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: {
276: PetscInt q,i,f;
277: const PetscScalar (*restrict pg)[PRMNODE_SIZE] = (const PetscScalar(*)[PRMNODE_SIZE])pn; /* Get generic array pointers to the node */
278: PetscScalar (*restrict dpg)[2][PRMNODE_SIZE] = (PetscScalar(*)[2][PRMNODE_SIZE])dp;
281: PetscArrayzero(dpg,4);
282: for (q=0; q<4; q++) {
283: for (i=0; i<4; i++) {
284: for (f=0; f<PRMNODE_SIZE; f++) {
285: dpg[q][0][f] += dphi[q][i][0]/hx * pg[i][f];
286: dpg[q][1][f] += dphi[q][i][1]/hy * pg[i][f];
287: }
288: }
289: }
290: return 0;
291: }
293: static inline PetscReal StaggeredMidpoint2D(PetscScalar a,PetscScalar b,PetscScalar c,PetscScalar d)
294: {return 0.5*PetscRealPart(0.75*a + 0.75*b + 0.25*c + 0.25*d);}
295: static inline PetscReal UpwindFlux1D(PetscReal u,PetscReal hL,PetscReal hR)
296: {return (u > 0) ? hL*u : hR*u;}
298: #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), \
299: 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))
300: #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), \
301: 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))
302: #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), \
303: 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))
304: #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), \
305: 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))
307: static void PrmNodeGetFaceMeasure(const PrmNode **p,PetscInt i,PetscInt j,PetscScalar h[])
308: {
309: /* West */
310: h[0] = StaggeredMidpoint2D(p[i][j].h,p[i-1][j].h,p[i-1][j-1].h,p[i][j-1].h);
311: h[1] = StaggeredMidpoint2D(p[i][j].h,p[i-1][j].h,p[i-1][j+1].h,p[i][j+1].h);
312: /* East */
313: h[2] = StaggeredMidpoint2D(p[i][j].h,p[i+1][j].h,p[i+1][j+1].h,p[i][j+1].h);
314: h[3] = StaggeredMidpoint2D(p[i][j].h,p[i+1][j].h,p[i+1][j-1].h,p[i][j-1].h);
315: /* South */
316: h[4] = StaggeredMidpoint2D(p[i][j].h,p[i][j-1].h,p[i+1][j-1].h,p[i+1][j].h);
317: h[5] = StaggeredMidpoint2D(p[i][j].h,p[i][j-1].h,p[i-1][j-1].h,p[i-1][j].h);
318: /* North */
319: h[6] = StaggeredMidpoint2D(p[i][j].h,p[i][j+1].h,p[i-1][j+1].h,p[i-1][j].h);
320: h[7] = StaggeredMidpoint2D(p[i][j].h,p[i][j+1].h,p[i+1][j+1].h,p[i+1][j].h);
321: }
323: /* Tests A and C are from the ISMIP-HOM paper (Pattyn et al. 2008) */
324: static void THIInitialize_HOM_A(THI thi,PetscReal x,PetscReal y,PrmNode *p)
325: {
326: Units units = thi->units;
327: PetscReal s = -x*PetscSinReal(thi->alpha);
328: p->b = s - 1000*units->meter + 500*units->meter * PetscSinReal(x*2*PETSC_PI/thi->Lx) * PetscSinReal(y*2*PETSC_PI/thi->Ly);
329: p->h = s - p->b;
330: p->beta2 = -1e-10; /* This value is not used, but it should not be huge because that would change the finite difference step size */
331: }
333: static void THIInitialize_HOM_C(THI thi,PetscReal x,PetscReal y,PrmNode *p)
334: {
335: Units units = thi->units;
336: PetscReal s = -x*PetscSinReal(thi->alpha);
337: p->b = s - 1000*units->meter;
338: p->h = s - p->b;
339: /* tau_b = beta2 v is a stress (Pa).
340: * 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. */
341: 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;
342: }
344: /* These are just toys */
346: /* From Fred Herman */
347: static void THIInitialize_HOM_F(THI thi,PetscReal x,PetscReal y,PrmNode *p)
348: {
349: Units units = thi->units;
350: PetscReal s = -x*PetscSinReal(thi->alpha);
351: p->b = s - 1000*units->meter + 100*units->meter * PetscSinReal(x*2*PETSC_PI/thi->Lx);/* * sin(y*2*PETSC_PI/thi->Ly); */
352: p->h = s - p->b;
353: p->h = (1-(atan((x-thi->Lx/2)/1.)+PETSC_PI/2.)/PETSC_PI)*500*units->meter+1*units->meter;
354: s = PetscRealPart(p->b + p->h);
355: p->beta2 = -1e-10;
356: /* p->beta2 = 1000 * units->Pascal * units->year / units->meter; */
357: }
359: /* Same bed as test A, free slip everywhere except for a discontinuous jump to a circular sticky region in the middle. */
360: static void THIInitialize_HOM_X(THI thi,PetscReal xx,PetscReal yy,PrmNode *p)
361: {
362: Units units = thi->units;
363: PetscReal x = xx*2*PETSC_PI/thi->Lx - PETSC_PI,y = yy*2*PETSC_PI/thi->Ly - PETSC_PI; /* [-pi,pi] */
364: PetscReal r = PetscSqrtReal(x*x + y*y),s = -x*PetscSinReal(thi->alpha);
365: p->b = s - 1000*units->meter + 500*units->meter * PetscSinReal(x + PETSC_PI) * PetscSinReal(y + PETSC_PI);
366: p->h = s - p->b;
367: p->beta2 = 1000 * (r < 1 ? 2 : 0) * units->Pascal * units->year / units->meter / thi->rhog;
368: }
370: /* Like Z, but with 200 meter cliffs */
371: static void THIInitialize_HOM_Y(THI thi,PetscReal xx,PetscReal yy,PrmNode *p)
372: {
373: Units units = thi->units;
374: PetscReal x = xx*2*PETSC_PI/thi->Lx - PETSC_PI,y = yy*2*PETSC_PI/thi->Ly - PETSC_PI; /* [-pi,pi] */
375: PetscReal r = PetscSqrtReal(x*x + y*y),s = -x*PetscSinReal(thi->alpha);
376: p->b = s - 1000*units->meter + 500*units->meter * PetscSinReal(x + PETSC_PI) * PetscSinReal(y + PETSC_PI);
377: if (PetscRealPart(p->b) > -700*units->meter) p->b += 200*units->meter;
378: p->h = s - p->b;
379: 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;
380: }
382: /* Same bed as A, smoothly varying slipperiness, similar to MATLAB's "sombrero" (uncorrelated with bathymetry) */
383: static void THIInitialize_HOM_Z(THI thi,PetscReal xx,PetscReal yy,PrmNode *p)
384: {
385: Units units = thi->units;
386: PetscReal x = xx*2*PETSC_PI/thi->Lx - PETSC_PI,y = yy*2*PETSC_PI/thi->Ly - PETSC_PI; /* [-pi,pi] */
387: PetscReal r = PetscSqrtReal(x*x + y*y),s = -x*PetscSinReal(thi->alpha);
388: p->b = s - 1000*units->meter + 500*units->meter * PetscSinReal(x + PETSC_PI) * PetscSinReal(y + PETSC_PI);
389: p->h = s - p->b;
390: 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;
391: }
393: static void THIFriction(THI thi,PetscReal rbeta2,PetscReal gam,PetscReal *beta2,PetscReal *dbeta2)
394: {
395: if (thi->friction.irefgam == 0) {
396: Units units = thi->units;
397: thi->friction.irefgam = 1./(0.5*PetscSqr(100 * units->meter / units->year));
398: thi->friction.eps2 = 0.5*PetscSqr(1.e-4 / thi->friction.irefgam);
399: }
400: if (thi->friction.exponent == 0) {
401: *beta2 = rbeta2;
402: *dbeta2 = 0;
403: } else {
404: *beta2 = rbeta2 * PetscPowReal(thi->friction.eps2 + gam*thi->friction.irefgam,thi->friction.exponent);
405: *dbeta2 = thi->friction.exponent * *beta2 / (thi->friction.eps2 + gam*thi->friction.irefgam) * thi->friction.irefgam;
406: }
407: }
409: static void THIViscosity(THI thi,PetscReal gam,PetscReal *eta,PetscReal *deta)
410: {
411: PetscReal Bd2,eps,exponent;
412: if (thi->viscosity.Bd2 == 0) {
413: Units units = thi->units;
414: const PetscReal
415: n = thi->viscosity.glen_n, /* Glen exponent */
416: p = 1. + 1./n, /* for Stokes */
417: A = 1.e-16 * PetscPowReal(units->Pascal,-n) / units->year, /* softness parameter (Pa^{-n}/s) */
418: B = PetscPowReal(A,-1./n); /* hardness parameter */
419: thi->viscosity.Bd2 = B/2;
420: thi->viscosity.exponent = (p-2)/2;
421: thi->viscosity.eps = 0.5*PetscSqr(1e-5 / units->year);
422: }
423: Bd2 = thi->viscosity.Bd2;
424: exponent = thi->viscosity.exponent;
425: eps = thi->viscosity.eps;
426: *eta = Bd2 * PetscPowReal(eps + gam,exponent);
427: *deta = exponent * (*eta) / (eps + gam);
428: }
430: static void THIErosion(THI thi,const Node *vel,PetscScalar *erate,Node *derate)
431: {
432: const PetscScalar magref2 = 1.e-10 + (PetscSqr(vel->u) + PetscSqr(vel->v)) / PetscSqr(thi->erosion.refvel),
433: rate = -thi->erosion.rate*PetscPowScalar(magref2, 0.5*thi->erosion.exponent);
434: if (erate) *erate = rate;
435: if (derate) {
436: if (thi->erosion.exponent == 1) {
437: derate->u = 0;
438: derate->v = 0;
439: } else {
440: derate->u = 0.5*thi->erosion.exponent * rate / magref2 * 2. * vel->u / PetscSqr(thi->erosion.refvel);
441: derate->v = 0.5*thi->erosion.exponent * rate / magref2 * 2. * vel->v / PetscSqr(thi->erosion.refvel);
442: }
443: }
444: }
446: static void RangeUpdate(PetscReal *min,PetscReal *max,PetscReal x)
447: {
448: if (x < *min) *min = x;
449: if (x > *max) *max = x;
450: }
452: static void PRangeClear(PRange *p)
453: {
454: p->cmin = p->min = 1e100;
455: p->cmax = p->max = -1e100;
456: }
458: static PetscErrorCode PRangeMinMax(PRange *p,PetscReal min,PetscReal max)
459: {
461: p->cmin = min;
462: p->cmax = max;
463: if (min < p->min) p->min = min;
464: if (max > p->max) p->max = max;
465: return 0;
466: }
468: static PetscErrorCode THIDestroy(THI *thi)
469: {
471: if (--((PetscObject)(*thi))->refct > 0) return 0;
472: PetscFree((*thi)->units);
473: PetscFree((*thi)->mattype);
474: PetscFree((*thi)->monitor_basename);
475: PetscHeaderDestroy(thi);
476: return 0;
477: }
479: static PetscErrorCode THICreate(MPI_Comm comm,THI *inthi)
480: {
481: static PetscBool registered = PETSC_FALSE;
482: THI thi;
483: Units units;
484: char monitor_basename[PETSC_MAX_PATH_LEN] = "thi-";
485: PetscErrorCode ierr;
488: *inthi = 0;
489: if (!registered) {
490: PetscClassIdRegister("Toy Hydrostatic Ice",&THI_CLASSID);
491: registered = PETSC_TRUE;
492: }
493: PetscHeaderCreate(thi,THI_CLASSID,"THI","Toy Hydrostatic Ice","THI",comm,THIDestroy,0);
495: PetscNew(&thi->units);
497: units = thi->units;
498: units->meter = 1e-2;
499: units->second = 1e-7;
500: units->kilogram = 1e-12;
502: PetscOptionsBegin(comm,NULL,"Scaled units options","");
503: {
504: PetscOptionsReal("-units_meter","1 meter in scaled length units","",units->meter,&units->meter,NULL);
505: PetscOptionsReal("-units_second","1 second in scaled time units","",units->second,&units->second,NULL);
506: PetscOptionsReal("-units_kilogram","1 kilogram in scaled mass units","",units->kilogram,&units->kilogram,NULL);
507: }
508: PetscOptionsEnd();
509: units->Pascal = units->kilogram / (units->meter * PetscSqr(units->second));
510: units->year = 31556926. * units->second, /* seconds per year */
512: thi->Lx = 10.e3;
513: thi->Ly = 10.e3;
514: thi->Lz = 1000;
515: thi->nlevels = 1;
516: thi->dirichlet_scale = 1;
517: thi->verbose = PETSC_FALSE;
519: thi->viscosity.glen_n = 3.;
520: thi->erosion.rate = 1e-3; /* m/a */
521: thi->erosion.exponent = 1.;
522: thi->erosion.refvel = 1.; /* m/a */
524: PetscOptionsBegin(comm,NULL,"Toy Hydrostatic Ice options","");
525: {
526: QuadratureType quad = QUAD_GAUSS;
527: char homexp[] = "A";
528: char mtype[256] = MATSBAIJ;
529: PetscReal L,m = 1.0;
530: PetscBool flg;
531: L = thi->Lx;
532: PetscOptionsReal("-thi_L","Domain size (m)","",L,&L,&flg);
533: if (flg) thi->Lx = thi->Ly = L;
534: PetscOptionsReal("-thi_Lx","X Domain size (m)","",thi->Lx,&thi->Lx,NULL);
535: PetscOptionsReal("-thi_Ly","Y Domain size (m)","",thi->Ly,&thi->Ly,NULL);
536: PetscOptionsReal("-thi_Lz","Z Domain size (m)","",thi->Lz,&thi->Lz,NULL);
537: PetscOptionsString("-thi_hom","ISMIP-HOM experiment (A or C)","",homexp,homexp,sizeof(homexp),NULL);
538: switch (homexp[0] = toupper(homexp[0])) {
539: case 'A':
540: thi->initialize = THIInitialize_HOM_A;
541: thi->no_slip = PETSC_TRUE;
542: thi->alpha = 0.5;
543: break;
544: case 'C':
545: thi->initialize = THIInitialize_HOM_C;
546: thi->no_slip = PETSC_FALSE;
547: thi->alpha = 0.1;
548: break;
549: case 'F':
550: thi->initialize = THIInitialize_HOM_F;
551: thi->no_slip = PETSC_FALSE;
552: thi->alpha = 0.5;
553: break;
554: case 'X':
555: thi->initialize = THIInitialize_HOM_X;
556: thi->no_slip = PETSC_FALSE;
557: thi->alpha = 0.3;
558: break;
559: case 'Y':
560: thi->initialize = THIInitialize_HOM_Y;
561: thi->no_slip = PETSC_FALSE;
562: thi->alpha = 0.5;
563: break;
564: case 'Z':
565: thi->initialize = THIInitialize_HOM_Z;
566: thi->no_slip = PETSC_FALSE;
567: thi->alpha = 0.5;
568: break;
569: default:
570: SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"HOM experiment '%c' not implemented",homexp[0]);
571: }
572: PetscOptionsEnum("-thi_quadrature","Quadrature to use for 3D elements","",QuadratureTypes,(PetscEnum)quad,(PetscEnum*)&quad,NULL);
573: switch (quad) {
574: case QUAD_GAUSS:
575: HexQInterp = HexQInterp_Gauss;
576: HexQDeriv = HexQDeriv_Gauss;
577: break;
578: case QUAD_LOBATTO:
579: HexQInterp = HexQInterp_Lobatto;
580: HexQDeriv = HexQDeriv_Lobatto;
581: break;
582: }
583: PetscOptionsReal("-thi_alpha","Bed angle (degrees)","",thi->alpha,&thi->alpha,NULL);
584: 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);
585: PetscOptionsReal("-thi_friction_m","Friction exponent, 0=Coulomb, 1=Navier","",m,&m,NULL);
586: thi->friction.exponent = (m-1)/2;
587: PetscOptionsReal("-thi_erosion_rate","Rate of erosion relative to sliding velocity at reference velocity (m/a)",NULL,thi->erosion.rate,&thi->erosion.rate,NULL);
588: PetscOptionsReal("-thi_erosion_exponent","Power of sliding velocity appearing in erosion relation",NULL,thi->erosion.exponent,&thi->erosion.exponent,NULL);
589: PetscOptionsReal("-thi_erosion_refvel","Reference sliding velocity for erosion (m/a)",NULL,thi->erosion.refvel,&thi->erosion.refvel,NULL);
590: thi->erosion.rate *= units->meter / units->year;
591: thi->erosion.refvel *= units->meter / units->year;
592: PetscOptionsReal("-thi_dirichlet_scale","Scale Dirichlet boundary conditions by this factor","",thi->dirichlet_scale,&thi->dirichlet_scale,NULL);
593: 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);
594: PetscOptionsReal("-thi_inertia","Coefficient of accelaration term in velocity system, physical is almost zero",NULL,thi->inertia,&thi->inertia,NULL);
595: PetscOptionsInt("-thi_nlevels","Number of levels of refinement","",thi->nlevels,&thi->nlevels,NULL);
596: PetscOptionsFList("-thi_mat_type","Matrix type","MatSetType",MatList,mtype,(char*)mtype,sizeof(mtype),NULL);
597: PetscStrallocpy(mtype,&thi->mattype);
598: PetscOptionsBool("-thi_verbose","Enable verbose output (like matrix sizes and statistics)","",thi->verbose,&thi->verbose,NULL);
599: PetscOptionsString("-thi_monitor","Basename to write state files to",NULL,monitor_basename,monitor_basename,sizeof(monitor_basename),&flg);
600: if (flg) {
601: PetscStrallocpy(monitor_basename,&thi->monitor_basename);
602: thi->monitor_interval = 1;
603: PetscOptionsInt("-thi_monitor_interval","Frequency at which to write state files",NULL,thi->monitor_interval,&thi->monitor_interval,NULL);
604: }
605: }
606: PetscOptionsEnd();
608: /* dimensionalize */
609: thi->Lx *= units->meter;
610: thi->Ly *= units->meter;
611: thi->Lz *= units->meter;
612: thi->alpha *= PETSC_PI / 180;
614: PRangeClear(&thi->eta);
615: PRangeClear(&thi->beta2);
617: {
618: PetscReal u = 1000*units->meter/(3e7*units->second),
619: gradu = u / (100*units->meter),eta,deta,
620: rho = 910 * units->kilogram/PetscPowRealInt(units->meter,3),
621: grav = 9.81 * units->meter/PetscSqr(units->second),
622: driving = rho * grav * PetscSinReal(thi->alpha) * 1000*units->meter;
623: THIViscosity(thi,0.5*gradu*gradu,&eta,&deta);
624: thi->rhog = rho * grav;
625: if (thi->verbose) {
626: 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);
627: 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);
628: 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);
629: THIViscosity(thi,0.5*PetscSqr(1e-3*gradu),&eta,&deta);
630: 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);
631: }
632: }
634: *inthi = thi;
635: return 0;
636: }
638: /* Our problem is periodic, but the domain has a mean slope of alpha so the bed does not line up between the upstream
639: * and downstream ends of the domain. This function fixes the ghost values so that the domain appears truly periodic in
640: * the horizontal. */
641: static PetscErrorCode THIFixGhosts(THI thi,DM da3,DM da2,Vec X3,Vec X2)
642: {
643: DMDALocalInfo info;
644: PrmNode **x2;
645: PetscInt i,j;
648: DMDAGetLocalInfo(da3,&info);
649: /* VecView(X2,PETSC_VIEWER_STDOUT_WORLD); */
650: DMDAVecGetArray(da2,X2,&x2);
651: for (i=info.gzs; i<info.gzs+info.gzm; i++) {
652: if (i > -1 && i < info.mz) continue;
653: for (j=info.gys; j<info.gys+info.gym; j++) {
654: x2[i][j].b += PetscSinReal(thi->alpha) * thi->Lx * (i<0 ? 1.0 : -1.0);
655: }
656: }
657: DMDAVecRestoreArray(da2,X2,&x2);
658: /* VecView(X2,PETSC_VIEWER_STDOUT_WORLD); */
659: return 0;
660: }
662: static PetscErrorCode THIInitializePrm(THI thi,DM da2prm,PrmNode **p)
663: {
664: PetscInt i,j,xs,xm,ys,ym,mx,my;
667: DMDAGetGhostCorners(da2prm,&ys,&xs,0,&ym,&xm,0);
668: DMDAGetInfo(da2prm,0, &my,&mx,0, 0,0,0, 0,0,0,0,0,0);
669: for (i=xs; i<xs+xm; i++) {
670: for (j=ys; j<ys+ym; j++) {
671: PetscReal xx = thi->Lx*i/mx,yy = thi->Ly*j/my;
672: thi->initialize(thi,xx,yy,&p[i][j]);
673: }
674: }
675: return 0;
676: }
678: static PetscErrorCode THIInitial(THI thi,DM pack,Vec X)
679: {
680: DM da3,da2;
681: PetscInt i,j,k,xs,xm,ys,ym,zs,zm,mx,my;
682: PetscReal hx,hy;
683: PrmNode **prm;
684: Node ***x;
685: Vec X3g,X2g,X2;
688: DMCompositeGetEntries(pack,&da3,&da2);
689: DMCompositeGetAccess(pack,X,&X3g,&X2g);
690: DMGetLocalVector(da2,&X2);
692: DMDAGetInfo(da3,0, 0,&my,&mx, 0,0,0, 0,0,0,0,0,0);
693: DMDAGetCorners(da3,&zs,&ys,&xs,&zm,&ym,&xm);
694: DMDAVecGetArray(da3,X3g,&x);
695: DMDAVecGetArray(da2,X2,&prm);
697: THIInitializePrm(thi,da2,prm);
699: hx = thi->Lx / mx;
700: hy = thi->Ly / my;
701: for (i=xs; i<xs+xm; i++) {
702: for (j=ys; j<ys+ym; j++) {
703: for (k=zs; k<zs+zm; k++) {
704: const PetscScalar zm1 = zm-1,
705: 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),
706: 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);
707: x[i][j][k].u = 0. * drivingx * prm[i][j].h*(PetscScalar)k/zm1;
708: x[i][j][k].v = 0. * drivingy * prm[i][j].h*(PetscScalar)k/zm1;
709: }
710: }
711: }
713: DMDAVecRestoreArray(da3,X3g,&x);
714: DMDAVecRestoreArray(da2,X2,&prm);
716: DMLocalToGlobalBegin(da2,X2,INSERT_VALUES,X2g);
717: DMLocalToGlobalEnd (da2,X2,INSERT_VALUES,X2g);
718: DMRestoreLocalVector(da2,&X2);
720: DMCompositeRestoreAccess(pack,X,&X3g,&X2g);
721: return 0;
722: }
724: 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)
725: {
726: PetscInt l,ll;
727: PetscScalar gam;
729: du[0] = du[1] = du[2] = 0;
730: dv[0] = dv[1] = dv[2] = 0;
731: *u = 0;
732: *v = 0;
733: for (l=0; l<8; l++) {
734: *u += phi[l] * n[l].u;
735: *v += phi[l] * n[l].v;
736: for (ll=0; ll<3; ll++) {
737: du[ll] += dphi[l][ll] * n[l].u;
738: dv[ll] += dphi[l][ll] * n[l].v;
739: }
740: }
741: 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]);
742: THIViscosity(thi,PetscRealPart(gam),eta,deta);
743: }
745: static PetscErrorCode THIFunctionLocal_3D(DMDALocalInfo *info,const Node ***x,const PrmNode **prm,const Node ***xdot,Node ***f,THI thi)
746: {
747: PetscInt xs,ys,xm,ym,zm,i,j,k,q,l;
748: PetscReal hx,hy,etamin,etamax,beta2min,beta2max;
751: xs = info->zs;
752: ys = info->ys;
753: xm = info->zm;
754: ym = info->ym;
755: zm = info->xm;
756: hx = thi->Lx / info->mz;
757: hy = thi->Ly / info->my;
759: etamin = 1e100;
760: etamax = 0;
761: beta2min = 1e100;
762: beta2max = 0;
764: for (i=xs; i<xs+xm; i++) {
765: for (j=ys; j<ys+ym; j++) {
766: PrmNode pn[4],dpn[4][2];
767: QuadExtract(prm,i,j,pn);
768: QuadComputeGrad4(QuadQDeriv,hx,hy,pn,dpn);
769: for (k=0; k<zm-1; k++) {
770: PetscInt ls = 0;
771: Node n[8],ndot[8],*fn[8];
772: PetscReal zn[8],etabase = 0;
774: PrmHexGetZ(pn,k,zm,zn);
775: HexExtract(x,i,j,k,n);
776: HexExtract(xdot,i,j,k,ndot);
777: HexExtractRef(f,i,j,k,fn);
778: if (thi->no_slip && k == 0) {
779: for (l=0; l<4; l++) n[l].u = n[l].v = 0;
780: /* The first 4 basis functions lie on the bottom layer, so their contribution is exactly 0, hence we can skip them */
781: ls = 4;
782: }
783: for (q=0; q<8; q++) {
784: PetscReal dz[3],phi[8],dphi[8][3],jw,eta,deta;
785: PetscScalar du[3],dv[3],u,v,udot=0,vdot=0;
786: for (l=ls; l<8; l++) {
787: udot += HexQInterp[q][l]*ndot[l].u;
788: vdot += HexQInterp[q][l]*ndot[l].v;
789: }
790: HexGrad(HexQDeriv[q],zn,dz);
791: HexComputeGeometry(q,hx,hy,dz,phi,dphi,&jw);
792: PointwiseNonlinearity(thi,n,phi,dphi,&u,&v,du,dv,&eta,&deta);
793: jw /= thi->rhog; /* scales residuals to be O(1) */
794: if (q == 0) etabase = eta;
795: RangeUpdate(&etamin,&etamax,eta);
796: for (l=ls; l<8; l++) { /* test functions */
797: const PetscScalar ds[2] = {dpn[q%4][0].h+dpn[q%4][0].b, dpn[q%4][1].h+dpn[q%4][1].b};
798: const PetscReal pp = phi[l],*dp = dphi[l];
799: 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];
800: 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];
801: fn[l]->u += pp*jw*udot*thi->inertia*pp;
802: fn[l]->v += pp*jw*vdot*thi->inertia*pp;
803: }
804: }
805: if (k == 0) { /* we are on a bottom face */
806: if (thi->no_slip) {
807: /* Note: Non-Galerkin coarse grid operators are very sensitive to the scaling of Dirichlet boundary
808: * conditions. After shenanigans above, etabase contains the effective viscosity at the closest quadrature
809: * point to the bed. We want the diagonal entry in the Dirichlet condition to have similar magnitude to the
810: * diagonal entry corresponding to the adjacent node. The fundamental scaling of the viscous part is in
811: * diagu, diagv below. This scaling is easy to recognize by considering the finite difference operator after
812: * scaling by element size. The no-slip Dirichlet condition is scaled by this factor, and also in the
813: * assembled matrix (see the similar block in THIJacobianLocal).
814: *
815: * Note that the residual at this Dirichlet node is linear in the state at this node, but also depends
816: * (nonlinearly in general) on the neighboring interior nodes through the local viscosity. This will make
817: * a matrix-free Jacobian have extra entries in the corresponding row. We assemble only the diagonal part,
818: * so the solution will exactly satisfy the boundary condition after the first linear iteration.
819: */
820: const PetscReal hz = PetscRealPart(pn[0].h)/(zm-1.);
821: 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);
822: fn[0]->u = thi->dirichlet_scale*diagu*x[i][j][k].u;
823: fn[0]->v = thi->dirichlet_scale*diagv*x[i][j][k].v;
824: } else { /* Integrate over bottom face to apply boundary condition */
825: 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) */
826: const PetscReal jw = 0.25*hx*hy,*phi = QuadQInterp[q];
827: PetscScalar u =0,v=0,rbeta2=0;
828: PetscReal beta2,dbeta2;
829: for (l=0; l<4; l++) {
830: u += phi[l]*n[l].u;
831: v += phi[l]*n[l].v;
832: rbeta2 += phi[l]*pn[l].beta2;
833: }
834: THIFriction(thi,PetscRealPart(rbeta2),PetscRealPart(u*u+v*v)/2,&beta2,&dbeta2);
835: RangeUpdate(&beta2min,&beta2max,beta2);
836: for (l=0; l<4; l++) {
837: const PetscReal pp = phi[l];
838: fn[ls+l]->u += pp*jw*beta2*u;
839: fn[ls+l]->v += pp*jw*beta2*v;
840: }
841: }
842: }
843: }
844: }
845: }
846: }
848: PRangeMinMax(&thi->eta,etamin,etamax);
849: PRangeMinMax(&thi->beta2,beta2min,beta2max);
850: return 0;
851: }
853: static PetscErrorCode THIFunctionLocal_2D(DMDALocalInfo *info,const Node ***x,const PrmNode **prm,const PrmNode **prmdot,PrmNode **f,THI thi)
854: {
855: PetscInt xs,ys,xm,ym,zm,i,j,k;
858: xs = info->zs;
859: ys = info->ys;
860: xm = info->zm;
861: ym = info->ym;
862: zm = info->xm;
864: for (i=xs; i<xs+xm; i++) {
865: for (j=ys; j<ys+ym; j++) {
866: PetscScalar div = 0,erate,h[8];
867: PrmNodeGetFaceMeasure(prm,i,j,h);
868: for (k=0; k<zm; k++) {
869: PetscScalar weight = (k==0 || k == zm-1) ? 0.5/(zm-1) : 1.0/(zm-1);
870: if (0) { /* centered flux */
871: 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)
872: - 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)
873: + 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)
874: + 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)
875: - 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)
876: - 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)
877: + 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)
878: + 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));
879: } else { /* Upwind flux */
880: div += weight*(-UpwindFluxXW(x,prm,h,i,j,k, 1)
881: -UpwindFluxXW(x,prm,h,i,j,k,-1)
882: +UpwindFluxXE(x,prm,h,i,j,k, 1)
883: +UpwindFluxXE(x,prm,h,i,j,k,-1)
884: -UpwindFluxYS(x,prm,h,i,j,k, 1)
885: -UpwindFluxYS(x,prm,h,i,j,k,-1)
886: +UpwindFluxYN(x,prm,h,i,j,k, 1)
887: +UpwindFluxYN(x,prm,h,i,j,k,-1));
888: }
889: }
890: /* printf("div[%d][%d] %g\n",i,j,div); */
891: THIErosion(thi,&x[i][j][0],&erate,NULL);
892: f[i][j].b = prmdot[i][j].b - erate;
893: f[i][j].h = prmdot[i][j].h + div;
894: f[i][j].beta2 = prmdot[i][j].beta2;
895: }
896: }
897: return 0;
898: }
900: static PetscErrorCode THIFunction(TS ts,PetscReal t,Vec X,Vec Xdot,Vec F,void *ctx)
901: {
902: THI thi = (THI)ctx;
903: DM pack,da3,da2;
904: Vec X3,X2,Xdot3,Xdot2,F3,F2,F3g,F2g;
905: const Node ***x3,***xdot3;
906: const PrmNode **x2,**xdot2;
907: Node ***f3;
908: PrmNode **f2;
909: DMDALocalInfo info3;
912: TSGetDM(ts,&pack);
913: DMCompositeGetEntries(pack,&da3,&da2);
914: DMDAGetLocalInfo(da3,&info3);
915: DMCompositeGetLocalVectors(pack,&X3,&X2);
916: DMCompositeGetLocalVectors(pack,&Xdot3,&Xdot2);
917: DMCompositeScatter(pack,X,X3,X2);
918: THIFixGhosts(thi,da3,da2,X3,X2);
919: DMCompositeScatter(pack,Xdot,Xdot3,Xdot2);
921: DMGetLocalVector(da3,&F3);
922: DMGetLocalVector(da2,&F2);
923: VecZeroEntries(F3);
925: DMDAVecGetArray(da3,X3,&x3);
926: DMDAVecGetArray(da2,X2,&x2);
927: DMDAVecGetArray(da3,Xdot3,&xdot3);
928: DMDAVecGetArray(da2,Xdot2,&xdot2);
929: DMDAVecGetArray(da3,F3,&f3);
930: DMDAVecGetArray(da2,F2,&f2);
932: THIFunctionLocal_3D(&info3,x3,x2,xdot3,f3,thi);
933: THIFunctionLocal_2D(&info3,x3,x2,xdot2,f2,thi);
935: DMDAVecRestoreArray(da3,X3,&x3);
936: DMDAVecRestoreArray(da2,X2,&x2);
937: DMDAVecRestoreArray(da3,Xdot3,&xdot3);
938: DMDAVecRestoreArray(da2,Xdot2,&xdot2);
939: DMDAVecRestoreArray(da3,F3,&f3);
940: DMDAVecRestoreArray(da2,F2,&f2);
942: DMCompositeRestoreLocalVectors(pack,&X3,&X2);
943: DMCompositeRestoreLocalVectors(pack,&Xdot3,&Xdot2);
945: VecZeroEntries(F);
946: DMCompositeGetAccess(pack,F,&F3g,&F2g);
947: DMLocalToGlobalBegin(da3,F3,ADD_VALUES,F3g);
948: DMLocalToGlobalEnd (da3,F3,ADD_VALUES,F3g);
949: DMLocalToGlobalBegin(da2,F2,INSERT_VALUES,F2g);
950: DMLocalToGlobalEnd (da2,F2,INSERT_VALUES,F2g);
952: if (thi->verbose) {
953: PetscViewer viewer;
954: PetscViewerASCIIGetStdout(PetscObjectComm((PetscObject)thi),&viewer);
955: PetscViewerASCIIPrintf(viewer,"3D_Velocity residual (bs=2):\n");
956: PetscViewerASCIIPushTab(viewer);
957: VecView(F3,viewer);
958: PetscViewerASCIIPopTab(viewer);
959: PetscViewerASCIIPrintf(viewer,"2D_Fields residual (bs=3):\n");
960: PetscViewerASCIIPushTab(viewer);
961: VecView(F2,viewer);
962: PetscViewerASCIIPopTab(viewer);
963: }
965: DMCompositeRestoreAccess(pack,F,&F3g,&F2g);
967: DMRestoreLocalVector(da3,&F3);
968: DMRestoreLocalVector(da2,&F2);
969: return 0;
970: }
972: static PetscErrorCode THIMatrixStatistics(THI thi,Mat B,PetscViewer viewer)
973: {
974: PetscReal nrm;
975: PetscInt m;
976: PetscMPIInt rank;
979: MatNorm(B,NORM_FROBENIUS,&nrm);
980: MatGetSize(B,&m,0);
981: MPI_Comm_rank(PetscObjectComm((PetscObject)B),&rank);
982: if (rank == 0) {
983: PetscScalar val0,val2;
984: MatGetValue(B,0,0,&val0);
985: MatGetValue(B,2,2,&val2);
986: 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);
987: }
988: return 0;
989: }
991: static PetscErrorCode THISurfaceStatistics(DM pack,Vec X,PetscReal *min,PetscReal *max,PetscReal *mean)
992: {
993: DM da3,da2;
994: Vec X3,X2;
995: Node ***x;
996: PetscInt i,j,xs,ys,zs,xm,ym,zm,mx,my,mz;
997: PetscReal umin = 1e100,umax=-1e100;
998: PetscScalar usum =0.0,gusum;
1001: DMCompositeGetEntries(pack,&da3,&da2);
1002: DMCompositeGetAccess(pack,X,&X3,&X2);
1003: *min = *max = *mean = 0;
1004: DMDAGetInfo(da3,0, &mz,&my,&mx, 0,0,0, 0,0,0,0,0,0);
1005: DMDAGetCorners(da3,&zs,&ys,&xs,&zm,&ym,&xm);
1007: DMDAVecGetArray(da3,X3,&x);
1008: for (i=xs; i<xs+xm; i++) {
1009: for (j=ys; j<ys+ym; j++) {
1010: PetscReal u = PetscRealPart(x[i][j][zm-1].u);
1011: RangeUpdate(&umin,&umax,u);
1012: usum += u;
1013: }
1014: }
1015: DMDAVecRestoreArray(da3,X3,&x);
1016: DMCompositeRestoreAccess(pack,X,&X3,&X2);
1018: MPI_Allreduce(&umin,min,1,MPIU_REAL,MPIU_MIN,PetscObjectComm((PetscObject)da3));
1019: MPI_Allreduce(&umax,max,1,MPIU_REAL,MPIU_MAX,PetscObjectComm((PetscObject)da3));
1020: MPI_Allreduce(&usum,&gusum,1,MPIU_SCALAR,MPIU_SUM,PetscObjectComm((PetscObject)da3));
1021: *mean = PetscRealPart(gusum) / (mx*my);
1022: return 0;
1023: }
1025: static PetscErrorCode THISolveStatistics(THI thi,TS ts,PetscInt coarsened,const char name[])
1026: {
1027: MPI_Comm comm;
1028: DM pack;
1029: Vec X,X3,X2;
1032: PetscObjectGetComm((PetscObject)thi,&comm);
1033: TSGetDM(ts,&pack);
1034: TSGetSolution(ts,&X);
1035: DMCompositeGetAccess(pack,X,&X3,&X2);
1036: PetscPrintf(comm,"Solution statistics after solve: %s\n",name);
1037: {
1038: PetscInt its,lits;
1039: SNESConvergedReason reason;
1040: SNES snes;
1041: TSGetSNES(ts,&snes);
1042: SNESGetIterationNumber(snes,&its);
1043: SNESGetConvergedReason(snes,&reason);
1044: SNESGetLinearSolveIterations(snes,&lits);
1045: PetscPrintf(comm,"%s: Number of SNES iterations = %d, total linear iterations = %d\n",SNESConvergedReasons[reason],its,lits);
1046: }
1047: {
1048: PetscReal nrm2,tmin[3]={1e100,1e100,1e100},tmax[3]={-1e100,-1e100,-1e100},min[3],max[3];
1049: PetscInt i,j,m;
1050: PetscScalar *x;
1051: VecNorm(X3,NORM_2,&nrm2);
1052: VecGetLocalSize(X3,&m);
1053: VecGetArray(X3,&x);
1054: for (i=0; i<m; i+=2) {
1055: PetscReal u = PetscRealPart(x[i]),v = PetscRealPart(x[i+1]),c = PetscSqrtReal(u*u+v*v);
1056: tmin[0] = PetscMin(u,tmin[0]);
1057: tmin[1] = PetscMin(v,tmin[1]);
1058: tmin[2] = PetscMin(c,tmin[2]);
1059: tmax[0] = PetscMax(u,tmax[0]);
1060: tmax[1] = PetscMax(v,tmax[1]);
1061: tmax[2] = PetscMax(c,tmax[2]);
1062: }
1063: VecRestoreArray(X,&x);
1064: MPI_Allreduce(tmin,min,3,MPIU_REAL,MPIU_MIN,PetscObjectComm((PetscObject)thi));
1065: MPI_Allreduce(tmax,max,3,MPIU_REAL,MPIU_MAX,PetscObjectComm((PetscObject)thi));
1066: /* Dimensionalize to meters/year */
1067: nrm2 *= thi->units->year / thi->units->meter;
1068: for (j=0; j<3; j++) {
1069: min[j] *= thi->units->year / thi->units->meter;
1070: max[j] *= thi->units->year / thi->units->meter;
1071: }
1072: 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]);
1073: {
1074: PetscReal umin,umax,umean;
1075: THISurfaceStatistics(pack,X,&umin,&umax,&umean);
1076: umin *= thi->units->year / thi->units->meter;
1077: umax *= thi->units->year / thi->units->meter;
1078: umean *= thi->units->year / thi->units->meter;
1079: PetscPrintf(comm,"Surface statistics: u in [%12.6e, %12.6e] mean %12.6e\n",umin,umax,umean);
1080: }
1081: /* These values stay nondimensional */
1082: PetscPrintf(comm,"Global eta range [%g, %g], converged range [%g, %g]\n",thi->eta.min,thi->eta.max,thi->eta.cmin,thi->eta.cmax);
1083: PetscPrintf(comm,"Global beta2 range [%g, %g], converged range [%g, %g]\n",thi->beta2.min,thi->beta2.max,thi->beta2.cmin,thi->beta2.cmax);
1084: }
1085: PetscPrintf(comm,"\n");
1086: DMCompositeRestoreAccess(pack,X,&X3,&X2);
1087: return 0;
1088: }
1090: static inline PetscInt DMDALocalIndex3D(DMDALocalInfo *info,PetscInt i,PetscInt j,PetscInt k)
1091: {return ((i-info->gzs)*info->gym + (j-info->gys))*info->gxm + (k-info->gxs);}
1092: static inline PetscInt DMDALocalIndex2D(DMDALocalInfo *info,PetscInt i,PetscInt j)
1093: {return (i-info->gzs)*info->gym + (j-info->gys);}
1095: static PetscErrorCode THIJacobianLocal_Momentum(DMDALocalInfo *info,const Node ***x,const PrmNode **prm,Mat B,Mat Bcpl,THI thi)
1096: {
1097: PetscInt xs,ys,xm,ym,zm,i,j,k,q,l,ll;
1098: PetscReal hx,hy;
1101: xs = info->zs;
1102: ys = info->ys;
1103: xm = info->zm;
1104: ym = info->ym;
1105: zm = info->xm;
1106: hx = thi->Lx / info->mz;
1107: hy = thi->Ly / info->my;
1109: for (i=xs; i<xs+xm; i++) {
1110: for (j=ys; j<ys+ym; j++) {
1111: PrmNode pn[4],dpn[4][2];
1112: QuadExtract(prm,i,j,pn);
1113: QuadComputeGrad4(QuadQDeriv,hx,hy,pn,dpn);
1114: for (k=0; k<zm-1; k++) {
1115: Node n[8];
1116: PetscReal zn[8],etabase = 0;
1117: PetscScalar Ke[8*NODE_SIZE][8*NODE_SIZE],Kcpl[8*NODE_SIZE][4*PRMNODE_SIZE];
1118: PetscInt ls = 0;
1120: PrmHexGetZ(pn,k,zm,zn);
1121: HexExtract(x,i,j,k,n);
1122: PetscMemzero(Ke,sizeof(Ke));
1123: PetscMemzero(Kcpl,sizeof(Kcpl));
1124: if (thi->no_slip && k == 0) {
1125: for (l=0; l<4; l++) n[l].u = n[l].v = 0;
1126: ls = 4;
1127: }
1128: for (q=0; q<8; q++) {
1129: PetscReal dz[3],phi[8],dphi[8][3],jw,eta,deta;
1130: PetscScalar du[3],dv[3],u,v;
1131: HexGrad(HexQDeriv[q],zn,dz);
1132: HexComputeGeometry(q,hx,hy,dz,phi,dphi,&jw);
1133: PointwiseNonlinearity(thi,n,phi,dphi,&u,&v,du,dv,&eta,&deta);
1134: jw /= thi->rhog; /* residuals are scaled by this factor */
1135: if (q == 0) etabase = eta;
1136: for (l=ls; l<8; l++) { /* test functions */
1137: const PetscReal pp=phi[l],*restrict dp = dphi[l];
1138: for (ll=ls; ll<8; ll++) { /* trial functions */
1139: const PetscReal *restrict dpl = dphi[ll];
1140: PetscScalar dgdu,dgdv;
1141: dgdu = 2.*du[0]*dpl[0] + dv[1]*dpl[0] + 0.5*(du[1]+dv[0])*dpl[1] + 0.5*du[2]*dpl[2];
1142: dgdv = 2.*dv[1]*dpl[1] + du[0]*dpl[1] + 0.5*(du[1]+dv[0])*dpl[0] + 0.5*dv[2]*dpl[2];
1143: /* Picard part */
1144: 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];
1145: Ke[l*2+0][ll*2+1] += dp[0]*jw*eta*2.*dpl[1] + dp[1]*jw*eta*dpl[0];
1146: Ke[l*2+1][ll*2+0] += dp[1]*jw*eta*2.*dpl[0] + dp[0]*jw*eta*dpl[1];
1147: 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];
1148: /* extra Newton terms */
1149: 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];
1150: 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];
1151: 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];
1152: 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];
1153: /* inertial part */
1154: Ke[l*2+0][ll*2+0] += pp*jw*thi->inertia*pp;
1155: Ke[l*2+1][ll*2+1] += pp*jw*thi->inertia*pp;
1156: }
1157: for (ll=0; ll<4; ll++) { /* Trial functions for surface/bed */
1158: const PetscReal dpl[] = {QuadQDeriv[q%4][ll][0]/hx, QuadQDeriv[q%4][ll][1]/hy}; /* surface = h + b */
1159: Kcpl[FieldIndex(Node,l,u)][FieldIndex(PrmNode,ll,h)] += pp*jw*thi->rhog*dpl[0];
1160: Kcpl[FieldIndex(Node,l,u)][FieldIndex(PrmNode,ll,b)] += pp*jw*thi->rhog*dpl[0];
1161: Kcpl[FieldIndex(Node,l,v)][FieldIndex(PrmNode,ll,h)] += pp*jw*thi->rhog*dpl[1];
1162: Kcpl[FieldIndex(Node,l,v)][FieldIndex(PrmNode,ll,b)] += pp*jw*thi->rhog*dpl[1];
1163: }
1164: }
1165: }
1166: if (k == 0) { /* on a bottom face */
1167: if (thi->no_slip) {
1168: const PetscReal hz = PetscRealPart(pn[0].h)/(zm-1);
1169: 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);
1170: Ke[0][0] = thi->dirichlet_scale*diagu;
1171: Ke[0][1] = 0;
1172: Ke[1][0] = 0;
1173: Ke[1][1] = thi->dirichlet_scale*diagv;
1174: } else {
1175: for (q=0; q<4; q++) { /* We remove the explicit scaling by 1/rhog because beta2 already has that scaling to be O(1) */
1176: const PetscReal jw = 0.25*hx*hy,*phi = QuadQInterp[q];
1177: PetscScalar u =0,v=0,rbeta2=0;
1178: PetscReal beta2,dbeta2;
1179: for (l=0; l<4; l++) {
1180: u += phi[l]*n[l].u;
1181: v += phi[l]*n[l].v;
1182: rbeta2 += phi[l]*pn[l].beta2;
1183: }
1184: THIFriction(thi,PetscRealPart(rbeta2),PetscRealPart(u*u+v*v)/2,&beta2,&dbeta2);
1185: for (l=0; l<4; l++) {
1186: const PetscReal pp = phi[l];
1187: for (ll=0; ll<4; ll++) {
1188: const PetscReal ppl = phi[ll];
1189: Ke[l*2+0][ll*2+0] += pp*jw*beta2*ppl + pp*jw*dbeta2*u*u*ppl;
1190: Ke[l*2+0][ll*2+1] += pp*jw*dbeta2*u*v*ppl;
1191: Ke[l*2+1][ll*2+0] += pp*jw*dbeta2*v*u*ppl;
1192: Ke[l*2+1][ll*2+1] += pp*jw*beta2*ppl + pp*jw*dbeta2*v*v*ppl;
1193: }
1194: }
1195: }
1196: }
1197: }
1198: {
1199: const PetscInt rc3blocked[8] = {
1200: DMDALocalIndex3D(info,i+0,j+0,k+0),
1201: DMDALocalIndex3D(info,i+1,j+0,k+0),
1202: DMDALocalIndex3D(info,i+1,j+1,k+0),
1203: DMDALocalIndex3D(info,i+0,j+1,k+0),
1204: DMDALocalIndex3D(info,i+0,j+0,k+1),
1205: DMDALocalIndex3D(info,i+1,j+0,k+1),
1206: DMDALocalIndex3D(info,i+1,j+1,k+1),
1207: DMDALocalIndex3D(info,i+0,j+1,k+1)
1208: },col2blocked[PRMNODE_SIZE*4] = {
1209: DMDALocalIndex2D(info,i+0,j+0),
1210: DMDALocalIndex2D(info,i+1,j+0),
1211: DMDALocalIndex2D(info,i+1,j+1),
1212: DMDALocalIndex2D(info,i+0,j+1)
1213: };
1214: #if !defined COMPUTE_LOWER_TRIANGULAR /* fill in lower-triangular part, this is really cheap compared to computing the entries */
1215: for (l=0; l<8; l++) {
1216: for (ll=l+1; ll<8; ll++) {
1217: Ke[ll*2+0][l*2+0] = Ke[l*2+0][ll*2+0];
1218: Ke[ll*2+1][l*2+0] = Ke[l*2+0][ll*2+1];
1219: Ke[ll*2+0][l*2+1] = Ke[l*2+1][ll*2+0];
1220: Ke[ll*2+1][l*2+1] = Ke[l*2+1][ll*2+1];
1221: }
1222: }
1223: #endif
1224: MatSetValuesBlockedLocal(B,8,rc3blocked,8,rc3blocked,&Ke[0][0],ADD_VALUES); /* velocity-velocity coupling can use blocked insertion */
1225: { /* The off-diagonal part cannot (yet) */
1226: PetscInt row3scalar[NODE_SIZE*8],col2scalar[PRMNODE_SIZE*4];
1227: for (l=0; l<8; l++) for (ll=0; ll<NODE_SIZE; ll++) row3scalar[l*NODE_SIZE+ll] = rc3blocked[l]*NODE_SIZE+ll;
1228: for (l=0; l<4; l++) for (ll=0; ll<PRMNODE_SIZE; ll++) col2scalar[l*PRMNODE_SIZE+ll] = col2blocked[l]*PRMNODE_SIZE+ll;
1229: MatSetValuesLocal(Bcpl,8*NODE_SIZE,row3scalar,4*PRMNODE_SIZE,col2scalar,&Kcpl[0][0],ADD_VALUES);
1230: }
1231: }
1232: }
1233: }
1234: }
1235: return 0;
1236: }
1238: static PetscErrorCode THIJacobianLocal_2D(DMDALocalInfo *info,const Node ***x3,const PrmNode **x2,const PrmNode **xdot2,PetscReal a,Mat B22,Mat B21,THI thi)
1239: {
1240: PetscInt xs,ys,xm,ym,zm,i,j,k;
1243: xs = info->zs;
1244: ys = info->ys;
1245: xm = info->zm;
1246: ym = info->ym;
1247: zm = info->xm;
1250: for (i=xs; i<xs+xm; i++) {
1251: for (j=ys; j<ys+ym; j++) {
1252: { /* Self-coupling */
1253: const PetscInt row[] = {DMDALocalIndex2D(info,i,j)};
1254: const PetscInt col[] = {DMDALocalIndex2D(info,i,j)};
1255: const PetscScalar vals[] = {
1256: a,0,0,
1257: 0,a,0,
1258: 0,0,a
1259: };
1260: MatSetValuesBlockedLocal(B22,1,row,1,col,vals,INSERT_VALUES);
1261: }
1262: for (k=0; k<zm; k++) { /* Coupling to velocity problem */
1263: /* Use a cheaper quadrature than for residual evaluation, because it is much sparser */
1264: const PetscInt row[] = {FieldIndex(PrmNode,DMDALocalIndex2D(info,i,j),h)};
1265: const PetscInt cols[] = {
1266: FieldIndex(Node,DMDALocalIndex3D(info,i-1,j,k),u),
1267: FieldIndex(Node,DMDALocalIndex3D(info,i ,j,k),u),
1268: FieldIndex(Node,DMDALocalIndex3D(info,i+1,j,k),u),
1269: FieldIndex(Node,DMDALocalIndex3D(info,i,j-1,k),v),
1270: FieldIndex(Node,DMDALocalIndex3D(info,i,j ,k),v),
1271: FieldIndex(Node,DMDALocalIndex3D(info,i,j+1,k),v)
1272: };
1273: const PetscScalar
1274: w = (k && k<zm-1) ? 0.5 : 0.25,
1275: hW = w*(x2[i-1][j ].h+x2[i ][j ].h)/(zm-1.),
1276: hE = w*(x2[i ][j ].h+x2[i+1][j ].h)/(zm-1.),
1277: hS = w*(x2[i ][j-1].h+x2[i ][j ].h)/(zm-1.),
1278: hN = w*(x2[i ][j ].h+x2[i ][j+1].h)/(zm-1.);
1279: PetscScalar *vals,
1280: vals_upwind[] = {((PetscRealPart(x3[i][j][k].u) > 0) ? -hW : 0),
1281: ((PetscRealPart(x3[i][j][k].u) > 0) ? +hE : -hW),
1282: ((PetscRealPart(x3[i][j][k].u) > 0) ? 0 : +hE),
1283: ((PetscRealPart(x3[i][j][k].v) > 0) ? -hS : 0),
1284: ((PetscRealPart(x3[i][j][k].v) > 0) ? +hN : -hS),
1285: ((PetscRealPart(x3[i][j][k].v) > 0) ? 0 : +hN)},
1286: vals_centered[] = {-0.5*hW, 0.5*(-hW+hE), 0.5*hE,
1287: -0.5*hS, 0.5*(-hS+hN), 0.5*hN};
1288: vals = 1 ? vals_upwind : vals_centered;
1289: if (k == 0) {
1290: Node derate;
1291: THIErosion(thi,&x3[i][j][0],NULL,&derate);
1292: vals[1] -= derate.u;
1293: vals[4] -= derate.v;
1294: }
1295: MatSetValuesLocal(B21,1,row,6,cols,vals,INSERT_VALUES);
1296: }
1297: }
1298: }
1299: return 0;
1300: }
1302: static PetscErrorCode THIJacobian(TS ts,PetscReal t,Vec X,Vec Xdot,PetscReal a,Mat A,Mat B,void *ctx)
1303: {
1304: THI thi = (THI)ctx;
1305: DM pack,da3,da2;
1306: Vec X3,X2,Xdot2;
1307: Mat B11,B12,B21,B22;
1308: DMDALocalInfo info3;
1309: IS *isloc;
1310: const Node ***x3;
1311: const PrmNode **x2,**xdot2;
1314: TSGetDM(ts,&pack);
1315: DMCompositeGetEntries(pack,&da3,&da2);
1316: DMDAGetLocalInfo(da3,&info3);
1317: DMCompositeGetLocalVectors(pack,&X3,&X2);
1318: DMCompositeGetLocalVectors(pack,NULL,&Xdot2);
1319: DMCompositeScatter(pack,X,X3,X2);
1320: THIFixGhosts(thi,da3,da2,X3,X2);
1321: DMCompositeScatter(pack,Xdot,NULL,Xdot2);
1323: MatZeroEntries(B);
1325: DMCompositeGetLocalISs(pack,&isloc);
1326: MatGetLocalSubMatrix(B,isloc[0],isloc[0],&B11);
1327: MatGetLocalSubMatrix(B,isloc[0],isloc[1],&B12);
1328: MatGetLocalSubMatrix(B,isloc[1],isloc[0],&B21);
1329: MatGetLocalSubMatrix(B,isloc[1],isloc[1],&B22);
1331: DMDAVecGetArray(da3,X3,&x3);
1332: DMDAVecGetArray(da2,X2,&x2);
1333: DMDAVecGetArray(da2,Xdot2,&xdot2);
1335: THIJacobianLocal_Momentum(&info3,x3,x2,B11,B12,thi);
1337: /* Need to switch from ADD_VALUES to INSERT_VALUES */
1338: MatAssemblyBegin(B,MAT_FLUSH_ASSEMBLY);
1339: MatAssemblyEnd(B,MAT_FLUSH_ASSEMBLY);
1341: THIJacobianLocal_2D(&info3,x3,x2,xdot2,a,B22,B21,thi);
1343: DMDAVecRestoreArray(da3,X3,&x3);
1344: DMDAVecRestoreArray(da2,X2,&x2);
1345: DMDAVecRestoreArray(da2,Xdot2,&xdot2);
1347: MatRestoreLocalSubMatrix(B,isloc[0],isloc[0],&B11);
1348: MatRestoreLocalSubMatrix(B,isloc[0],isloc[1],&B12);
1349: MatRestoreLocalSubMatrix(B,isloc[1],isloc[0],&B21);
1350: MatRestoreLocalSubMatrix(B,isloc[1],isloc[1],&B22);
1351: ISDestroy(&isloc[0]);
1352: ISDestroy(&isloc[1]);
1353: PetscFree(isloc);
1355: DMCompositeRestoreLocalVectors(pack,&X3,&X2);
1356: DMCompositeRestoreLocalVectors(pack,0,&Xdot2);
1358: MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
1359: MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
1360: if (A != B) {
1361: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
1362: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
1363: }
1364: if (thi->verbose) THIMatrixStatistics(thi,B,PETSC_VIEWER_STDOUT_WORLD);
1365: return 0;
1366: }
1368: /* VTK's XML formats are so brain-dead that they can't handle multiple grids in the same file. Since the communication
1369: * can be shared between the two grids, we write two files at once, one for velocity (living on a 3D grid defined by
1370: * h=thickness and b=bed) and another for all properties living on the 2D grid.
1371: */
1372: static PetscErrorCode THIDAVecView_VTK_XML(THI thi,DM pack,Vec X,const char filename[],const char filename2[])
1373: {
1374: const PetscInt dof = NODE_SIZE,dof2 = PRMNODE_SIZE;
1375: Units units = thi->units;
1376: MPI_Comm comm;
1377: PetscViewer viewer3,viewer2;
1378: PetscMPIInt rank,size,tag,nn,nmax,nn2,nmax2;
1379: PetscInt mx,my,mz,r,range[6];
1380: PetscScalar *x,*x2;
1381: DM da3,da2;
1382: Vec X3,X2;
1385: PetscObjectGetComm((PetscObject)thi,&comm);
1386: DMCompositeGetEntries(pack,&da3,&da2);
1387: DMCompositeGetAccess(pack,X,&X3,&X2);
1388: DMDAGetInfo(da3,0, &mz,&my,&mx, 0,0,0, 0,0,0,0,0,0);
1389: MPI_Comm_size(comm,&size);
1390: MPI_Comm_rank(comm,&rank);
1391: PetscViewerASCIIOpen(comm,filename,&viewer3);
1392: PetscViewerASCIIOpen(comm,filename2,&viewer2);
1393: PetscViewerASCIIPrintf(viewer3,"<VTKFile type=\"StructuredGrid\" version=\"0.1\" byte_order=\"LittleEndian\">\n");
1394: PetscViewerASCIIPrintf(viewer2,"<VTKFile type=\"StructuredGrid\" version=\"0.1\" byte_order=\"LittleEndian\">\n");
1395: PetscViewerASCIIPrintf(viewer3," <StructuredGrid WholeExtent=\"%d %d %d %d %d %d\">\n",0,mz-1,0,my-1,0,mx-1);
1396: PetscViewerASCIIPrintf(viewer2," <StructuredGrid WholeExtent=\"%d %d %d %d %d %d\">\n",0,0,0,my-1,0,mx-1);
1398: DMDAGetCorners(da3,range,range+1,range+2,range+3,range+4,range+5);
1399: PetscMPIIntCast(range[3]*range[4]*range[5]*dof,&nn);
1400: MPI_Reduce(&nn,&nmax,1,MPI_INT,MPI_MAX,0,comm);
1401: PetscMPIIntCast(range[4]*range[5]*dof2,&nn2);
1402: MPI_Reduce(&nn2,&nmax2,1,MPI_INT,MPI_MAX,0,comm);
1403: tag = ((PetscObject)viewer3)->tag;
1404: VecGetArrayRead(X3,(const PetscScalar**)&x);
1405: VecGetArrayRead(X2,(const PetscScalar**)&x2);
1406: if (rank == 0) {
1407: PetscScalar *array,*array2;
1408: PetscMalloc2(nmax,&array,nmax2,&array2);
1409: for (r=0; r<size; r++) {
1410: PetscInt i,j,k,f,xs,xm,ys,ym,zs,zm;
1411: Node *y3;
1412: PetscScalar (*y2)[PRMNODE_SIZE];
1413: MPI_Status status;
1415: if (r) {
1416: MPI_Recv(range,6,MPIU_INT,r,tag,comm,MPI_STATUS_IGNORE);
1417: }
1418: zs = range[0];ys = range[1];xs = range[2];zm = range[3];ym = range[4];xm = range[5];
1420: if (r) {
1421: MPI_Recv(array,nmax,MPIU_SCALAR,r,tag,comm,&status);
1422: MPI_Get_count(&status,MPIU_SCALAR,&nn);
1424: y3 = (Node*)array;
1425: MPI_Recv(array2,nmax2,MPIU_SCALAR,r,tag,comm,&status);
1426: MPI_Get_count(&status,MPIU_SCALAR,&nn2);
1428: y2 = (PetscScalar(*)[PRMNODE_SIZE])array2;
1429: } else {
1430: y3 = (Node*)x;
1431: y2 = (PetscScalar(*)[PRMNODE_SIZE])x2;
1432: }
1433: PetscViewerASCIIPrintf(viewer3," <Piece Extent=\"%D %D %D %D %D %D\">\n",zs,zs+zm-1,ys,ys+ym-1,xs,xs+xm-1);
1434: PetscViewerASCIIPrintf(viewer2," <Piece Extent=\"%d %d %D %D %D %D\">\n",0,0,ys,ys+ym-1,xs,xs+xm-1);
1436: PetscViewerASCIIPrintf(viewer3," <Points>\n");
1437: PetscViewerASCIIPrintf(viewer2," <Points>\n");
1438: PetscViewerASCIIPrintf(viewer3," <DataArray type=\"Float32\" NumberOfComponents=\"3\" format=\"ascii\">\n");
1439: PetscViewerASCIIPrintf(viewer2," <DataArray type=\"Float32\" NumberOfComponents=\"3\" format=\"ascii\">\n");
1440: for (i=xs; i<xs+xm; i++) {
1441: for (j=ys; j<ys+ym; j++) {
1442: PetscReal
1443: xx = thi->Lx*i/mx,
1444: yy = thi->Ly*j/my,
1445: b = PetscRealPart(y2[i*ym+j][FieldOffset(PrmNode,b)]),
1446: h = PetscRealPart(y2[i*ym+j][FieldOffset(PrmNode,h)]);
1447: for (k=zs; k<zs+zm; k++) {
1448: PetscReal zz = b + h*k/(mz-1.);
1449: PetscViewerASCIIPrintf(viewer3,"%f %f %f\n",xx,yy,zz);
1450: }
1451: PetscViewerASCIIPrintf(viewer2,"%f %f %f\n",xx,yy,(double)0.0);
1452: }
1453: }
1454: PetscViewerASCIIPrintf(viewer3," </DataArray>\n");
1455: PetscViewerASCIIPrintf(viewer2," </DataArray>\n");
1456: PetscViewerASCIIPrintf(viewer3," </Points>\n");
1457: PetscViewerASCIIPrintf(viewer2," </Points>\n");
1459: { /* Velocity and rank (3D) */
1460: PetscViewerASCIIPrintf(viewer3," <PointData>\n");
1461: PetscViewerASCIIPrintf(viewer3," <DataArray type=\"Float32\" Name=\"velocity\" NumberOfComponents=\"3\" format=\"ascii\">\n");
1462: for (i=0; i<nn/dof; i++) {
1463: PetscViewerASCIIPrintf(viewer3,"%f %f %f\n",PetscRealPart(y3[i].u)*units->year/units->meter,PetscRealPart(y3[i].v)*units->year/units->meter,0.0);
1464: }
1465: PetscViewerASCIIPrintf(viewer3," </DataArray>\n");
1467: PetscViewerASCIIPrintf(viewer3," <DataArray type=\"Int32\" Name=\"rank\" NumberOfComponents=\"1\" format=\"ascii\">\n");
1468: for (i=0; i<nn; i+=dof) {
1469: PetscViewerASCIIPrintf(viewer3,"%D\n",r);
1470: }
1471: PetscViewerASCIIPrintf(viewer3," </DataArray>\n");
1472: PetscViewerASCIIPrintf(viewer3," </PointData>\n");
1473: }
1475: { /* 2D */
1476: PetscViewerASCIIPrintf(viewer2," <PointData>\n");
1477: for (f=0; f<PRMNODE_SIZE; f++) {
1478: const char *fieldname;
1479: DMDAGetFieldName(da2,f,&fieldname);
1480: PetscViewerASCIIPrintf(viewer2," <DataArray type=\"Float32\" Name=\"%s\" format=\"ascii\">\n",fieldname);
1481: for (i=0; i<nn2/PRMNODE_SIZE; i++) {
1482: PetscViewerASCIIPrintf(viewer2,"%g\n",y2[i][f]);
1483: }
1484: PetscViewerASCIIPrintf(viewer2," </DataArray>\n");
1485: }
1486: PetscViewerASCIIPrintf(viewer2," </PointData>\n");
1487: }
1489: PetscViewerASCIIPrintf(viewer3," </Piece>\n");
1490: PetscViewerASCIIPrintf(viewer2," </Piece>\n");
1491: }
1492: PetscFree2(array,array2);
1493: } else {
1494: MPI_Send(range,6,MPIU_INT,0,tag,comm);
1495: MPI_Send(x,nn,MPIU_SCALAR,0,tag,comm);
1496: MPI_Send(x2,nn2,MPIU_SCALAR,0,tag,comm);
1497: }
1498: VecRestoreArrayRead(X3,(const PetscScalar**)&x);
1499: VecRestoreArrayRead(X2,(const PetscScalar**)&x2);
1500: PetscViewerASCIIPrintf(viewer3," </StructuredGrid>\n");
1501: PetscViewerASCIIPrintf(viewer2," </StructuredGrid>\n");
1503: DMCompositeRestoreAccess(pack,X,&X3,&X2);
1504: PetscViewerASCIIPrintf(viewer3,"</VTKFile>\n");
1505: PetscViewerASCIIPrintf(viewer2,"</VTKFile>\n");
1506: PetscViewerDestroy(&viewer3);
1507: PetscViewerDestroy(&viewer2);
1508: return 0;
1509: }
1511: static PetscErrorCode THITSMonitor(TS ts,PetscInt step,PetscReal t,Vec X,void *ctx)
1512: {
1513: THI thi = (THI)ctx;
1514: DM pack;
1515: char filename3[PETSC_MAX_PATH_LEN],filename2[PETSC_MAX_PATH_LEN];
1518: if (step < 0) return 0; /* negative one is used to indicate an interpolated solution */
1519: PetscPrintf(PetscObjectComm((PetscObject)ts),"%3D: t=%g\n",step,(double)t);
1520: if (thi->monitor_interval && step % thi->monitor_interval) return 0;
1521: TSGetDM(ts,&pack);
1522: PetscSNPrintf(filename3,sizeof(filename3),"%s-3d-%03d.vts",thi->monitor_basename,step);
1523: PetscSNPrintf(filename2,sizeof(filename2),"%s-2d-%03d.vts",thi->monitor_basename,step);
1524: THIDAVecView_VTK_XML(thi,pack,X,filename3,filename2);
1525: return 0;
1526: }
1528: static PetscErrorCode THICreateDM3d(THI thi,DM *dm3d)
1529: {
1530: MPI_Comm comm;
1531: PetscInt M = 3,N = 3,P = 2;
1532: DM da;
1536: PetscObjectGetComm((PetscObject)thi,&comm);
1537: PetscOptionsBegin(comm,NULL,"Grid resolution options","");
1538: {
1539: PetscOptionsInt("-M","Number of elements in x-direction on coarse level","",M,&M,NULL);
1540: N = M;
1541: PetscOptionsInt("-N","Number of elements in y-direction on coarse level (if different from M)","",N,&N,NULL);
1542: PetscOptionsInt("-P","Number of elements in z-direction on coarse level","",P,&P,NULL);
1543: }
1544: PetscOptionsEnd();
1545: 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);
1546: DMSetFromOptions(da);
1547: DMSetUp(da);
1548: DMDASetFieldName(da,0,"x-velocity");
1549: DMDASetFieldName(da,1,"y-velocity");
1550: *dm3d = da;
1551: return 0;
1552: }
1554: int main(int argc,char *argv[])
1555: {
1556: MPI_Comm comm;
1557: DM pack,da3,da2;
1558: TS ts;
1559: THI thi;
1560: Vec X;
1561: Mat B;
1562: PetscInt i,steps;
1563: PetscReal ftime;
1565: PetscInitialize(&argc,&argv,0,help);
1566: comm = PETSC_COMM_WORLD;
1568: THICreate(comm,&thi);
1569: THICreateDM3d(thi,&da3);
1570: {
1571: PetscInt Mx,My,mx,my,s;
1572: DMDAStencilType st;
1573: DMDAGetInfo(da3,0, 0,&My,&Mx, 0,&my,&mx, 0,&s,0,0,0,&st);
1574: DMDACreate2d(PetscObjectComm((PetscObject)thi),DM_BOUNDARY_PERIODIC,DM_BOUNDARY_PERIODIC,st,My,Mx,my,mx,sizeof(PrmNode)/sizeof(PetscScalar),s,0,0,&da2);
1575: DMSetUp(da2);
1576: }
1578: PetscObjectSetName((PetscObject)da3,"3D_Velocity");
1579: DMSetOptionsPrefix(da3,"f3d_");
1580: DMDASetFieldName(da3,0,"u");
1581: DMDASetFieldName(da3,1,"v");
1582: PetscObjectSetName((PetscObject)da2,"2D_Fields");
1583: DMSetOptionsPrefix(da2,"f2d_");
1584: DMDASetFieldName(da2,0,"b");
1585: DMDASetFieldName(da2,1,"h");
1586: DMDASetFieldName(da2,2,"beta2");
1587: DMCompositeCreate(comm,&pack);
1588: DMCompositeAddDM(pack,da3);
1589: DMCompositeAddDM(pack,da2);
1590: DMDestroy(&da3);
1591: DMDestroy(&da2);
1592: DMSetUp(pack);
1593: DMCreateMatrix(pack,&B);
1594: MatSetOption(B,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_FALSE);
1595: MatSetOptionsPrefix(B,"thi_");
1597: for (i=0; i<thi->nlevels; i++) {
1598: PetscReal Lx = thi->Lx / thi->units->meter,Ly = thi->Ly / thi->units->meter,Lz = thi->Lz / thi->units->meter;
1599: PetscInt Mx,My,Mz;
1600: DMCompositeGetEntries(pack,&da3,&da2);
1601: DMDAGetInfo(da3,0, &Mz,&My,&Mx, 0,0,0, 0,0,0,0,0,0);
1602: 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));
1603: }
1605: DMCreateGlobalVector(pack,&X);
1606: THIInitial(thi,pack,X);
1608: TSCreate(comm,&ts);
1609: TSSetDM(ts,pack);
1610: TSSetProblemType(ts,TS_NONLINEAR);
1611: TSMonitorSet(ts,THITSMonitor,thi,NULL);
1612: TSSetType(ts,TSTHETA);
1613: TSSetIFunction(ts,NULL,THIFunction,thi);
1614: TSSetIJacobian(ts,B,B,THIJacobian,thi);
1615: TSSetMaxTime(ts,10.0);
1616: TSSetExactFinalTime(ts,TS_EXACTFINALTIME_STEPOVER);
1617: TSSetSolution(ts,X);
1618: TSSetTimeStep(ts,1e-3);
1619: TSSetFromOptions(ts);
1621: TSSolve(ts,X);
1622: TSGetSolveTime(ts,&ftime);
1623: TSGetStepNumber(ts,&steps);
1624: PetscPrintf(PETSC_COMM_WORLD,"Steps %D final time %g\n",steps,(double)ftime);
1626: if (0) THISolveStatistics(thi,ts,0,"Full");
1628: {
1629: PetscBool flg;
1630: char filename[PETSC_MAX_PATH_LEN] = "";
1631: PetscOptionsGetString(NULL,NULL,"-o",filename,sizeof(filename),&flg);
1632: if (flg) {
1633: THIDAVecView_VTK_XML(thi,pack,X,filename,NULL);
1634: }
1635: }
1637: VecDestroy(&X);
1638: MatDestroy(&B);
1639: DMDestroy(&pack);
1640: TSDestroy(&ts);
1641: THIDestroy(&thi);
1642: PetscFinalize();
1643: return 0;
1644: }