Actual source code: ex14.c
petsc-3.4.5 2014-06-29
1: static const char help[] = "Toy hydrostatic ice flow with multigrid in 3D.\n\
2: \n\
3: Solves the hydrostatic (aka Blatter/Pattyn/First Order) equations for ice sheet flow\n\
4: using multigrid. The ice uses a power-law rheology with \"Glen\" exponent 3 (corresponds\n\
5: to p=4/3 in a p-Laplacian). The focus is on ISMIP-HOM experiments which assume periodic\n\
6: boundary conditions in the x- and y-directions.\n\
7: \n\
8: Equations are rescaled so that the domain size and solution are O(1), details of this scaling\n\
9: can be controlled by the options -units_meter, -units_second, and -units_kilogram.\n\
10: \n\
11: A VTK StructuredGrid output file can be written using the option -o filename.vts\n\
12: \n\n";
14: /*
15: The equations for horizontal velocity (u,v) are
17: - [eta (4 u_x + 2 v_y)]_x - [eta (u_y + v_x)]_y - [eta u_z]_z + rho g s_x = 0
18: - [eta (4 v_y + 2 u_x)]_y - [eta (u_y + v_x)]_x - [eta v_z]_z + rho g s_y = 0
20: where
22: eta = B/2 (epsilon + gamma)^((p-2)/2)
24: is the nonlinear effective viscosity with regularization epsilon and hardness parameter B,
25: written in terms of the second invariant
27: gamma = u_x^2 + v_y^2 + u_x v_y + (1/4) (u_y + v_x)^2 + (1/4) u_z^2 + (1/4) v_z^2
29: The surface boundary conditions are the natural conditions. The basal boundary conditions
30: are either no-slip, or Navier (linear) slip with spatially variant friction coefficient beta^2.
32: In the code, the equations for (u,v) are multiplied through by 1/(rho g) so that residuals are O(1).
34: The discretization is Q1 finite elements, managed by a DMDA. The grid is never distorted in the
35: map (x,y) plane, but the bed and surface may be bumpy. This is handled as usual in FEM, through
36: the Jacobian of the coordinate transformation from a reference element to the physical element.
38: Since ice-flow is tightly coupled in the z-direction (within columns), the DMDA is managed
39: specially so that columns are never distributed, and are always contiguous in memory.
40: This amounts to reversing the meaning of X,Y,Z compared to the DMDA's internal interpretation,
41: and then indexing as vec[i][j][k]. The exotic coarse spaces require 2D DMDAs which are made to
42: use compatible domain decomposition relative to the 3D DMDAs.
44: */
46: #include <petscts.h>
47: #include <petscdmda.h>
48: #include <petscdmcomposite.h>
49: #include <ctype.h> /* toupper() */
51: #if defined __SSE2__
52: # include <emmintrin.h>
53: #endif
55: /* The SSE2 kernels are only for PetscScalar=double on architectures that support it */
56: #define USE_SSE2_KERNELS (!defined NO_SSE2 \
57: && !defined PETSC_USE_COMPLEX \
58: && !defined PETSC_USE_REAL_SINGLE \
59: && defined __SSE2__)
61: #if !defined __STDC_VERSION__ || __STDC_VERSION__ < 199901L
62: # if defined __cplusplus /* C++ restrict is nonstandard and compilers have inconsistent rules about where it can be used */
63: # define restrict
64: # else
65: # define restrict PETSC_RESTRICT
66: # endif
67: #endif
69: static PetscClassId THI_CLASSID;
71: typedef enum {QUAD_GAUSS,QUAD_LOBATTO} QuadratureType;
72: static const char *QuadratureTypes[] = {"gauss","lobatto","QuadratureType","QUAD_",0};
73: static const PetscReal HexQWeights[8] = {1,1,1,1,1,1,1,1};
74: static const PetscReal HexQNodes[] = {-0.57735026918962573, 0.57735026918962573};
75: #define G 0.57735026918962573
76: #define H (0.5*(1.+G))
77: #define L (0.5*(1.-G))
78: #define M (-0.5)
79: #define P (0.5)
80: /* Special quadrature: Lobatto in horizontal, Gauss in vertical */
81: static const PetscReal HexQInterp_Lobatto[8][8] = {{H,0,0,0,L,0,0,0},
82: {0,H,0,0,0,L,0,0},
83: {0,0,H,0,0,0,L,0},
84: {0,0,0,H,0,0,0,L},
85: {L,0,0,0,H,0,0,0},
86: {0,L,0,0,0,H,0,0},
87: {0,0,L,0,0,0,H,0},
88: {0,0,0,L,0,0,0,H}};
89: static const PetscReal HexQDeriv_Lobatto[8][8][3] = {
90: {{M*H,M*H,M},{P*H,0,0} ,{0,0,0} ,{0,P*H,0} ,{M*L,M*L,P},{P*L,0,0} ,{0,0,0} ,{0,P*L,0} },
91: {{M*H,0,0} ,{P*H,M*H,M},{0,P*H,0} ,{0,0,0} ,{M*L,0,0} ,{P*L,M*L,P},{0,P*L,0} ,{0,0,0} },
92: {{0,0,0} ,{0,M*H,0} ,{P*H,P*H,M},{M*H,0,0} ,{0,0,0} ,{0,M*L,0} ,{P*L,P*L,P},{M*L,0,0} },
93: {{0,M*H,0} ,{0,0,0} ,{P*H,0,0} ,{M*H,P*H,M},{0,M*L,0} ,{0,0,0} ,{P*L,0,0} ,{M*L,P*L,P}},
94: {{M*L,M*L,M},{P*L,0,0} ,{0,0,0} ,{0,P*L,0} ,{M*H,M*H,P},{P*H,0,0} ,{0,0,0} ,{0,P*H,0} },
95: {{M*L,0,0} ,{P*L,M*L,M},{0,P*L,0} ,{0,0,0} ,{M*H,0,0} ,{P*H,M*H,P},{0,P*H,0} ,{0,0,0} },
96: {{0,0,0} ,{0,M*L,0} ,{P*L,P*L,M},{M*L,0,0} ,{0,0,0} ,{0,M*H,0} ,{P*H,P*H,P},{M*H,0,0} },
97: {{0,M*L,0} ,{0,0,0} ,{P*L,0,0} ,{M*L,P*L,M},{0,M*H,0} ,{0,0,0} ,{P*H,0,0} ,{M*H,P*H,P}}};
98: /* Stanndard Gauss */
99: static const PetscReal HexQInterp_Gauss[8][8] = {{H*H*H,L*H*H,L*L*H,H*L*H, H*H*L,L*H*L,L*L*L,H*L*L},
100: {L*H*H,H*H*H,H*L*H,L*L*H, L*H*L,H*H*L,H*L*L,L*L*L},
101: {L*L*H,H*L*H,H*H*H,L*H*H, L*L*L,H*L*L,H*H*L,L*H*L},
102: {H*L*H,L*L*H,L*H*H,H*H*H, H*L*L,L*L*L,L*H*L,H*H*L},
103: {H*H*L,L*H*L,L*L*L,H*L*L, H*H*H,L*H*H,L*L*H,H*L*H},
104: {L*H*L,H*H*L,H*L*L,L*L*L, L*H*H,H*H*H,H*L*H,L*L*H},
105: {L*L*L,H*L*L,H*H*L,L*H*L, L*L*H,H*L*H,H*H*H,L*H*H},
106: {H*L*L,L*L*L,L*H*L,H*H*L, H*L*H,L*L*H,L*H*H,H*H*H}};
107: static const PetscReal HexQDeriv_Gauss[8][8][3] = {
108: {{M*H*H,H*M*H,H*H*M},{P*H*H,L*M*H,L*H*M},{P*L*H,L*P*H,L*L*M},{M*L*H,H*P*H,H*L*M}, {M*H*L,H*M*L,H*H*P},{P*H*L,L*M*L,L*H*P},{P*L*L,L*P*L,L*L*P},{M*L*L,H*P*L,H*L*P}},
109: {{M*H*H,L*M*H,L*H*M},{P*H*H,H*M*H,H*H*M},{P*L*H,H*P*H,H*L*M},{M*L*H,L*P*H,L*L*M}, {M*H*L,L*M*L,L*H*P},{P*H*L,H*M*L,H*H*P},{P*L*L,H*P*L,H*L*P},{M*L*L,L*P*L,L*L*P}},
110: {{M*L*H,L*M*H,L*L*M},{P*L*H,H*M*H,H*L*M},{P*H*H,H*P*H,H*H*M},{M*H*H,L*P*H,L*H*M}, {M*L*L,L*M*L,L*L*P},{P*L*L,H*M*L,H*L*P},{P*H*L,H*P*L,H*H*P},{M*H*L,L*P*L,L*H*P}},
111: {{M*L*H,H*M*H,H*L*M},{P*L*H,L*M*H,L*L*M},{P*H*H,L*P*H,L*H*M},{M*H*H,H*P*H,H*H*M}, {M*L*L,H*M*L,H*L*P},{P*L*L,L*M*L,L*L*P},{P*H*L,L*P*L,L*H*P},{M*H*L,H*P*L,H*H*P}},
112: {{M*H*L,H*M*L,H*H*M},{P*H*L,L*M*L,L*H*M},{P*L*L,L*P*L,L*L*M},{M*L*L,H*P*L,H*L*M}, {M*H*H,H*M*H,H*H*P},{P*H*H,L*M*H,L*H*P},{P*L*H,L*P*H,L*L*P},{M*L*H,H*P*H,H*L*P}},
113: {{M*H*L,L*M*L,L*H*M},{P*H*L,H*M*L,H*H*M},{P*L*L,H*P*L,H*L*M},{M*L*L,L*P*L,L*L*M}, {M*H*H,L*M*H,L*H*P},{P*H*H,H*M*H,H*H*P},{P*L*H,H*P*H,H*L*P},{M*L*H,L*P*H,L*L*P}},
114: {{M*L*L,L*M*L,L*L*M},{P*L*L,H*M*L,H*L*M},{P*H*L,H*P*L,H*H*M},{M*H*L,L*P*L,L*H*M}, {M*L*H,L*M*H,L*L*P},{P*L*H,H*M*H,H*L*P},{P*H*H,H*P*H,H*H*P},{M*H*H,L*P*H,L*H*P}},
115: {{M*L*L,H*M*L,H*L*M},{P*L*L,L*M*L,L*L*M},{P*H*L,L*P*L,L*H*M},{M*H*L,H*P*L,H*H*M}, {M*L*H,H*M*H,H*L*P},{P*L*H,L*M*H,L*L*P},{P*H*H,L*P*H,L*H*P},{M*H*H,H*P*H,H*H*P}}};
116: static const PetscReal (*HexQInterp)[8],(*HexQDeriv)[8][3];
117: /* Standard 2x2 Gauss quadrature for the bottom layer. */
118: static const PetscReal QuadQInterp[4][4] = {{H*H,L*H,L*L,H*L},
119: {L*H,H*H,H*L,L*L},
120: {L*L,H*L,H*H,L*H},
121: {H*L,L*L,L*H,H*H}};
122: static const PetscReal QuadQDeriv[4][4][2] = {
123: {{M*H,M*H},{P*H,M*L},{P*L,P*L},{M*L,P*H}},
124: {{M*H,M*L},{P*H,M*H},{P*L,P*H},{M*L,P*L}},
125: {{M*L,M*L},{P*L,M*H},{P*H,P*H},{M*H,P*L}},
126: {{M*L,M*H},{P*L,M*L},{P*H,P*L},{M*H,P*H}}};
127: #undef G
128: #undef H
129: #undef L
130: #undef M
131: #undef P
133: #define HexExtract(x,i,j,k,n) do { \
134: (n)[0] = (x)[i][j][k]; \
135: (n)[1] = (x)[i+1][j][k]; \
136: (n)[2] = (x)[i+1][j+1][k]; \
137: (n)[3] = (x)[i][j+1][k]; \
138: (n)[4] = (x)[i][j][k+1]; \
139: (n)[5] = (x)[i+1][j][k+1]; \
140: (n)[6] = (x)[i+1][j+1][k+1]; \
141: (n)[7] = (x)[i][j+1][k+1]; \
142: } while (0)
144: #define HexExtractRef(x,i,j,k,n) do { \
145: (n)[0] = &(x)[i][j][k]; \
146: (n)[1] = &(x)[i+1][j][k]; \
147: (n)[2] = &(x)[i+1][j+1][k]; \
148: (n)[3] = &(x)[i][j+1][k]; \
149: (n)[4] = &(x)[i][j][k+1]; \
150: (n)[5] = &(x)[i+1][j][k+1]; \
151: (n)[6] = &(x)[i+1][j+1][k+1]; \
152: (n)[7] = &(x)[i][j+1][k+1]; \
153: } while (0)
155: #define QuadExtract(x,i,j,n) do { \
156: (n)[0] = (x)[i][j]; \
157: (n)[1] = (x)[i+1][j]; \
158: (n)[2] = (x)[i+1][j+1]; \
159: (n)[3] = (x)[i][j+1]; \
160: } while (0)
162: static PetscScalar Sqr(PetscScalar a) {return a*a;}
164: static void HexGrad(const PetscReal dphi[][3],const PetscReal zn[],PetscReal dz[])
165: {
166: PetscInt i;
167: dz[0] = dz[1] = dz[2] = 0;
168: for (i=0; i<8; i++) {
169: dz[0] += dphi[i][0] * zn[i];
170: dz[1] += dphi[i][1] * zn[i];
171: dz[2] += dphi[i][2] * zn[i];
172: }
173: }
175: static void HexComputeGeometry(PetscInt q,PetscReal hx,PetscReal hy,const PetscReal dz[restrict],PetscReal phi[restrict],PetscReal dphi[restrict][3],PetscReal *restrict jw)
176: {
177: const PetscReal
178: jac[3][3] = {{hx/2,0,0}, {0,hy/2,0}, {dz[0],dz[1],dz[2]}}
179: ,ijac[3][3] = {{1/jac[0][0],0,0}, {0,1/jac[1][1],0}, {-jac[2][0]/(jac[0][0]*jac[2][2]),-jac[2][1]/(jac[1][1]*jac[2][2]),1/jac[2][2]}}
180: ,jdet = jac[0][0]*jac[1][1]*jac[2][2];
181: PetscInt i;
183: for (i=0; i<8; i++) {
184: const PetscReal *dphir = HexQDeriv[q][i];
185: phi[i] = HexQInterp[q][i];
186: dphi[i][0] = dphir[0]*ijac[0][0] + dphir[1]*ijac[1][0] + dphir[2]*ijac[2][0];
187: dphi[i][1] = dphir[0]*ijac[0][1] + dphir[1]*ijac[1][1] + dphir[2]*ijac[2][1];
188: dphi[i][2] = dphir[0]*ijac[0][2] + dphir[1]*ijac[1][2] + dphir[2]*ijac[2][2];
189: }
190: *jw = 1.0 * jdet;
191: }
193: typedef struct _p_THI *THI;
194: typedef struct _n_Units *Units;
196: typedef struct {
197: PetscScalar u,v;
198: } Node;
200: typedef struct {
201: PetscScalar b; /* bed */
202: PetscScalar h; /* thickness */
203: PetscScalar beta2; /* friction */
204: } PrmNode;
206: #define FieldSize(ntype) ((PetscInt)(sizeof(ntype)/sizeof(PetscScalar)))
207: #define FieldOffset(ntype,member) ((PetscInt)(offsetof(ntype,member)/sizeof(PetscScalar)))
208: #define FieldIndex(ntype,i,member) ((PetscInt)((i)*FieldSize(ntype) + FieldOffset(ntype,member)))
209: #define NODE_SIZE FieldSize(Node)
210: #define PRMNODE_SIZE FieldSize(PrmNode)
212: typedef struct {
213: PetscReal min,max,cmin,cmax;
214: } PRange;
216: struct _p_THI {
217: PETSCHEADER(int);
218: void (*initialize)(THI,PetscReal x,PetscReal y,PrmNode *p);
219: PetscInt nlevels;
220: PetscInt zlevels;
221: PetscReal Lx,Ly,Lz; /* Model domain */
222: PetscReal alpha; /* Bed angle */
223: Units units;
224: PetscReal dirichlet_scale;
225: PetscReal ssa_friction_scale;
226: PetscReal inertia;
227: PRange eta;
228: PRange beta2;
229: struct {
230: PetscReal Bd2,eps,exponent,glen_n;
231: } viscosity;
232: struct {
233: PetscReal irefgam,eps2,exponent;
234: } friction;
235: struct {
236: PetscReal rate,exponent,refvel;
237: } erosion;
238: PetscReal rhog;
239: PetscBool no_slip;
240: PetscBool verbose;
241: MatType mattype;
242: char *monitor_basename;
243: PetscInt monitor_interval;
244: };
246: struct _n_Units {
247: /* fundamental */
248: PetscReal meter;
249: PetscReal kilogram;
250: PetscReal second;
251: /* derived */
252: PetscReal Pascal;
253: PetscReal year;
254: };
256: static void PrmHexGetZ(const PrmNode pn[],PetscInt k,PetscInt zm,PetscReal zn[])
257: {
258: const PetscScalar zm1 = zm-1,
259: znl[8] = {pn[0].b + pn[0].h*(PetscScalar)k/zm1,
260: pn[1].b + pn[1].h*(PetscScalar)k/zm1,
261: pn[2].b + pn[2].h*(PetscScalar)k/zm1,
262: pn[3].b + pn[3].h*(PetscScalar)k/zm1,
263: pn[0].b + pn[0].h*(PetscScalar)(k+1)/zm1,
264: pn[1].b + pn[1].h*(PetscScalar)(k+1)/zm1,
265: pn[2].b + pn[2].h*(PetscScalar)(k+1)/zm1,
266: pn[3].b + pn[3].h*(PetscScalar)(k+1)/zm1};
267: PetscInt i;
268: for (i=0; i<8; i++) zn[i] = PetscRealPart(znl[i]);
269: }
273: /* Compute a gradient of all the 2D fields at four quadrature points. Output for [quadrature_point][direction].field_name */
274: static PetscErrorCode QuadComputeGrad4(const PetscReal dphi[][4][2],PetscReal hx,PetscReal hy,const PrmNode pn[4],PrmNode dp[4][2])
275: {
277: PetscInt q,i,f;
278: const PetscScalar (*restrict pg)[PRMNODE_SIZE] = (const PetscScalar(*)[PRMNODE_SIZE])pn; /* Get generic array pointers to the node */
279: PetscScalar (*restrict dpg)[2][PRMNODE_SIZE] = (PetscScalar(*)[2][PRMNODE_SIZE])dp;
282: PetscMemzero(dpg,4*sizeof(dpg[0]));
283: for (q=0; q<4; q++) {
284: for (i=0; i<4; i++) {
285: for (f=0; f<PRMNODE_SIZE; f++) {
286: dpg[q][0][f] += dphi[q][i][0]/hx * pg[i][f];
287: dpg[q][1][f] += dphi[q][i][1]/hy * pg[i][f];
288: }
289: }
290: }
291: return(0);
292: }
294: static inline PetscReal StaggeredMidpoint2D(PetscScalar a,PetscScalar b,PetscScalar c,PetscScalar d)
295: {return 0.5*PetscRealPart(0.75*a + 0.75*b + 0.25*c + 0.25*d);}
296: static inline PetscReal UpwindFlux1D(PetscReal u,PetscReal hL,PetscReal hR)
297: {return (u > 0) ? hL*u : hR*u;}
299: #define UpwindFluxXW(x3,x2,h,i,j,k,dj) UpwindFlux1D(StaggeredMidpoint2D(x3[i][j][k].u,x3[i-1][j][k].u, x3[i-1][j+dj][k].u,x3[i][k+dj][k].u), \
300: PetscRealPart(0.75*x2[i-1][j ].h+0.25*x2[i-1][j+dj].h), PetscRealPart(0.75*x2[i ][j ].h+0.25*x2[i ][j+dj].h))
301: #define UpwindFluxXE(x3,x2,h,i,j,k,dj) UpwindFlux1D(StaggeredMidpoint2D(x3[i][j][k].u,x3[i+1][j][k].u, x3[i+1][j+dj][k].u,x3[i][k+dj][k].u), \
302: PetscRealPart(0.75*x2[i ][j ].h+0.25*x2[i ][j+dj].h), PetscRealPart(0.75*x2[i+1][j ].h+0.25*x2[i+1][j+dj].h))
303: #define UpwindFluxYS(x3,x2,h,i,j,k,di) UpwindFlux1D(StaggeredMidpoint2D(x3[i][j][k].v,x3[i][j-1][k].v, x3[i+di][j-1][k].v,x3[i+di][j][k].v), \
304: PetscRealPart(0.75*x2[i ][j-1].h+0.25*x2[i+di][j-1].h), PetscRealPart(0.75*x2[i ][j ].h+0.25*x2[i+di][j ].h))
305: #define UpwindFluxYN(x3,x2,h,i,j,k,di) UpwindFlux1D(StaggeredMidpoint2D(x3[i][j][k].v,x3[i][j+1][k].v, x3[i+di][j+1][k].v,x3[i+di][j][k].v), \
306: PetscRealPart(0.75*x2[i ][j ].h+0.25*x2[i+di][j ].h), PetscRealPart(0.75*x2[i ][j+1].h+0.25*x2[i+di][j+1].h))
308: static void PrmNodeGetFaceMeasure(const PrmNode **p,PetscInt i,PetscInt j,PetscScalar h[])
309: {
310: /* West */
311: h[0] = StaggeredMidpoint2D(p[i][j].h,p[i-1][j].h,p[i-1][j-1].h,p[i][j-1].h);
312: h[1] = StaggeredMidpoint2D(p[i][j].h,p[i-1][j].h,p[i-1][j+1].h,p[i][j+1].h);
313: /* East */
314: h[2] = StaggeredMidpoint2D(p[i][j].h,p[i+1][j].h,p[i+1][j+1].h,p[i][j+1].h);
315: h[3] = StaggeredMidpoint2D(p[i][j].h,p[i+1][j].h,p[i+1][j-1].h,p[i][j-1].h);
316: /* South */
317: h[4] = StaggeredMidpoint2D(p[i][j].h,p[i][j-1].h,p[i+1][j-1].h,p[i+1][j].h);
318: h[5] = StaggeredMidpoint2D(p[i][j].h,p[i][j-1].h,p[i-1][j-1].h,p[i-1][j].h);
319: /* North */
320: h[6] = StaggeredMidpoint2D(p[i][j].h,p[i][j+1].h,p[i-1][j+1].h,p[i-1][j].h);
321: h[7] = StaggeredMidpoint2D(p[i][j].h,p[i][j+1].h,p[i+1][j+1].h,p[i+1][j].h);
322: }
324: /* Tests A and C are from the ISMIP-HOM paper (Pattyn et al. 2008) */
325: static void THIInitialize_HOM_A(THI thi,PetscReal x,PetscReal y,PrmNode *p)
326: {
327: Units units = thi->units;
328: PetscReal s = -x*sin(thi->alpha);
329: p->b = s - 1000*units->meter + 500*units->meter * sin(x*2*PETSC_PI/thi->Lx) * sin(y*2*PETSC_PI/thi->Ly);
330: p->h = s - p->b;
331: p->beta2 = -1e-10; /* This value is not used, but it should not be huge because that would change the finite difference step size */
332: }
334: static void THIInitialize_HOM_C(THI thi,PetscReal x,PetscReal y,PrmNode *p)
335: {
336: Units units = thi->units;
337: PetscReal s = -x*sin(thi->alpha);
338: p->b = s - 1000*units->meter;
339: p->h = s - p->b;
340: /* tau_b = beta2 v is a stress (Pa).
341: * This is a big number in our units (it needs to balance the driving force from the surface), so we scale it by 1/rhog, just like the residual. */
342: p->beta2 = 1000 * (1 + sin(x*2*PETSC_PI/thi->Lx)*sin(y*2*PETSC_PI/thi->Ly)) * units->Pascal * units->year / units->meter / thi->rhog;
343: }
345: /* These are just toys */
347: /* From Fred Herman */
348: static void THIInitialize_HOM_F(THI thi,PetscReal x,PetscReal y,PrmNode *p)
349: {
350: Units units = thi->units;
351: PetscReal s = -x*sin(thi->alpha);
352: p->b = s - 1000*units->meter + 100*units->meter * sin(x*2*PETSC_PI/thi->Lx);/* * sin(y*2*PETSC_PI/thi->Ly); */
353: p->h = s - p->b;
354: p->h = (1-(atan((x-thi->Lx/2)/1.)+PETSC_PI/2.)/PETSC_PI)*500*units->meter+1*units->meter;
355: s = PetscRealPart(p->b + p->h);
356: p->beta2 = -1e-10;
357: /* p->beta2 = 1000 * units->Pascal * units->year / units->meter; */
358: }
360: /* Same bed as test A, free slip everywhere except for a discontinuous jump to a circular sticky region in the middle. */
361: static void THIInitialize_HOM_X(THI thi,PetscReal xx,PetscReal yy,PrmNode *p)
362: {
363: Units units = thi->units;
364: PetscReal x = xx*2*PETSC_PI/thi->Lx - PETSC_PI,y = yy*2*PETSC_PI/thi->Ly - PETSC_PI; /* [-pi,pi] */
365: PetscReal r = PetscSqrtReal(x*x + y*y),s = -x*sin(thi->alpha);
366: p->b = s - 1000*units->meter + 500*units->meter * sin(x + PETSC_PI) * sin(y + PETSC_PI);
367: p->h = s - p->b;
368: p->beta2 = 1000 * (r < 1 ? 2 : 0) * units->Pascal * units->year / units->meter / thi->rhog;
369: }
371: /* Like Z, but with 200 meter cliffs */
372: static void THIInitialize_HOM_Y(THI thi,PetscReal xx,PetscReal yy,PrmNode *p)
373: {
374: Units units = thi->units;
375: PetscReal x = xx*2*PETSC_PI/thi->Lx - PETSC_PI,y = yy*2*PETSC_PI/thi->Ly - PETSC_PI; /* [-pi,pi] */
376: PetscReal r = PetscSqrtReal(x*x + y*y),s = -x*sin(thi->alpha);
377: p->b = s - 1000*units->meter + 500*units->meter * sin(x + PETSC_PI) * sin(y + PETSC_PI);
378: if (PetscRealPart(p->b) > -700*units->meter) p->b += 200*units->meter;
379: p->h = s - p->b;
380: p->beta2 = 1000 * (1. + sin(PetscSqrtReal(16*r))/PetscSqrtReal(1e-2 + 16*r)*cos(x*3/2)*cos(y*3/2)) * units->Pascal * units->year / units->meter / thi->rhog;
381: }
383: /* Same bed as A, smoothly varying slipperiness, similar to MATLAB's "sombrero" (uncorrelated with bathymetry) */
384: static void THIInitialize_HOM_Z(THI thi,PetscReal xx,PetscReal yy,PrmNode *p)
385: {
386: Units units = thi->units;
387: PetscReal x = xx*2*PETSC_PI/thi->Lx - PETSC_PI,y = yy*2*PETSC_PI/thi->Ly - PETSC_PI; /* [-pi,pi] */
388: PetscReal r = PetscSqrtReal(x*x + y*y),s = -x*sin(thi->alpha);
389: p->b = s - 1000*units->meter + 500*units->meter * sin(x + PETSC_PI) * sin(y + PETSC_PI);
390: p->h = s - p->b;
391: p->beta2 = 1000 * (1. + sin(PetscSqrtReal(16*r))/PetscSqrtReal(1e-2 + 16*r)*cos(x*3/2)*cos(y*3/2)) * units->Pascal * units->year / units->meter / thi->rhog;
392: }
394: static void THIFriction(THI thi,PetscReal rbeta2,PetscReal gam,PetscReal *beta2,PetscReal *dbeta2)
395: {
396: if (thi->friction.irefgam == 0) {
397: Units units = thi->units;
398: thi->friction.irefgam = 1./(0.5*PetscSqr(100 * units->meter / units->year));
399: thi->friction.eps2 = 0.5*PetscSqr(1.e-4 / thi->friction.irefgam);
400: }
401: if (thi->friction.exponent == 0) {
402: *beta2 = rbeta2;
403: *dbeta2 = 0;
404: } else {
405: *beta2 = rbeta2 * pow(thi->friction.eps2 + gam*thi->friction.irefgam,thi->friction.exponent);
406: *dbeta2 = thi->friction.exponent * *beta2 / (thi->friction.eps2 + gam*thi->friction.irefgam) * thi->friction.irefgam;
407: }
408: }
410: static void THIViscosity(THI thi,PetscReal gam,PetscReal *eta,PetscReal *deta)
411: {
412: PetscReal Bd2,eps,exponent;
413: if (thi->viscosity.Bd2 == 0) {
414: Units units = thi->units;
415: const PetscReal
416: n = thi->viscosity.glen_n, /* Glen exponent */
417: p = 1. + 1./n, /* for Stokes */
418: A = 1.e-16 * pow(units->Pascal,-n) / units->year, /* softness parameter (Pa^{-n}/s) */
419: B = pow(A,-1./n); /* hardness parameter */
420: thi->viscosity.Bd2 = B/2;
421: thi->viscosity.exponent = (p-2)/2;
422: thi->viscosity.eps = 0.5*PetscSqr(1e-5 / units->year);
423: }
424: Bd2 = thi->viscosity.Bd2;
425: exponent = thi->viscosity.exponent;
426: eps = thi->viscosity.eps;
427: *eta = Bd2 * pow(eps + gam,exponent);
428: *deta = exponent * (*eta) / (eps + gam);
429: }
431: static void THIErosion(THI thi,const Node *vel,PetscScalar *erate,Node *derate)
432: {
433: const PetscScalar magref2 = 1.e-10 + (PetscSqr(vel->u) + PetscSqr(vel->v)) / PetscSqr(thi->erosion.refvel),
434: rate = -thi->erosion.rate*PetscPowScalar(magref2, 0.5*thi->erosion.exponent);
435: if (erate) *erate = rate;
436: if (derate) {
437: if (thi->erosion.exponent == 1) {
438: derate->u = 0;
439: derate->v = 0;
440: } else {
441: derate->u = 0.5*thi->erosion.exponent * rate / magref2 * 2. * vel->u / PetscSqr(thi->erosion.refvel);
442: derate->v = 0.5*thi->erosion.exponent * rate / magref2 * 2. * vel->v / PetscSqr(thi->erosion.refvel);
443: }
444: }
445: }
447: static void RangeUpdate(PetscReal *min,PetscReal *max,PetscReal x)
448: {
449: if (x < *min) *min = x;
450: if (x > *max) *max = x;
451: }
453: static void PRangeClear(PRange *p)
454: {
455: p->cmin = p->min = 1e100;
456: p->cmax = p->max = -1e100;
457: }
461: static PetscErrorCode PRangeMinMax(PRange *p,PetscReal min,PetscReal max)
462: {
465: p->cmin = min;
466: p->cmax = max;
467: if (min < p->min) p->min = min;
468: if (max > p->max) p->max = max;
469: return(0);
470: }
474: static PetscErrorCode THIDestroy(THI *thi)
475: {
479: if (--((PetscObject)(*thi))->refct > 0) return(0);
480: PetscFree((*thi)->units);
481: PetscFree((*thi)->mattype);
482: PetscFree((*thi)->monitor_basename);
483: PetscHeaderDestroy(thi);
484: return(0);
485: }
489: static PetscErrorCode THICreate(MPI_Comm comm,THI *inthi)
490: {
491: static PetscBool registered = PETSC_FALSE;
492: THI thi;
493: Units units;
494: char monitor_basename[PETSC_MAX_PATH_LEN] = "thi-";
495: PetscErrorCode ierr;
498: *inthi = 0;
499: if (!registered) {
500: PetscClassIdRegister("Toy Hydrostatic Ice",&THI_CLASSID);
501: registered = PETSC_TRUE;
502: }
503: PetscHeaderCreate(thi,_p_THI,0,THI_CLASSID,"THI","Toy Hydrostatic Ice","THI",comm,THIDestroy,0);
505: PetscNew(struct _n_Units,&thi->units);
507: units = thi->units;
508: units->meter = 1e-2;
509: units->second = 1e-7;
510: units->kilogram = 1e-12;
512: PetscOptionsBegin(comm,NULL,"Scaled units options","");
513: {
514: PetscOptionsReal("-units_meter","1 meter in scaled length units","",units->meter,&units->meter,NULL);
515: PetscOptionsReal("-units_second","1 second in scaled time units","",units->second,&units->second,NULL);
516: PetscOptionsReal("-units_kilogram","1 kilogram in scaled mass units","",units->kilogram,&units->kilogram,NULL);
517: }
518: PetscOptionsEnd();
519: units->Pascal = units->kilogram / (units->meter * PetscSqr(units->second));
520: units->year = 31556926. * units->second, /* seconds per year */
522: thi->Lx = 10.e3;
523: thi->Ly = 10.e3;
524: thi->Lz = 1000;
525: thi->nlevels = 1;
526: thi->dirichlet_scale = 1;
527: thi->verbose = PETSC_FALSE;
529: thi->viscosity.glen_n = 3.;
530: thi->erosion.rate = 1e-3; /* m/a */
531: thi->erosion.exponent = 1.;
532: thi->erosion.refvel = 1.; /* m/a */
534: PetscOptionsBegin(comm,NULL,"Toy Hydrostatic Ice options","");
535: {
536: QuadratureType quad = QUAD_GAUSS;
537: char homexp[] = "A";
538: char mtype[256] = MATSBAIJ;
539: PetscReal L,m = 1.0;
540: PetscBool flg;
541: L = thi->Lx;
542: PetscOptionsReal("-thi_L","Domain size (m)","",L,&L,&flg);
543: if (flg) thi->Lx = thi->Ly = L;
544: PetscOptionsReal("-thi_Lx","X Domain size (m)","",thi->Lx,&thi->Lx,NULL);
545: PetscOptionsReal("-thi_Ly","Y Domain size (m)","",thi->Ly,&thi->Ly,NULL);
546: PetscOptionsReal("-thi_Lz","Z Domain size (m)","",thi->Lz,&thi->Lz,NULL);
547: PetscOptionsString("-thi_hom","ISMIP-HOM experiment (A or C)","",homexp,homexp,sizeof(homexp),NULL);
548: switch (homexp[0] = toupper(homexp[0])) {
549: case 'A':
550: thi->initialize = THIInitialize_HOM_A;
551: thi->no_slip = PETSC_TRUE;
552: thi->alpha = 0.5;
553: break;
554: case 'C':
555: thi->initialize = THIInitialize_HOM_C;
556: thi->no_slip = PETSC_FALSE;
557: thi->alpha = 0.1;
558: break;
559: case 'F':
560: thi->initialize = THIInitialize_HOM_F;
561: thi->no_slip = PETSC_FALSE;
562: thi->alpha = 0.5;
563: break;
564: case 'X':
565: thi->initialize = THIInitialize_HOM_X;
566: thi->no_slip = PETSC_FALSE;
567: thi->alpha = 0.3;
568: break;
569: case 'Y':
570: thi->initialize = THIInitialize_HOM_Y;
571: thi->no_slip = PETSC_FALSE;
572: thi->alpha = 0.5;
573: break;
574: case 'Z':
575: thi->initialize = THIInitialize_HOM_Z;
576: thi->no_slip = PETSC_FALSE;
577: thi->alpha = 0.5;
578: break;
579: default:
580: SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"HOM experiment '%c' not implemented",homexp[0]);
581: }
582: PetscOptionsEnum("-thi_quadrature","Quadrature to use for 3D elements","",QuadratureTypes,(PetscEnum)quad,(PetscEnum*)&quad,NULL);
583: switch (quad) {
584: case QUAD_GAUSS:
585: HexQInterp = HexQInterp_Gauss;
586: HexQDeriv = HexQDeriv_Gauss;
587: break;
588: case QUAD_LOBATTO:
589: HexQInterp = HexQInterp_Lobatto;
590: HexQDeriv = HexQDeriv_Lobatto;
591: break;
592: }
593: PetscOptionsReal("-thi_alpha","Bed angle (degrees)","",thi->alpha,&thi->alpha,NULL);
594: PetscOptionsReal("-thi_viscosity_glen_n","Exponent in Glen flow law, 1=linear, infty=ideal plastic",NULL,thi->viscosity.glen_n,&thi->viscosity.glen_n,NULL);
595: PetscOptionsReal("-thi_friction_m","Friction exponent, 0=Coulomb, 1=Navier","",m,&m,NULL);
596: thi->friction.exponent = (m-1)/2;
597: PetscOptionsReal("-thi_erosion_rate","Rate of erosion relative to sliding velocity at reference velocity (m/a)",NULL,thi->erosion.rate,&thi->erosion.rate,NULL);
598: PetscOptionsReal("-thi_erosion_exponent","Power of sliding velocity appearing in erosion relation",NULL,thi->erosion.exponent,&thi->erosion.exponent,NULL);
599: PetscOptionsReal("-thi_erosion_refvel","Reference sliding velocity for erosion (m/a)",NULL,thi->erosion.refvel,&thi->erosion.refvel,NULL);
600: thi->erosion.rate *= units->meter / units->year;
601: thi->erosion.refvel *= units->meter / units->year;
602: PetscOptionsReal("-thi_dirichlet_scale","Scale Dirichlet boundary conditions by this factor","",thi->dirichlet_scale,&thi->dirichlet_scale,NULL);
603: PetscOptionsReal("-thi_ssa_friction_scale","Scale slip boundary conditions by this factor in SSA (2D) assembly","",thi->ssa_friction_scale,&thi->ssa_friction_scale,NULL);
604: PetscOptionsReal("-thi_inertia","Coefficient of accelaration term in velocity system, physical is almost zero",NULL,thi->inertia,&thi->inertia,NULL);
605: PetscOptionsInt("-thi_nlevels","Number of levels of refinement","",thi->nlevels,&thi->nlevels,NULL);
606: PetscOptionsList("-thi_mat_type","Matrix type","MatSetType",MatList,mtype,(char*)mtype,sizeof(mtype),NULL);
607: PetscStrallocpy(mtype,&thi->mattype);
608: PetscOptionsBool("-thi_verbose","Enable verbose output (like matrix sizes and statistics)","",thi->verbose,&thi->verbose,NULL);
609: PetscOptionsString("-thi_monitor","Basename to write state files to",NULL,monitor_basename,monitor_basename,sizeof(monitor_basename),&flg);
610: if (flg) {
611: PetscStrallocpy(monitor_basename,&thi->monitor_basename);
612: thi->monitor_interval = 1;
613: PetscOptionsInt("-thi_monitor_interval","Frequency at which to write state files",NULL,thi->monitor_interval,&thi->monitor_interval,NULL);
614: }
615: }
616: PetscOptionsEnd();
618: /* dimensionalize */
619: thi->Lx *= units->meter;
620: thi->Ly *= units->meter;
621: thi->Lz *= units->meter;
622: thi->alpha *= PETSC_PI / 180;
624: PRangeClear(&thi->eta);
625: PRangeClear(&thi->beta2);
627: {
628: PetscReal u = 1000*units->meter/(3e7*units->second),
629: gradu = u / (100*units->meter),eta,deta,
630: rho = 910 * units->kilogram/pow(units->meter,3),
631: grav = 9.81 * units->meter/PetscSqr(units->second),
632: driving = rho * grav * sin(thi->alpha) * 1000*units->meter;
633: THIViscosity(thi,0.5*gradu*gradu,&eta,&deta);
634: thi->rhog = rho * grav;
635: if (thi->verbose) {
636: PetscPrintf(PetscObjectComm((PetscObject)thi),"Units: meter %8.2g second %8.2g kg %8.2g Pa %8.2g\n",units->meter,units->second,units->kilogram,units->Pascal);
637: PetscPrintf(PetscObjectComm((PetscObject)thi),"Domain (%6.2g,%6.2g,%6.2g), pressure %8.2g, driving stress %8.2g\n",thi->Lx,thi->Ly,thi->Lz,rho*grav*1e3*units->meter,driving);
638: PetscPrintf(PetscObjectComm((PetscObject)thi),"Large velocity 1km/a %8.2g, velocity gradient %8.2g, eta %8.2g, stress %8.2g, ratio %8.2g\n",u,gradu,eta,2*eta*gradu,2*eta*gradu/driving);
639: THIViscosity(thi,0.5*PetscSqr(1e-3*gradu),&eta,&deta);
640: PetscPrintf(PetscObjectComm((PetscObject)thi),"Small velocity 1m/a %8.2g, velocity gradient %8.2g, eta %8.2g, stress %8.2g, ratio %8.2g\n",1e-3*u,1e-3*gradu,eta,2*eta*1e-3*gradu,2*eta*1e-3*gradu/driving);
641: }
642: }
644: *inthi = thi;
645: return(0);
646: }
650: /* Our problem is periodic, but the domain has a mean slope of alpha so the bed does not line up between the upstream
651: * and downstream ends of the domain. This function fixes the ghost values so that the domain appears truly periodic in
652: * the horizontal. */
653: static PetscErrorCode THIFixGhosts(THI thi,DM da3,DM da2,Vec X3,Vec X2)
654: {
656: DMDALocalInfo info;
657: PrmNode **x2;
658: PetscInt i,j;
661: DMDAGetLocalInfo(da3,&info);
662: /* VecView(X2,PETSC_VIEWER_STDOUT_WORLD); */
663: DMDAVecGetArray(da2,X2,&x2);
664: for (i=info.gzs; i<info.gzs+info.gzm; i++) {
665: if (i > -1 && i < info.mz) continue;
666: for (j=info.gys; j<info.gys+info.gym; j++) {
667: x2[i][j].b += sin(thi->alpha) * thi->Lx * (i<0 ? 1.0 : -1.0);
668: }
669: }
670: DMDAVecRestoreArray(da2,X2,&x2);
671: /* VecView(X2,PETSC_VIEWER_STDOUT_WORLD); */
672: return(0);
673: }
677: static PetscErrorCode THIInitializePrm(THI thi,DM da2prm,PrmNode **p)
678: {
679: PetscInt i,j,xs,xm,ys,ym,mx,my;
683: DMDAGetGhostCorners(da2prm,&ys,&xs,0,&ym,&xm,0);
684: DMDAGetInfo(da2prm,0, &my,&mx,0, 0,0,0, 0,0,0,0,0,0);
685: for (i=xs; i<xs+xm; i++) {
686: for (j=ys; j<ys+ym; j++) {
687: PetscReal xx = thi->Lx*i/mx,yy = thi->Ly*j/my;
688: thi->initialize(thi,xx,yy,&p[i][j]);
689: }
690: }
691: return(0);
692: }
696: static PetscErrorCode THIInitial(THI thi,DM pack,Vec X)
697: {
698: DM da3,da2;
699: PetscInt i,j,k,xs,xm,ys,ym,zs,zm,mx,my;
700: PetscReal hx,hy;
701: PrmNode **prm;
702: Node ***x;
703: Vec X3g,X2g,X2;
707: DMCompositeGetEntries(pack,&da3,&da2);
708: DMCompositeGetAccess(pack,X,&X3g,&X2g);
709: DMGetLocalVector(da2,&X2);
711: DMDAGetInfo(da3,0, 0,&my,&mx, 0,0,0, 0,0,0,0,0,0);
712: DMDAGetCorners(da3,&zs,&ys,&xs,&zm,&ym,&xm);
713: DMDAVecGetArray(da3,X3g,&x);
714: DMDAVecGetArray(da2,X2,&prm);
716: THIInitializePrm(thi,da2,prm);
718: hx = thi->Lx / mx;
719: hy = thi->Ly / my;
720: for (i=xs; i<xs+xm; i++) {
721: for (j=ys; j<ys+ym; j++) {
722: for (k=zs; k<zs+zm; k++) {
723: const PetscScalar zm1 = zm-1,
724: drivingx = thi->rhog * (prm[i+1][j].b+prm[i+1][j].h - prm[i-1][j].b-prm[i-1][j].h) / (2*hx),
725: drivingy = thi->rhog * (prm[i][j+1].b+prm[i][j+1].h - prm[i][j-1].b-prm[i][j-1].h) / (2*hy);
726: x[i][j][k].u = 0. * drivingx * prm[i][j].h*(PetscScalar)k/zm1;
727: x[i][j][k].v = 0. * drivingy * prm[i][j].h*(PetscScalar)k/zm1;
728: }
729: }
730: }
732: DMDAVecRestoreArray(da3,X3g,&x);
733: DMDAVecRestoreArray(da2,X2,&prm);
735: DMLocalToGlobalBegin(da2,X2,INSERT_VALUES,X2g);
736: DMLocalToGlobalEnd (da2,X2,INSERT_VALUES,X2g);
737: DMRestoreLocalVector(da2,&X2);
739: DMCompositeRestoreAccess(pack,X,&X3g,&X2g);
740: return(0);
741: }
743: static void PointwiseNonlinearity(THI thi,const Node n[restrict 8],const PetscReal phi[restrict 3],PetscReal dphi[restrict 8][3],PetscScalar *restrict u,PetscScalar *restrict v,PetscScalar du[restrict 3],PetscScalar dv[restrict 3],PetscReal *eta,PetscReal *deta)
744: {
745: PetscInt l,ll;
746: PetscScalar gam;
748: du[0] = du[1] = du[2] = 0;
749: dv[0] = dv[1] = dv[2] = 0;
750: *u = 0;
751: *v = 0;
752: for (l=0; l<8; l++) {
753: *u += phi[l] * n[l].u;
754: *v += phi[l] * n[l].v;
755: for (ll=0; ll<3; ll++) {
756: du[ll] += dphi[l][ll] * n[l].u;
757: dv[ll] += dphi[l][ll] * n[l].v;
758: }
759: }
760: gam = Sqr(du[0]) + Sqr(dv[1]) + du[0]*dv[1] + 0.25*Sqr(du[1]+dv[0]) + 0.25*Sqr(du[2]) + 0.25*Sqr(dv[2]);
761: THIViscosity(thi,PetscRealPart(gam),eta,deta);
762: }
766: static PetscErrorCode THIFunctionLocal_3D(DMDALocalInfo *info,const Node ***x,const PrmNode **prm,const Node ***xdot,Node ***f,THI thi)
767: {
768: PetscInt xs,ys,xm,ym,zm,i,j,k,q,l;
769: PetscReal hx,hy,etamin,etamax,beta2min,beta2max;
773: xs = info->zs;
774: ys = info->ys;
775: xm = info->zm;
776: ym = info->ym;
777: zm = info->xm;
778: hx = thi->Lx / info->mz;
779: hy = thi->Ly / info->my;
781: etamin = 1e100;
782: etamax = 0;
783: beta2min = 1e100;
784: beta2max = 0;
786: for (i=xs; i<xs+xm; i++) {
787: for (j=ys; j<ys+ym; j++) {
788: PrmNode pn[4],dpn[4][2];
789: QuadExtract(prm,i,j,pn);
790: QuadComputeGrad4(QuadQDeriv,hx,hy,pn,dpn);
791: for (k=0; k<zm-1; k++) {
792: PetscInt ls = 0;
793: Node n[8],ndot[8],*fn[8];
794: PetscReal zn[8],etabase = 0;
795: PrmHexGetZ(pn,k,zm,zn);
796: HexExtract(x,i,j,k,n);
797: HexExtract(xdot,i,j,k,ndot);
798: HexExtractRef(f,i,j,k,fn);
799: if (thi->no_slip && k == 0) {
800: for (l=0; l<4; l++) n[l].u = n[l].v = 0;
801: /* The first 4 basis functions lie on the bottom layer, so their contribution is exactly 0, hence we can skip them */
802: ls = 4;
803: }
804: for (q=0; q<8; q++) {
805: PetscReal dz[3],phi[8],dphi[8][3],jw,eta,deta;
806: PetscScalar du[3],dv[3],u,v,udot=0,vdot=0;
807: for (l=ls; l<8; l++) {
808: udot += HexQInterp[q][l]*ndot[l].u;
809: vdot += HexQInterp[q][l]*ndot[l].v;
810: }
811: HexGrad(HexQDeriv[q],zn,dz);
812: HexComputeGeometry(q,hx,hy,dz,phi,dphi,&jw);
813: PointwiseNonlinearity(thi,n,phi,dphi,&u,&v,du,dv,&eta,&deta);
814: jw /= thi->rhog; /* scales residuals to be O(1) */
815: if (q == 0) etabase = eta;
816: RangeUpdate(&etamin,&etamax,eta);
817: for (l=ls; l<8; l++) { /* test functions */
818: const PetscScalar ds[2] = {dpn[q%4][0].h+dpn[q%4][0].b, dpn[q%4][1].h+dpn[q%4][1].b};
819: const PetscReal pp = phi[l],*dp = dphi[l];
820: fn[l]->u += dp[0]*jw*eta*(4.*du[0]+2.*dv[1]) + dp[1]*jw*eta*(du[1]+dv[0]) + dp[2]*jw*eta*du[2] + pp*jw*thi->rhog*ds[0];
821: fn[l]->v += dp[1]*jw*eta*(2.*du[0]+4.*dv[1]) + dp[0]*jw*eta*(du[1]+dv[0]) + dp[2]*jw*eta*dv[2] + pp*jw*thi->rhog*ds[1];
822: fn[l]->u += pp*jw*udot*thi->inertia*pp;
823: fn[l]->v += pp*jw*vdot*thi->inertia*pp;
824: }
825: }
826: if (k == 0) { /* we are on a bottom face */
827: if (thi->no_slip) {
828: /* Note: Non-Galerkin coarse grid operators are very sensitive to the scaling of Dirichlet boundary
829: * conditions. After shenanigans above, etabase contains the effective viscosity at the closest quadrature
830: * point to the bed. We want the diagonal entry in the Dirichlet condition to have similar magnitude to the
831: * diagonal entry corresponding to the adjacent node. The fundamental scaling of the viscous part is in
832: * diagu, diagv below. This scaling is easy to recognize by considering the finite difference operator after
833: * scaling by element size. The no-slip Dirichlet condition is scaled by this factor, and also in the
834: * assembled matrix (see the similar block in THIJacobianLocal).
835: *
836: * Note that the residual at this Dirichlet node is linear in the state at this node, but also depends
837: * (nonlinearly in general) on the neighboring interior nodes through the local viscosity. This will make
838: * a matrix-free Jacobian have extra entries in the corresponding row. We assemble only the diagonal part,
839: * so the solution will exactly satisfy the boundary condition after the first linear iteration.
840: */
841: const PetscReal hz = PetscRealPart(pn[0].h)/(zm-1.);
842: const PetscScalar diagu = 2*etabase/thi->rhog*(hx*hy/hz + hx*hz/hy + 4*hy*hz/hx),diagv = 2*etabase/thi->rhog*(hx*hy/hz + 4*hx*hz/hy + hy*hz/hx);
843: fn[0]->u = thi->dirichlet_scale*diagu*x[i][j][k].u;
844: fn[0]->v = thi->dirichlet_scale*diagv*x[i][j][k].v;
845: } else { /* Integrate over bottom face to apply boundary condition */
846: for (q=0; q<4; q++) { /* We remove the explicit scaling of the residual by 1/rhog because beta2 already has that scaling to be O(1) */
847: const PetscReal jw = 0.25*hx*hy,*phi = QuadQInterp[q];
848: PetscScalar u =0,v=0,rbeta2=0;
849: PetscReal beta2,dbeta2;
850: for (l=0; l<4; l++) {
851: u += phi[l]*n[l].u;
852: v += phi[l]*n[l].v;
853: rbeta2 += phi[l]*pn[l].beta2;
854: }
855: THIFriction(thi,PetscRealPart(rbeta2),PetscRealPart(u*u+v*v)/2,&beta2,&dbeta2);
856: RangeUpdate(&beta2min,&beta2max,beta2);
857: for (l=0; l<4; l++) {
858: const PetscReal pp = phi[l];
859: fn[ls+l]->u += pp*jw*beta2*u;
860: fn[ls+l]->v += pp*jw*beta2*v;
861: }
862: }
863: }
864: }
865: }
866: }
867: }
869: PRangeMinMax(&thi->eta,etamin,etamax);
870: PRangeMinMax(&thi->beta2,beta2min,beta2max);
871: return(0);
872: }
876: static PetscErrorCode THIFunctionLocal_2D(DMDALocalInfo *info,const Node ***x,const PrmNode **prm,const PrmNode **prmdot,PrmNode **f,THI thi)
877: {
878: PetscInt xs,ys,xm,ym,zm,i,j,k;
881: xs = info->zs;
882: ys = info->ys;
883: xm = info->zm;
884: ym = info->ym;
885: zm = info->xm;
887: for (i=xs; i<xs+xm; i++) {
888: for (j=ys; j<ys+ym; j++) {
889: PetscScalar div = 0,erate,h[8];
890: PrmNodeGetFaceMeasure(prm,i,j,h);
891: for (k=0; k<zm; k++) {
892: PetscScalar weight = (k==0 || k == zm-1) ? 0.5/(zm-1) : 1.0/(zm-1);
893: if (0) { /* centered flux */
894: div += (- weight*h[0] * StaggeredMidpoint2D(x[i][j][k].u,x[i-1][j][k].u, x[i-1][j-1][k].u,x[i][j-1][k].u)
895: - weight*h[1] * StaggeredMidpoint2D(x[i][j][k].u,x[i-1][j][k].u, x[i-1][j+1][k].u,x[i][j+1][k].u)
896: + weight*h[2] * StaggeredMidpoint2D(x[i][j][k].u,x[i+1][j][k].u, x[i+1][j+1][k].u,x[i][j+1][k].u)
897: + weight*h[3] * StaggeredMidpoint2D(x[i][j][k].u,x[i+1][j][k].u, x[i+1][j-1][k].u,x[i][j-1][k].u)
898: - weight*h[4] * StaggeredMidpoint2D(x[i][j][k].v,x[i][j-1][k].v, x[i+1][j-1][k].v,x[i+1][j][k].v)
899: - weight*h[5] * StaggeredMidpoint2D(x[i][j][k].v,x[i][j-1][k].v, x[i-1][j-1][k].v,x[i-1][j][k].v)
900: + weight*h[6] * StaggeredMidpoint2D(x[i][j][k].v,x[i][j+1][k].v, x[i-1][j+1][k].v,x[i-1][j][k].v)
901: + weight*h[7] * StaggeredMidpoint2D(x[i][j][k].v,x[i][j+1][k].v, x[i+1][j+1][k].v,x[i+1][j][k].v));
902: } else { /* Upwind flux */
903: div += weight*(-UpwindFluxXW(x,prm,h,i,j,k, 1)
904: -UpwindFluxXW(x,prm,h,i,j,k,-1)
905: +UpwindFluxXE(x,prm,h,i,j,k, 1)
906: +UpwindFluxXE(x,prm,h,i,j,k,-1)
907: -UpwindFluxYS(x,prm,h,i,j,k, 1)
908: -UpwindFluxYS(x,prm,h,i,j,k,-1)
909: +UpwindFluxYN(x,prm,h,i,j,k, 1)
910: +UpwindFluxYN(x,prm,h,i,j,k,-1));
911: }
912: }
913: /* printf("div[%d][%d] %g\n",i,j,div); */
914: THIErosion(thi,&x[i][j][0],&erate,NULL);
915: f[i][j].b = prmdot[i][j].b - erate;
916: f[i][j].h = prmdot[i][j].h + div;
917: f[i][j].beta2 = prmdot[i][j].beta2;
918: }
919: }
920: return(0);
921: }
925: static PetscErrorCode THIFunction(TS ts,PetscReal t,Vec X,Vec Xdot,Vec F,void *ctx)
926: {
928: THI thi = (THI)ctx;
929: DM pack,da3,da2;
930: Vec X3,X2,Xdot3,Xdot2,F3,F2,F3g,F2g;
931: const Node ***x3,***xdot3;
932: const PrmNode **x2,**xdot2;
933: Node ***f3;
934: PrmNode **f2;
935: DMDALocalInfo info3;
938: TSGetDM(ts,&pack);
939: DMCompositeGetEntries(pack,&da3,&da2);
940: DMDAGetLocalInfo(da3,&info3);
941: DMCompositeGetLocalVectors(pack,&X3,&X2);
942: DMCompositeGetLocalVectors(pack,&Xdot3,&Xdot2);
943: DMCompositeScatter(pack,X,X3,X2);
944: THIFixGhosts(thi,da3,da2,X3,X2);
945: DMCompositeScatter(pack,Xdot,Xdot3,Xdot2);
947: DMGetLocalVector(da3,&F3);
948: DMGetLocalVector(da2,&F2);
949: VecZeroEntries(F3);
951: DMDAVecGetArray(da3,X3,&x3);
952: DMDAVecGetArray(da2,X2,&x2);
953: DMDAVecGetArray(da3,Xdot3,&xdot3);
954: DMDAVecGetArray(da2,Xdot2,&xdot2);
955: DMDAVecGetArray(da3,F3,&f3);
956: DMDAVecGetArray(da2,F2,&f2);
958: THIFunctionLocal_3D(&info3,x3,x2,xdot3,f3,thi);
959: THIFunctionLocal_2D(&info3,x3,x2,xdot2,f2,thi);
961: DMDAVecRestoreArray(da3,X3,&x3);
962: DMDAVecRestoreArray(da2,X2,&x2);
963: DMDAVecRestoreArray(da3,Xdot3,&xdot3);
964: DMDAVecRestoreArray(da2,Xdot2,&xdot2);
965: DMDAVecRestoreArray(da3,F3,&f3);
966: DMDAVecRestoreArray(da2,F2,&f2);
968: DMCompositeRestoreLocalVectors(pack,&X3,&X2);
969: DMCompositeRestoreLocalVectors(pack,&Xdot3,&Xdot2);
971: VecZeroEntries(F);
972: DMCompositeGetAccess(pack,F,&F3g,&F2g);
973: DMLocalToGlobalBegin(da3,F3,ADD_VALUES,F3g);
974: DMLocalToGlobalEnd (da3,F3,ADD_VALUES,F3g);
975: DMLocalToGlobalBegin(da2,F2,INSERT_VALUES,F2g);
976: DMLocalToGlobalEnd (da2,F2,INSERT_VALUES,F2g);
978: if (thi->verbose) {
979: PetscViewer viewer;
980: PetscViewerASCIIGetStdout(PetscObjectComm((PetscObject)thi),&viewer);
981: PetscViewerASCIIPrintf(viewer,"3D_Velocity residual (bs=2):\n");
982: PetscViewerASCIIPushTab(viewer);
983: VecView(F3,viewer);
984: PetscViewerASCIIPopTab(viewer);
985: PetscViewerASCIIPrintf(viewer,"2D_Fields residual (bs=3):\n");
986: PetscViewerASCIIPushTab(viewer);
987: VecView(F2,viewer);
988: PetscViewerASCIIPopTab(viewer);
989: }
991: DMCompositeRestoreAccess(pack,F,&F3g,&F2g);
993: DMRestoreLocalVector(da3,&F3);
994: DMRestoreLocalVector(da2,&F2);
995: return(0);
996: }
1000: static PetscErrorCode THIMatrixStatistics(THI thi,Mat B,PetscViewer viewer)
1001: {
1003: PetscReal nrm;
1004: PetscInt m;
1005: PetscMPIInt rank;
1008: MatNorm(B,NORM_FROBENIUS,&nrm);
1009: MatGetSize(B,&m,0);
1010: MPI_Comm_rank(PetscObjectComm((PetscObject)B),&rank);
1011: if (!rank) {
1012: PetscScalar val0,val2;
1013: MatGetValue(B,0,0,&val0);
1014: MatGetValue(B,2,2,&val2);
1015: PetscViewerASCIIPrintf(viewer,"Matrix dim %8d norm %8.2e, (0,0) %8.2e (2,2) %8.2e, eta [%8.2e,%8.2e] beta2 [%8.2e,%8.2e]\n",m,nrm,PetscRealPart(val0),PetscRealPart(val2),thi->eta.cmin,thi->eta.cmax,thi->beta2.cmin,thi->beta2.cmax);
1016: }
1017: return(0);
1018: }
1022: static PetscErrorCode THISurfaceStatistics(DM pack,Vec X,PetscReal *min,PetscReal *max,PetscReal *mean)
1023: {
1025: DM da3,da2;
1026: Vec X3,X2;
1027: Node ***x;
1028: PetscInt i,j,xs,ys,zs,xm,ym,zm,mx,my,mz;
1029: PetscReal umin = 1e100,umax=-1e100;
1030: PetscScalar usum =0.0,gusum;
1033: DMCompositeGetEntries(pack,&da3,&da2);
1034: DMCompositeGetAccess(pack,X,&X3,&X2);
1035: *min = *max = *mean = 0;
1036: DMDAGetInfo(da3,0, &mz,&my,&mx, 0,0,0, 0,0,0,0,0,0);
1037: DMDAGetCorners(da3,&zs,&ys,&xs,&zm,&ym,&xm);
1038: if (zs != 0 || zm != mz) SETERRQ(PETSC_COMM_SELF,1,"Unexpected decomposition");
1039: DMDAVecGetArray(da3,X3,&x);
1040: for (i=xs; i<xs+xm; i++) {
1041: for (j=ys; j<ys+ym; j++) {
1042: PetscReal u = PetscRealPart(x[i][j][zm-1].u);
1043: RangeUpdate(&umin,&umax,u);
1044: usum += u;
1045: }
1046: }
1047: DMDAVecRestoreArray(da3,X3,&x);
1048: DMCompositeRestoreAccess(pack,X,&X3,&X2);
1050: MPI_Allreduce(&umin,min,1,MPIU_REAL,MPIU_MIN,PetscObjectComm((PetscObject)da3));
1051: MPI_Allreduce(&umax,max,1,MPIU_REAL,MPIU_MAX,PetscObjectComm((PetscObject)da3));
1052: MPI_Allreduce(&usum,&gusum,1,MPIU_SCALAR,MPIU_SUM,PetscObjectComm((PetscObject)da3));
1053: *mean = PetscRealPart(gusum) / (mx*my);
1054: return(0);
1055: }
1059: static PetscErrorCode THISolveStatistics(THI thi,TS ts,PetscInt coarsened,const char name[])
1060: {
1061: MPI_Comm comm;
1062: DM pack;
1063: Vec X,X3,X2;
1067: PetscObjectGetComm((PetscObject)thi,&comm);
1068: TSGetDM(ts,&pack);
1069: TSGetSolution(ts,&X);
1070: DMCompositeGetAccess(pack,X,&X3,&X2);
1071: PetscPrintf(comm,"Solution statistics after solve: %s\n",name);
1072: {
1073: PetscInt its,lits;
1074: SNESConvergedReason reason;
1075: SNES snes;
1076: TSGetSNES(ts,&snes);
1077: SNESGetIterationNumber(snes,&its);
1078: SNESGetConvergedReason(snes,&reason);
1079: SNESGetLinearSolveIterations(snes,&lits);
1080: PetscPrintf(comm,"%s: Number of SNES iterations = %d, total linear iterations = %d\n",SNESConvergedReasons[reason],its,lits);
1081: }
1082: {
1083: PetscReal nrm2,tmin[3]={1e100,1e100,1e100},tmax[3]={-1e100,-1e100,-1e100},min[3],max[3];
1084: PetscInt i,j,m;
1085: PetscScalar *x;
1086: VecNorm(X3,NORM_2,&nrm2);
1087: VecGetLocalSize(X3,&m);
1088: VecGetArray(X3,&x);
1089: for (i=0; i<m; i+=2) {
1090: PetscReal u = PetscRealPart(x[i]),v = PetscRealPart(x[i+1]),c = PetscSqrtReal(u*u+v*v);
1091: tmin[0] = PetscMin(u,tmin[0]);
1092: tmin[1] = PetscMin(v,tmin[1]);
1093: tmin[2] = PetscMin(c,tmin[2]);
1094: tmax[0] = PetscMax(u,tmax[0]);
1095: tmax[1] = PetscMax(v,tmax[1]);
1096: tmax[2] = PetscMax(c,tmax[2]);
1097: }
1098: VecRestoreArray(X,&x);
1099: MPI_Allreduce(tmin,min,3,MPIU_REAL,MPIU_MIN,PetscObjectComm((PetscObject)thi));
1100: MPI_Allreduce(tmax,max,3,MPIU_REAL,MPIU_MAX,PetscObjectComm((PetscObject)thi));
1101: /* Dimensionalize to meters/year */
1102: nrm2 *= thi->units->year / thi->units->meter;
1103: for (j=0; j<3; j++) {
1104: min[j] *= thi->units->year / thi->units->meter;
1105: max[j] *= thi->units->year / thi->units->meter;
1106: }
1107: PetscPrintf(comm,"|X|_2 %g u in [%g, %g] v in [%g, %g] c in [%g, %g] \n",nrm2,min[0],max[0],min[1],max[1],min[2],max[2]);
1108: {
1109: PetscReal umin,umax,umean;
1110: THISurfaceStatistics(pack,X,&umin,&umax,&umean);
1111: umin *= thi->units->year / thi->units->meter;
1112: umax *= thi->units->year / thi->units->meter;
1113: umean *= thi->units->year / thi->units->meter;
1114: PetscPrintf(comm,"Surface statistics: u in [%12.6e, %12.6e] mean %12.6e\n",umin,umax,umean);
1115: }
1116: /* These values stay nondimensional */
1117: PetscPrintf(comm,"Global eta range [%g, %g], converged range [%g, %g]\n",thi->eta.min,thi->eta.max,thi->eta.cmin,thi->eta.cmax);
1118: PetscPrintf(comm,"Global beta2 range [%g, %g], converged range [%g, %g]\n",thi->beta2.min,thi->beta2.max,thi->beta2.cmin,thi->beta2.cmax);
1119: }
1120: PetscPrintf(comm,"\n");
1121: DMCompositeRestoreAccess(pack,X,&X3,&X2);
1122: return(0);
1123: }
1125: static inline PetscInt DMDALocalIndex3D(DMDALocalInfo *info,PetscInt i,PetscInt j,PetscInt k)
1126: {return ((i-info->gzs)*info->gym + (j-info->gys))*info->gxm + (k-info->gxs);}
1127: static inline PetscInt DMDALocalIndex2D(DMDALocalInfo *info,PetscInt i,PetscInt j)
1128: {return (i-info->gzs)*info->gym + (j-info->gys);}
1132: static PetscErrorCode THIJacobianLocal_Momentum(DMDALocalInfo *info,const Node ***x,const PrmNode **prm,Mat B,Mat Bcpl,THI thi)
1133: {
1134: PetscInt xs,ys,xm,ym,zm,i,j,k,q,l,ll;
1135: PetscReal hx,hy;
1139: xs = info->zs;
1140: ys = info->ys;
1141: xm = info->zm;
1142: ym = info->ym;
1143: zm = info->xm;
1144: hx = thi->Lx / info->mz;
1145: hy = thi->Ly / info->my;
1147: for (i=xs; i<xs+xm; i++) {
1148: for (j=ys; j<ys+ym; j++) {
1149: PrmNode pn[4],dpn[4][2];
1150: QuadExtract(prm,i,j,pn);
1151: QuadComputeGrad4(QuadQDeriv,hx,hy,pn,dpn);
1152: for (k=0; k<zm-1; k++) {
1153: Node n[8];
1154: PetscReal zn[8],etabase = 0;
1155: PetscScalar Ke[8*NODE_SIZE][8*NODE_SIZE],Kcpl[8*NODE_SIZE][4*PRMNODE_SIZE];
1156: PetscInt ls = 0;
1158: PrmHexGetZ(pn,k,zm,zn);
1159: HexExtract(x,i,j,k,n);
1160: PetscMemzero(Ke,sizeof(Ke));
1161: PetscMemzero(Kcpl,sizeof(Kcpl));
1162: if (thi->no_slip && k == 0) {
1163: for (l=0; l<4; l++) n[l].u = n[l].v = 0;
1164: ls = 4;
1165: }
1166: for (q=0; q<8; q++) {
1167: PetscReal dz[3],phi[8],dphi[8][3],jw,eta,deta;
1168: PetscScalar du[3],dv[3],u,v;
1169: HexGrad(HexQDeriv[q],zn,dz);
1170: HexComputeGeometry(q,hx,hy,dz,phi,dphi,&jw);
1171: PointwiseNonlinearity(thi,n,phi,dphi,&u,&v,du,dv,&eta,&deta);
1172: jw /= thi->rhog; /* residuals are scaled by this factor */
1173: if (q == 0) etabase = eta;
1174: for (l=ls; l<8; l++) { /* test functions */
1175: const PetscReal pp=phi[l],*restrict dp = dphi[l];
1176: for (ll=ls; ll<8; ll++) { /* trial functions */
1177: const PetscReal *restrict dpl = dphi[ll];
1178: PetscScalar dgdu,dgdv;
1179: dgdu = 2.*du[0]*dpl[0] + dv[1]*dpl[0] + 0.5*(du[1]+dv[0])*dpl[1] + 0.5*du[2]*dpl[2];
1180: dgdv = 2.*dv[1]*dpl[1] + du[0]*dpl[1] + 0.5*(du[1]+dv[0])*dpl[0] + 0.5*dv[2]*dpl[2];
1181: /* Picard part */
1182: Ke[l*2+0][ll*2+0] += dp[0]*jw*eta*4.*dpl[0] + dp[1]*jw*eta*dpl[1] + dp[2]*jw*eta*dpl[2];
1183: Ke[l*2+0][ll*2+1] += dp[0]*jw*eta*2.*dpl[1] + dp[1]*jw*eta*dpl[0];
1184: Ke[l*2+1][ll*2+0] += dp[1]*jw*eta*2.*dpl[0] + dp[0]*jw*eta*dpl[1];
1185: Ke[l*2+1][ll*2+1] += dp[1]*jw*eta*4.*dpl[1] + dp[0]*jw*eta*dpl[0] + dp[2]*jw*eta*dpl[2];
1186: /* extra Newton terms */
1187: Ke[l*2+0][ll*2+0] += dp[0]*jw*deta*dgdu*(4.*du[0]+2.*dv[1]) + dp[1]*jw*deta*dgdu*(du[1]+dv[0]) + dp[2]*jw*deta*dgdu*du[2];
1188: Ke[l*2+0][ll*2+1] += dp[0]*jw*deta*dgdv*(4.*du[0]+2.*dv[1]) + dp[1]*jw*deta*dgdv*(du[1]+dv[0]) + dp[2]*jw*deta*dgdv*du[2];
1189: Ke[l*2+1][ll*2+0] += dp[1]*jw*deta*dgdu*(4.*dv[1]+2.*du[0]) + dp[0]*jw*deta*dgdu*(du[1]+dv[0]) + dp[2]*jw*deta*dgdu*dv[2];
1190: Ke[l*2+1][ll*2+1] += dp[1]*jw*deta*dgdv*(4.*dv[1]+2.*du[0]) + dp[0]*jw*deta*dgdv*(du[1]+dv[0]) + dp[2]*jw*deta*dgdv*dv[2];
1191: /* inertial part */
1192: Ke[l*2+0][ll*2+0] += pp*jw*thi->inertia*pp;
1193: Ke[l*2+1][ll*2+1] += pp*jw*thi->inertia*pp;
1194: }
1195: for (ll=0; ll<4; ll++) { /* Trial functions for surface/bed */
1196: const PetscReal dpl[] = {QuadQDeriv[q%4][ll][0]/hx, QuadQDeriv[q%4][ll][1]/hy}; /* surface = h + b */
1197: Kcpl[FieldIndex(Node,l,u)][FieldIndex(PrmNode,ll,h)] += pp*jw*thi->rhog*dpl[0];
1198: Kcpl[FieldIndex(Node,l,u)][FieldIndex(PrmNode,ll,b)] += pp*jw*thi->rhog*dpl[0];
1199: Kcpl[FieldIndex(Node,l,v)][FieldIndex(PrmNode,ll,h)] += pp*jw*thi->rhog*dpl[1];
1200: Kcpl[FieldIndex(Node,l,v)][FieldIndex(PrmNode,ll,b)] += pp*jw*thi->rhog*dpl[1];
1201: }
1202: }
1203: }
1204: if (k == 0) { /* on a bottom face */
1205: if (thi->no_slip) {
1206: const PetscReal hz = PetscRealPart(pn[0].h)/(zm-1);
1207: const PetscScalar diagu = 2*etabase/thi->rhog*(hx*hy/hz + hx*hz/hy + 4*hy*hz/hx),diagv = 2*etabase/thi->rhog*(hx*hy/hz + 4*hx*hz/hy + hy*hz/hx);
1208: Ke[0][0] = thi->dirichlet_scale*diagu;
1209: Ke[0][1] = 0;
1210: Ke[1][0] = 0;
1211: Ke[1][1] = thi->dirichlet_scale*diagv;
1212: } else {
1213: for (q=0; q<4; q++) { /* We remove the explicit scaling by 1/rhog because beta2 already has that scaling to be O(1) */
1214: const PetscReal jw = 0.25*hx*hy,*phi = QuadQInterp[q];
1215: PetscScalar u =0,v=0,rbeta2=0;
1216: PetscReal beta2,dbeta2;
1217: for (l=0; l<4; l++) {
1218: u += phi[l]*n[l].u;
1219: v += phi[l]*n[l].v;
1220: rbeta2 += phi[l]*pn[l].beta2;
1221: }
1222: THIFriction(thi,PetscRealPart(rbeta2),PetscRealPart(u*u+v*v)/2,&beta2,&dbeta2);
1223: for (l=0; l<4; l++) {
1224: const PetscReal pp = phi[l];
1225: for (ll=0; ll<4; ll++) {
1226: const PetscReal ppl = phi[ll];
1227: Ke[l*2+0][ll*2+0] += pp*jw*beta2*ppl + pp*jw*dbeta2*u*u*ppl;
1228: Ke[l*2+0][ll*2+1] += pp*jw*dbeta2*u*v*ppl;
1229: Ke[l*2+1][ll*2+0] += pp*jw*dbeta2*v*u*ppl;
1230: Ke[l*2+1][ll*2+1] += pp*jw*beta2*ppl + pp*jw*dbeta2*v*v*ppl;
1231: }
1232: }
1233: }
1234: }
1235: }
1236: {
1237: const PetscInt rc3blocked[8] = {
1238: DMDALocalIndex3D(info,i+0,j+0,k+0),
1239: DMDALocalIndex3D(info,i+1,j+0,k+0),
1240: DMDALocalIndex3D(info,i+1,j+1,k+0),
1241: DMDALocalIndex3D(info,i+0,j+1,k+0),
1242: DMDALocalIndex3D(info,i+0,j+0,k+1),
1243: DMDALocalIndex3D(info,i+1,j+0,k+1),
1244: DMDALocalIndex3D(info,i+1,j+1,k+1),
1245: DMDALocalIndex3D(info,i+0,j+1,k+1)
1246: },col2blocked[PRMNODE_SIZE*4] = {
1247: DMDALocalIndex2D(info,i+0,j+0),
1248: DMDALocalIndex2D(info,i+1,j+0),
1249: DMDALocalIndex2D(info,i+1,j+1),
1250: DMDALocalIndex2D(info,i+0,j+1)
1251: };
1252: #if !defined COMPUTE_LOWER_TRIANGULAR /* fill in lower-triangular part, this is really cheap compared to computing the entries */
1253: for (l=0; l<8; l++) {
1254: for (ll=l+1; ll<8; ll++) {
1255: Ke[ll*2+0][l*2+0] = Ke[l*2+0][ll*2+0];
1256: Ke[ll*2+1][l*2+0] = Ke[l*2+0][ll*2+1];
1257: Ke[ll*2+0][l*2+1] = Ke[l*2+1][ll*2+0];
1258: Ke[ll*2+1][l*2+1] = Ke[l*2+1][ll*2+1];
1259: }
1260: }
1261: #endif
1262: MatSetValuesBlockedLocal(B,8,rc3blocked,8,rc3blocked,&Ke[0][0],ADD_VALUES); /* velocity-velocity coupling can use blocked insertion */
1263: { /* The off-diagonal part cannot (yet) */
1264: PetscInt row3scalar[NODE_SIZE*8],col2scalar[PRMNODE_SIZE*4];
1265: for (l=0; l<8; l++) for (ll=0; ll<NODE_SIZE; ll++) row3scalar[l*NODE_SIZE+ll] = rc3blocked[l]*NODE_SIZE+ll;
1266: for (l=0; l<4; l++) for (ll=0; ll<PRMNODE_SIZE; ll++) col2scalar[l*PRMNODE_SIZE+ll] = col2blocked[l]*PRMNODE_SIZE+ll;
1267: MatSetValuesLocal(Bcpl,8*NODE_SIZE,row3scalar,4*PRMNODE_SIZE,col2scalar,&Kcpl[0][0],ADD_VALUES);
1268: }
1269: }
1270: }
1271: }
1272: }
1273: return(0);
1274: }
1278: static PetscErrorCode THIJacobianLocal_2D(DMDALocalInfo *info,const Node ***x3,const PrmNode **x2,const PrmNode **xdot2,PetscReal a,Mat B22,Mat B21,THI thi)
1279: {
1281: PetscInt xs,ys,xm,ym,zm,i,j,k;
1284: xs = info->zs;
1285: ys = info->ys;
1286: xm = info->zm;
1287: ym = info->ym;
1288: zm = info->xm;
1290: if (zm > 1024) SETERRQ(((PetscObject)info->da)->comm,PETSC_ERR_SUP,"Need to allocate more space");
1291: for (i=xs; i<xs+xm; i++) {
1292: for (j=ys; j<ys+ym; j++) {
1293: { /* Self-coupling */
1294: const PetscInt row[] = {DMDALocalIndex2D(info,i,j)};
1295: const PetscInt col[] = {DMDALocalIndex2D(info,i,j)};
1296: const PetscScalar vals[] = {
1297: a,0,0,
1298: 0,a,0,
1299: 0,0,a
1300: };
1301: MatSetValuesBlockedLocal(B22,1,row,1,col,vals,INSERT_VALUES);
1302: }
1303: for (k=0; k<zm; k++) { /* Coupling to velocity problem */
1304: /* Use a cheaper quadrature than for residual evaluation, because it is much sparser */
1305: const PetscInt row[] = {FieldIndex(PrmNode,DMDALocalIndex2D(info,i,j),h)};
1306: const PetscInt cols[] = {
1307: FieldIndex(Node,DMDALocalIndex3D(info,i-1,j,k),u),
1308: FieldIndex(Node,DMDALocalIndex3D(info,i ,j,k),u),
1309: FieldIndex(Node,DMDALocalIndex3D(info,i+1,j,k),u),
1310: FieldIndex(Node,DMDALocalIndex3D(info,i,j-1,k),v),
1311: FieldIndex(Node,DMDALocalIndex3D(info,i,j ,k),v),
1312: FieldIndex(Node,DMDALocalIndex3D(info,i,j+1,k),v)
1313: };
1314: const PetscScalar
1315: w = (k && k<zm-1) ? 0.5 : 0.25,
1316: hW = w*(x2[i-1][j ].h+x2[i ][j ].h)/(zm-1.),
1317: hE = w*(x2[i ][j ].h+x2[i+1][j ].h)/(zm-1.),
1318: hS = w*(x2[i ][j-1].h+x2[i ][j ].h)/(zm-1.),
1319: hN = w*(x2[i ][j ].h+x2[i ][j+1].h)/(zm-1.);
1320: PetscScalar *vals,
1321: vals_upwind[] = {((PetscRealPart(x3[i][j][k].u) > 0) ? -hW : 0),
1322: ((PetscRealPart(x3[i][j][k].u) > 0) ? +hE : -hW),
1323: ((PetscRealPart(x3[i][j][k].u) > 0) ? 0 : +hE),
1324: ((PetscRealPart(x3[i][j][k].v) > 0) ? -hS : 0),
1325: ((PetscRealPart(x3[i][j][k].v) > 0) ? +hN : -hS),
1326: ((PetscRealPart(x3[i][j][k].v) > 0) ? 0 : +hN)},
1327: vals_centered[] = {-0.5*hW, 0.5*(-hW+hE), 0.5*hE,
1328: -0.5*hS, 0.5*(-hS+hN), 0.5*hN};
1329: vals = 1 ? vals_upwind : vals_centered;
1330: if (k == 0) {
1331: Node derate;
1332: THIErosion(thi,&x3[i][j][0],NULL,&derate);
1333: vals[1] -= derate.u;
1334: vals[4] -= derate.v;
1335: }
1336: MatSetValuesLocal(B21,1,row,6,cols,vals,INSERT_VALUES);
1337: }
1338: }
1339: }
1340: return(0);
1341: }
1345: static PetscErrorCode THIJacobian(TS ts,PetscReal t,Vec X,Vec Xdot,PetscReal a,Mat *A,Mat *B,MatStructure *mstr,void *ctx)
1346: {
1348: THI thi = (THI)ctx;
1349: DM pack,da3,da2;
1350: Vec X3,X2,Xdot2;
1351: Mat B11,B12,B21,B22;
1352: DMDALocalInfo info3;
1353: IS *isloc;
1354: const Node ***x3;
1355: const PrmNode **x2,**xdot2;
1358: TSGetDM(ts,&pack);
1359: DMCompositeGetEntries(pack,&da3,&da2);
1360: DMDAGetLocalInfo(da3,&info3);
1361: DMCompositeGetLocalVectors(pack,&X3,&X2);
1362: DMCompositeGetLocalVectors(pack,NULL,&Xdot2);
1363: DMCompositeScatter(pack,X,X3,X2);
1364: THIFixGhosts(thi,da3,da2,X3,X2);
1365: DMCompositeScatter(pack,Xdot,NULL,Xdot2);
1367: MatZeroEntries(*B);
1369: DMCompositeGetLocalISs(pack,&isloc);
1370: MatGetLocalSubMatrix(*B,isloc[0],isloc[0],&B11);
1371: MatGetLocalSubMatrix(*B,isloc[0],isloc[1],&B12);
1372: MatGetLocalSubMatrix(*B,isloc[1],isloc[0],&B21);
1373: MatGetLocalSubMatrix(*B,isloc[1],isloc[1],&B22);
1375: DMDAVecGetArray(da3,X3,&x3);
1376: DMDAVecGetArray(da2,X2,&x2);
1377: DMDAVecGetArray(da2,Xdot2,&xdot2);
1379: THIJacobianLocal_Momentum(&info3,x3,x2,B11,B12,thi);
1381: /* Need to switch from ADD_VALUES to INSERT_VALUES */
1382: MatAssemblyBegin(*B,MAT_FLUSH_ASSEMBLY);
1383: MatAssemblyEnd(*B,MAT_FLUSH_ASSEMBLY);
1385: THIJacobianLocal_2D(&info3,x3,x2,xdot2,a,B22,B21,thi);
1387: DMDAVecRestoreArray(da3,X3,&x3);
1388: DMDAVecRestoreArray(da2,X2,&x2);
1389: DMDAVecRestoreArray(da2,Xdot2,&xdot2);
1391: MatRestoreLocalSubMatrix(*B,isloc[0],isloc[0],&B11);
1392: MatRestoreLocalSubMatrix(*B,isloc[0],isloc[1],&B12);
1393: MatRestoreLocalSubMatrix(*B,isloc[1],isloc[0],&B21);
1394: MatRestoreLocalSubMatrix(*B,isloc[1],isloc[1],&B22);
1395: ISDestroy(&isloc[0]);
1396: ISDestroy(&isloc[1]);
1397: PetscFree(isloc);
1399: DMCompositeRestoreLocalVectors(pack,&X3,&X2);
1400: DMCompositeRestoreLocalVectors(pack,0,&Xdot2);
1402: MatAssemblyBegin(*B,MAT_FINAL_ASSEMBLY);
1403: MatAssemblyEnd(*B,MAT_FINAL_ASSEMBLY);
1404: if (*A != *B) {
1405: MatAssemblyBegin(*A,MAT_FINAL_ASSEMBLY);
1406: MatAssemblyEnd(*A,MAT_FINAL_ASSEMBLY);
1407: }
1408: *mstr = SAME_NONZERO_PATTERN;
1409: if (thi->verbose) {THIMatrixStatistics(thi,*B,PETSC_VIEWER_STDOUT_WORLD);}
1410: return(0);
1411: }
1415: /* VTK's XML formats are so brain-dead that they can't handle multiple grids in the same file. Since the communication
1416: * can be shared between the two grids, we write two files at once, one for velocity (living on a 3D grid defined by
1417: * h=thickness and b=bed) and another for all properties living on the 2D grid.
1418: */
1419: static PetscErrorCode THIDAVecView_VTK_XML(THI thi,DM pack,Vec X,const char filename[],const char filename2[])
1420: {
1421: const PetscInt dof = NODE_SIZE,dof2 = PRMNODE_SIZE;
1422: Units units = thi->units;
1423: MPI_Comm comm;
1425: PetscViewer viewer3,viewer2;
1426: PetscMPIInt rank,size,tag,nn,nmax,nn2,nmax2;
1427: PetscInt mx,my,mz,r,range[6];
1428: PetscScalar *x,*x2;
1429: DM da3,da2;
1430: Vec X3,X2;
1433: PetscObjectGetComm((PetscObject)thi,&comm);
1434: DMCompositeGetEntries(pack,&da3,&da2);
1435: DMCompositeGetAccess(pack,X,&X3,&X2);
1436: DMDAGetInfo(da3,0, &mz,&my,&mx, 0,0,0, 0,0,0,0,0,0);
1437: MPI_Comm_size(comm,&size);
1438: MPI_Comm_rank(comm,&rank);
1439: PetscViewerASCIIOpen(comm,filename,&viewer3);
1440: PetscViewerASCIIOpen(comm,filename2,&viewer2);
1441: PetscViewerASCIIPrintf(viewer3,"<VTKFile type=\"StructuredGrid\" version=\"0.1\" byte_order=\"LittleEndian\">\n");
1442: PetscViewerASCIIPrintf(viewer2,"<VTKFile type=\"StructuredGrid\" version=\"0.1\" byte_order=\"LittleEndian\">\n");
1443: PetscViewerASCIIPrintf(viewer3," <StructuredGrid WholeExtent=\"%d %d %d %d %d %d\">\n",0,mz-1,0,my-1,0,mx-1);
1444: PetscViewerASCIIPrintf(viewer2," <StructuredGrid WholeExtent=\"%d %d %d %d %d %d\">\n",0,0,0,my-1,0,mx-1);
1446: DMDAGetCorners(da3,range,range+1,range+2,range+3,range+4,range+5);
1447: PetscMPIIntCast(range[3]*range[4]*range[5]*dof,&nn);
1448: MPI_Reduce(&nn,&nmax,1,MPI_INT,MPI_MAX,0,comm);
1449: PetscMPIIntCast(range[4]*range[5]*dof2,&nn2);
1450: MPI_Reduce(&nn2,&nmax2,1,MPI_INT,MPI_MAX,0,comm);
1451: tag = ((PetscObject)viewer3)->tag;
1452: VecGetArray(X3,&x);
1453: VecGetArray(X2,&x2);
1454: if (!rank) {
1455: PetscScalar *array,*array2;
1456: PetscMalloc2(nmax,PetscScalar,&array,nmax2,PetscScalar,&array2);
1457: for (r=0; r<size; r++) {
1458: PetscInt i,j,k,f,xs,xm,ys,ym,zs,zm;
1459: Node *y3;
1460: PetscScalar (*y2)[PRMNODE_SIZE];
1461: MPI_Status status;
1462: if (r) {
1463: MPI_Recv(range,6,MPIU_INT,r,tag,comm,MPI_STATUS_IGNORE);
1464: }
1465: zs = range[0];ys = range[1];xs = range[2];zm = range[3];ym = range[4];xm = range[5];
1466: if (xm*ym*zm*dof > nmax) SETERRQ(PETSC_COMM_SELF,1,"should not happen");
1467: if (r) {
1468: MPI_Recv(array,nmax,MPIU_SCALAR,r,tag,comm,&status);
1469: MPI_Get_count(&status,MPIU_SCALAR,&nn);
1470: if (nn != xm*ym*zm*dof) SETERRQ(PETSC_COMM_SELF,1,"corrupt da3 send");
1471: y3 = (Node*)array;
1472: MPI_Recv(array2,nmax2,MPIU_SCALAR,r,tag,comm,&status);
1473: MPI_Get_count(&status,MPIU_SCALAR,&nn2);
1474: if (nn2 != xm*ym*dof2) SETERRQ(PETSC_COMM_SELF,1,"corrupt da2 send");
1475: y2 = (PetscScalar(*)[PRMNODE_SIZE])array2;
1476: } else {
1477: y3 = (Node*)x;
1478: y2 = (PetscScalar(*)[PRMNODE_SIZE])x2;
1479: }
1480: PetscViewerASCIIPrintf(viewer3," <Piece Extent=\"%d %d %d %d %d %d\">\n",zs,zs+zm-1,ys,ys+ym-1,xs,xs+xm-1);
1481: PetscViewerASCIIPrintf(viewer2," <Piece Extent=\"%d %d %d %d %d %d\">\n",0,0,ys,ys+ym-1,xs,xs+xm-1);
1483: PetscViewerASCIIPrintf(viewer3," <Points>\n");
1484: PetscViewerASCIIPrintf(viewer2," <Points>\n");
1485: PetscViewerASCIIPrintf(viewer3," <DataArray type=\"Float32\" NumberOfComponents=\"3\" format=\"ascii\">\n");
1486: PetscViewerASCIIPrintf(viewer2," <DataArray type=\"Float32\" NumberOfComponents=\"3\" format=\"ascii\">\n");
1487: for (i=xs; i<xs+xm; i++) {
1488: for (j=ys; j<ys+ym; j++) {
1489: PetscReal
1490: xx = thi->Lx*i/mx,
1491: yy = thi->Ly*j/my,
1492: b = PetscRealPart(y2[i*ym+j][FieldOffset(PrmNode,b)]),
1493: h = PetscRealPart(y2[i*ym+j][FieldOffset(PrmNode,h)]);
1494: for (k=zs; k<zs+zm; k++) {
1495: PetscReal zz = b + h*k/(mz-1.);
1496: PetscViewerASCIIPrintf(viewer3,"%f %f %f\n",xx,yy,zz);
1497: }
1498: PetscViewerASCIIPrintf(viewer2,"%f %f %f\n",xx,yy,(double)0.0);
1499: }
1500: }
1501: PetscViewerASCIIPrintf(viewer3," </DataArray>\n");
1502: PetscViewerASCIIPrintf(viewer2," </DataArray>\n");
1503: PetscViewerASCIIPrintf(viewer3," </Points>\n");
1504: PetscViewerASCIIPrintf(viewer2," </Points>\n");
1506: { /* Velocity and rank (3D) */
1507: PetscViewerASCIIPrintf(viewer3," <PointData>\n");
1508: PetscViewerASCIIPrintf(viewer3," <DataArray type=\"Float32\" Name=\"velocity\" NumberOfComponents=\"3\" format=\"ascii\">\n");
1509: for (i=0; i<nn/dof; i++) {
1510: PetscViewerASCIIPrintf(viewer3,"%f %f %f\n",PetscRealPart(y3[i].u)*units->year/units->meter,PetscRealPart(y3[i].v)*units->year/units->meter,0.0);
1511: }
1512: PetscViewerASCIIPrintf(viewer3," </DataArray>\n");
1514: PetscViewerASCIIPrintf(viewer3," <DataArray type=\"Int32\" Name=\"rank\" NumberOfComponents=\"1\" format=\"ascii\">\n");
1515: for (i=0; i<nn; i+=dof) {
1516: PetscViewerASCIIPrintf(viewer3,"%d\n",r);
1517: }
1518: PetscViewerASCIIPrintf(viewer3," </DataArray>\n");
1519: PetscViewerASCIIPrintf(viewer3," </PointData>\n");
1520: }
1522: { /* 2D */
1523: PetscViewerASCIIPrintf(viewer2," <PointData>\n");
1524: for (f=0; f<PRMNODE_SIZE; f++) {
1525: const char *fieldname;
1526: DMDAGetFieldName(da2,f,&fieldname);
1527: PetscViewerASCIIPrintf(viewer2," <DataArray type=\"Float32\" Name=\"%s\" format=\"ascii\">\n",fieldname);
1528: for (i=0; i<nn2/PRMNODE_SIZE; i++) {
1529: PetscViewerASCIIPrintf(viewer2,"%g\n",y2[i][f]);
1530: }
1531: PetscViewerASCIIPrintf(viewer2," </DataArray>\n");
1532: }
1533: PetscViewerASCIIPrintf(viewer2," </PointData>\n");
1534: }
1536: PetscViewerASCIIPrintf(viewer3," </Piece>\n");
1537: PetscViewerASCIIPrintf(viewer2," </Piece>\n");
1538: }
1539: PetscFree2(array,array2);
1540: } else {
1541: MPI_Send(range,6,MPIU_INT,0,tag,comm);
1542: MPI_Send(x,nn,MPIU_SCALAR,0,tag,comm);
1543: MPI_Send(x2,nn2,MPIU_SCALAR,0,tag,comm);
1544: }
1545: VecRestoreArray(X3,&x);
1546: VecRestoreArray(X2,&x2);
1547: PetscViewerASCIIPrintf(viewer3," </StructuredGrid>\n");
1548: PetscViewerASCIIPrintf(viewer2," </StructuredGrid>\n");
1550: DMCompositeRestoreAccess(pack,X,&X3,&X2);
1551: PetscViewerASCIIPrintf(viewer3,"</VTKFile>\n");
1552: PetscViewerASCIIPrintf(viewer2,"</VTKFile>\n");
1553: PetscViewerDestroy(&viewer3);
1554: PetscViewerDestroy(&viewer2);
1555: return(0);
1556: }
1560: static PetscErrorCode THITSMonitor(TS ts,PetscInt step,PetscReal t,Vec X,void *ctx)
1561: {
1563: THI thi = (THI)ctx;
1564: DM pack;
1565: char filename3[PETSC_MAX_PATH_LEN],filename2[PETSC_MAX_PATH_LEN];
1568: PetscPrintf(PetscObjectComm((PetscObject)ts),"%3D: t=%G\n",step,t);
1569: if (thi->monitor_interval && step % thi->monitor_interval) return(0);
1570: TSGetDM(ts,&pack);
1571: PetscSNPrintf(filename3,sizeof(filename3),"%s-3d-%03d.vts",thi->monitor_basename,step);
1572: PetscSNPrintf(filename2,sizeof(filename2),"%s-2d-%03d.vts",thi->monitor_basename,step);
1573: THIDAVecView_VTK_XML(thi,pack,X,filename3,filename2);
1574: return(0);
1575: }
1580: static PetscErrorCode THICreateDM3d(THI thi,DM *dm3d)
1581: {
1582: MPI_Comm comm;
1583: PetscInt M = 3,N = 3,P = 2;
1584: DM da;
1588: PetscObjectGetComm((PetscObject)thi,&comm);
1589: PetscOptionsBegin(comm,NULL,"Grid resolution options","");
1590: {
1591: PetscOptionsInt("-M","Number of elements in x-direction on coarse level","",M,&M,NULL);
1592: N = M;
1593: PetscOptionsInt("-N","Number of elements in y-direction on coarse level (if different from M)","",N,&N,NULL);
1594: PetscOptionsInt("-P","Number of elements in z-direction on coarse level","",P,&P,NULL);
1595: }
1596: PetscOptionsEnd();
1597: DMDACreate3d(comm,DMDA_BOUNDARY_NONE,DMDA_BOUNDARY_PERIODIC,DMDA_BOUNDARY_PERIODIC,DMDA_STENCIL_BOX,P,N,M,1,PETSC_DETERMINE,PETSC_DETERMINE,sizeof(Node)/sizeof(PetscScalar),1,0,0,0,&da);
1598: DMDASetFieldName(da,0,"x-velocity");
1599: DMDASetFieldName(da,1,"y-velocity");
1600: *dm3d = da;
1601: return(0);
1602: }
1606: int main(int argc,char *argv[])
1607: {
1608: MPI_Comm comm;
1609: DM pack,da3,da2;
1610: TS ts;
1611: THI thi;
1612: Vec X;
1613: Mat B;
1614: PetscInt i,steps;
1615: PetscReal ftime;
1618: PetscInitialize(&argc,&argv,0,help);
1619: comm = PETSC_COMM_WORLD;
1621: THICreate(comm,&thi);
1622: THICreateDM3d(thi,&da3);
1623: {
1624: PetscInt Mx,My,mx,my,s;
1625: DMDAStencilType st;
1626: DMDAGetInfo(da3,0, 0,&My,&Mx, 0,&my,&mx, 0,&s,0,0,0,&st);
1627: DMDACreate2d(PetscObjectComm((PetscObject)thi),DMDA_BOUNDARY_PERIODIC,DMDA_BOUNDARY_PERIODIC,st,My,Mx,my,mx,sizeof(PrmNode)/sizeof(PetscScalar),s,0,0,&da2);
1628: }
1630: PetscObjectSetName((PetscObject)da3,"3D_Velocity");
1631: DMSetOptionsPrefix(da3,"f3d_");
1632: DMDASetFieldName(da3,0,"u");
1633: DMDASetFieldName(da3,1,"v");
1634: PetscObjectSetName((PetscObject)da2,"2D_Fields");
1635: DMSetOptionsPrefix(da2,"f2d_");
1636: DMDASetFieldName(da2,0,"b");
1637: DMDASetFieldName(da2,1,"h");
1638: DMDASetFieldName(da2,2,"beta2");
1639: DMCompositeCreate(comm,&pack);
1640: DMCompositeAddDM(pack,da3);
1641: DMCompositeAddDM(pack,da2);
1642: DMDestroy(&da3);
1643: DMDestroy(&da2);
1644: DMSetUp(pack);
1645: DMCreateMatrix(pack,NULL,&B);
1646: MatSetOption(B,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_FALSE);
1647: MatSetOptionsPrefix(B,"thi_");
1649: for (i=0; i<thi->nlevels; i++) {
1650: PetscReal Lx = thi->Lx / thi->units->meter,Ly = thi->Ly / thi->units->meter,Lz = thi->Lz / thi->units->meter;
1651: PetscInt Mx,My,Mz;
1652: DMCompositeGetEntries(pack,&da3,&da2);
1653: DMDAGetInfo(da3,0, &Mz,&My,&Mx, 0,0,0, 0,0,0,0,0,0);
1654: PetscPrintf(PetscObjectComm((PetscObject)thi),"Level %d domain size (m) %8.2g x %8.2g x %8.2g, num elements %3d x %3d x %3d (%8d), size (m) %g x %g x %g\n",i,Lx,Ly,Lz,Mx,My,Mz,Mx*My*Mz,Lx/Mx,Ly/My,1000./(Mz-1));
1655: }
1657: DMCreateGlobalVector(pack,&X);
1658: THIInitial(thi,pack,X);
1660: TSCreate(comm,&ts);
1661: TSSetDM(ts,pack);
1662: TSSetProblemType(ts,TS_NONLINEAR);
1663: TSMonitorSet(ts,THITSMonitor,thi,NULL);
1664: TSSetType(ts,TSTHETA);
1665: TSSetIFunction(ts,NULL,THIFunction,thi);
1666: TSSetIJacobian(ts,B,B,THIJacobian,thi);
1667: TSSetDuration(ts,100,10.0);
1668: TSSetSolution(ts,X);
1669: TSSetInitialTimeStep(ts,0.,1e-3);
1670: TSSetFromOptions(ts);
1672: TSSolve(ts,X);
1673: TSGetSolveTime(ts,&ftime);
1674: TSGetTimeStepNumber(ts,&steps);
1675: PetscPrintf(PETSC_COMM_WORLD,"Steps %D final time %G\n",steps,ftime);
1677: if (0) {THISolveStatistics(thi,ts,0,"Full");}
1679: {
1680: PetscBool flg;
1681: char filename[PETSC_MAX_PATH_LEN] = "";
1682: PetscOptionsGetString(NULL,"-o",filename,sizeof(filename),&flg);
1683: if (flg) {
1684: THIDAVecView_VTK_XML(thi,pack,X,filename,NULL);
1685: }
1686: }
1688: VecDestroy(&X);
1689: MatDestroy(&B);
1690: DMDestroy(&pack);
1691: TSDestroy(&ts);
1692: THIDestroy(&thi);
1693: PetscFinalize();
1694: return 0;
1695: }