscViewerASCIIPrintf(viewer3," </DataArray>\n");
1487: PetscViewerASCIIPrintf(viewer3," </PointData>\n");
1488: }
1490: { /* 2D */
1491: PetscViewerASCIIPrintf(viewer2," <PointData>\n");
1492: for (f=0; f<PRMNODE_SIZE; f++) {
1493: const char *fieldname;
1494: DMDAGetFieldName(da2,f,&fieldname);
1495: PetscViewerASCIIPrintf(viewer2," <DataArray type=\"Float32\" Name=\"%s\" format=\"ascii\">\n",fieldname);
1496: for (i=0; i<nn2/PRMNODE_SIZE; i++) {
1497: PetscViewerASCIIPrintf(viewer2,"%g\n",y2[i][f]);
1498: }
1499: PetscViewerASCIIPrintf(viewer2," </DataArray>\n");
1500: }
1501: PetscViewerASCIIPrintf(viewer2," </PointData>\n");
1502: }
1504: PetscViewerASCIIPrintf(viewer3," </Piece>\n");
1505: PetscViewerASCIIPrintf(viewer2," </Piece>\n");
1506: }
1507: PetscFree2(array,array2);
1508: } else {
1509: MPI_Send(range,6,MPIU_INT,0,tag,comm);
1510: MPI_Send(x,nn,MPIU_SCALAR,0,tag,comm);
1511: MPI_Send(x2,nn2,MPIU_SCALAR,0,tag,comm);
1512: }
1513: VecRestoreArrayRead(X3,(const PetscScalar**)&x);
1514: VecRestoreArrayRead(X2,(const PetscScalar**)&x2);
1515: PetscViewerASCIIPrintf(viewer3," </StructuredGrid>\n");
1516: PetscViewerASCIIPrintf(viewer2," </StructuredGrid>\n");
1518: DMCompositeRestoreAccess(pack,X,&X3,&X2);
1519: PetscViewerASCIIPrintf(viewer3,"</VTKFile>\n");
1520: PetscViewerASCIIPrintf(viewer2,"</VTKFile>\n");
1521: PetscViewerDestroy(&viewer3);
1522: PetscViewerDestroy(&viewer2);
1523: return(0);
1524: }
1526: static PetscErrorCode THITSMonitor(TS ts,PetscInt step,PetscReal t,Vec X,void *ctx)
1527: {
1529: THI thi = (THI)ctx;
1530: DM pack;
1531: char filename3[PETSC_MAX_PATH_LEN],filename2[PETSC_MAX_PATH_LEN];
1534: if (step < 0) return(0); /* negative one is used to indicate an interpolated solution */
1535: PetscPrintf(PetscObjectComm((PetscObject)ts),"%3D: t=%g\n",step,(double)t);
1536: if (thi->monitor_interval && step % thi->monitor_interval) return(0);
1537: TSGetDM(ts,&pack);
1538: PetscSNPrintf(filename3,sizeof(filename3),"%s-3d-%03d.vts",thi->monitor_basename,step);
1539: PetscSNPrintf(filename2,sizeof(filename2),"%s-2d-%03d.vts",thi->monitor_basename,step);
1540: THIDAVecView_VTK_XML(thi,pack,X,filename3,filename2);
1541: return(0);
1542: }
1544: static PetscErrorCode THICreateDM3d(THI thi,DM *dm3d)
1545: {
1546: MPI_Comm comm;
1547: PetscInt M = 3,N = 3,P = 2;
1548: DM da;
1552: PetscObjectGetComm((PetscObject)thi,&comm);
1553: PetscOptionsBegin(comm,NULL,"Grid resolution options","");
1554: {
1555: PetscOptionsInt("-M","Number of elements in x-direction on coarse level","",M,&M,NULL);
1556: N = M;
1557: PetscOptionsInt("-N","Number of elements in y-direction on coarse level (if different from M)","",N,&N,NULL);
1558: PetscOptionsInt("-P","Number of elements in z-direction on coarse level","",P,&P,NULL);
1559: }
1560: PetscOptionsEnd();
1561: 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);
1562: DMSetFromOptions(da);
1563: DMSetUp(da);
1564: DMDASetFieldName(da,0,"x-velocity");
1565: DMDASetFieldName(da,1,"y-velocity");
1566: *dm3d = da;
1567: return(0);
1568: }
1570: int main(int argc,char *argv[])
1571: {
1572: MPI_Comm comm;
1573: DM pack,da3,da2;
1574: TS ts;
1575: THI thi;
1576: Vec X;
1577: Mat B;
1578: PetscInt i,steps;
1579: PetscReal ftime;
1582: PetscInitialize(&argc,&argv,0,help);if (ierr) return ierr;
1583: comm = PETSC_COMM_WORLD;
1585: THICreate(comm,&thi);
1586: THICreateDM3d(thi,&da3);
1587: {
1588: PetscInt Mx,My,mx,my,s;
1589: DMDAStencilType st;
1590: DMDAGetInfo(da3,0, 0,&My,&Mx, 0,&my,&mx, 0,&s,0,0,0,&st);
1591: DMDACreate2d(PetscObjectComm((PetscObject)thi),DM_BOUNDARY_PERIODIC,DM_BOUNDARY_PERIODIC,st,My,Mx,my,mx,sizeof(PrmNode)/sizeof(PetscScalar),s,0,0,&da2);
1592: DMSetUp(da2);
1593: }
1595: PetscObjectSetName((PetscObject)da3,"3D_Velocity");
1596: DMSetOptionsPrefix(da3,"f3d_");
1597: DMDASetFieldName(da3,0,"u");
1598: DMDASetFieldName(da3,1,"v");
1599: PetscObjectSetName((PetscObject)da2,"2D_Fields");
1600: DMSetOptionsPrefix(da2,"f2d_");
1601: DMDASetFieldName(da2,0,"b");
1602: DMDASetFieldName(da2,1,"h");
1603: DMDASetFieldName(da2,2,"beta2");
1604: DMCompositeCreate(comm,&pack);
1605: DMCompositeAddDM(pack,da3);
1606: DMCompositeAddDM(pack,da2);
1607: DMDestroy(&da3);
1608: DMDestroy(&da2);
1609: DMSetUp(pack);
1610: DMCreateMatrix(pack,&B);
1611: MatSetOption(B,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_FALSE);
1612: MatSetOptionsPrefix(B,"thi_");
1614: for (i=0; i<thi->nlevels; i++) {
1615: PetscReal Lx = thi->Lx / thi->units->meter,Ly = thi->Ly / thi->units->meter,Lz = thi->Lz / thi->units->meter;
1616: PetscInt Mx,My,Mz;
1617: DMCompositeGetEntries(pack,&da3,&da2);
1618: DMDAGetInfo(da3,0, &Mz,&My,&Mx, 0,0,0, 0,0,0,0,0,0);
1619: 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));
1620: }
1622: DMCreateGlobalVector(pack,&X);
1623: THIInitial(thi,pack,X);
1625: TSCreate(comm,&ts);
1626: TSSetDM(ts,pack);
1627: TSSetProblemType(ts,TS_NONLINEAR);
1628: TSMonitorSet(ts,THITSMonitor,thi,NULL);
1629: TSSetType(ts,TSTHETA);
1630: TSSetIFunction(ts,NULL,THIFunction,thi);
1631: TSSetIJacobian(ts,B,B,THIJacobian,thi);
1632: TSSetMaxTime(ts,10.0);
1633: TSSetExactFinalTime(ts,TS_EXACTFINALTIME_STEPOVER);
1634: TSSetSolution(ts,X);
1635: TSSetTimeStep(ts,1e-3);
1636: TSSetFromOptions(ts);
1638: TSSolve(ts,X);
1639: TSGetSolveTime(ts,&ftime);
1640: TSGetStepNumber(ts,&steps);
1641: PetscPrintf(PETSC_COMM_WORLD,"Steps %D final time %g\n",steps,(double)ftime);
1643: if (0) {THISolveStatistics(thi,ts,0,"Full");}
1645: {
1646: PetscBool flg;
1647: char filename[PETSC_MAX_PATH_LEN] = "";
1648: PetscOptionsGetString(NULL,NULL,"-o",filename,sizeof(filename),&flg);
1649: if (flg) {
1650: THIDAVecView_VTK_XML(thi,pack,X,filename,NULL);
1651: }
1652: }
1654: VecDestroy(&X);
1655: MatDestroy(&B);
1656: DMDestroy(&pack);
1657: TSDestroy(&ts);
1658: THIDestroy(&thi);
1659: PetscFinalize();
1660: return ierr;
1661: }