Actual source code: ex14.c
petsc-3.5.4 2015-05-23
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() */
52: #if defined __SSE2__
53: # include <emmintrin.h>
54: #endif
56: /* The SSE2 kernels are only for PetscScalar=double on architectures that support it */
57: #define USE_SSE2_KERNELS (!defined NO_SSE2 \
58: && !defined PETSC_USE_COMPLEX \
59: && !defined PETSC_USE_REAL_SINGLE \
60: && defined __SSE2__)
62: #if !defined __STDC_VERSION__ || __STDC_VERSION__ < 199901L
63: # if defined __cplusplus /* C++ restrict is nonstandard and compilers have inconsistent rules about where it can be used */
64: # define restrict
65: # else
66: # define restrict PETSC_RESTRICT
67: # endif
68: #endif
70: static PetscClassId THI_CLASSID;
72: typedef enum {QUAD_GAUSS,QUAD_LOBATTO} QuadratureType;
73: static const char *QuadratureTypes[] = {"gauss","lobatto","QuadratureType","QUAD_",0};
74: static const PetscReal HexQWeights[8] = {1,1,1,1,1,1,1,1};
75: static const PetscReal HexQNodes[] = {-0.57735026918962573, 0.57735026918962573};
76: #define G 0.57735026918962573
77: #define H (0.5*(1.+G))
78: #define L (0.5*(1.-G))
79: #define M (-0.5)
80: #define P (0.5)
81: /* Special quadrature: Lobatto in horizontal, Gauss in vertical */
82: static const PetscReal HexQInterp_Lobatto[8][8] = {{H,0,0,0,L,0,0,0},
83: {0,H,0,0,0,L,0,0},
84: {0,0,H,0,0,0,L,0},
85: {0,0,0,H,0,0,0,L},
86: {L,0,0,0,H,0,0,0},
87: {0,L,0,0,0,H,0,0},
88: {0,0,L,0,0,0,H,0},
89: {0,0,0,L,0,0,0,H}};
90: static const PetscReal HexQDeriv_Lobatto[8][8][3] = {
91: {{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} },
92: {{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} },
93: {{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} },
94: {{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}},
95: {{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} },
96: {{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} },
97: {{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} },
98: {{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}}};
99: /* Stanndard Gauss */
100: 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},
101: {L*H*H,H*H*H,H*L*H,L*L*H, L*H*L,H*H*L,H*L*L,L*L*L},
102: {L*L*H,H*L*H,H*H*H,L*H*H, L*L*L,H*L*L,H*H*L,L*H*L},
103: {H*L*H,L*L*H,L*H*H,H*H*H, H*L*L,L*L*L,L*H*L,H*H*L},
104: {H*H*L,L*H*L,L*L*L,H*L*L, H*H*H,L*H*H,L*L*H,H*L*H},
105: {L*H*L,H*H*L,H*L*L,L*L*L, L*H*H,H*H*H,H*L*H,L*L*H},
106: {L*L*L,H*L*L,H*H*L,L*H*L, L*L*H,H*L*H,H*H*H,L*H*H},
107: {H*L*L,L*L*L,L*H*L,H*H*L, H*L*H,L*L*H,L*H*H,H*H*H}};
108: static const PetscReal HexQDeriv_Gauss[8][8][3] = {
109: {{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}},
110: {{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}},
111: {{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}},
112: {{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}},
113: {{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}},
114: {{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}},
115: {{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}},
116: {{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}}};
117: static const PetscReal (*HexQInterp)[8],(*HexQDeriv)[8][3];
118: /* Standard 2x2 Gauss quadrature for the bottom layer. */
119: static const PetscReal QuadQInterp[4][4] = {{H*H,L*H,L*L,H*L},
120: {L*H,H*H,H*L,L*L},
121: {L*L,H*L,H*H,L*H},
122: {H*L,L*L,L*H,H*H}};
123: static const PetscReal QuadQDeriv[4][4][2] = {
124: {{M*H,M*H},{P*H,M*L},{P*L,P*L},{M*L,P*H}},
125: {{M*H,M*L},{P*H,M*H},{P*L,P*H},{M*L,P*L}},
126: {{M*L,M*L},{P*L,M*H},{P*H,P*H},{M*H,P*L}},
127: {{M*L,M*H},{P*L,M*L},{P*H,P*L},{M*H,P*H}}};
128: #undef G
129: #undef H
130: #undef L
131: #undef M
132: #undef P
134: #define HexExtract(x,i,j,k,n) do { \
135: (n)[0] = (x)[i][j][k]; \
136: (n)[1] = (x)[i+1][j][k]; \
137: (n)[2] = (x)[i+1][j+1][k]; \
138: (n)[3] = (x)[i][j+1][k]; \
139: (n)[4] = (x)[i][j][k+1]; \
140: (n)[5] = (x)[i+1][j][k+1]; \
141: (n)[6] = (x)[i+1][j+1][k+1]; \
142: (n)[7] = (x)[i][j+1][k+1]; \
143: } while (0)
145: #define HexExtractRef(x,i,j,k,n) do { \
146: (n)[0] = &(x)[i][j][k]; \
147: (n)[1] = &(x)[i+1][j][k]; \
148: (n)[2] = &(x)[i+1][j+1][k]; \
149: (n)[3] = &(x)[i][j+1][k]; \
150: (n)[4] = &(x)[i][j][k+1]; \
151: (n)[5] = &(x)[i+1][j][k+1]; \
152: (n)[6] = &(x)[i+1][j+1][k+1]; \
153: (n)[7] = &(x)[i][j+1][k+1]; \
154: } while (0)
156: #define QuadExtract(x,i,j,n) do { \
157: (n)[0] = (x)[i][j]; \
158: (n)[1] = (x)[i+1][j]; \
159: (n)[2] = (x)[i+1][j+1]; \
160: (n)[3] = (x)[i][j+1]; \
161: } while (0)
163: static PetscScalar Sqr(PetscScalar a) {return a*a;}
165: static void HexGrad(const PetscReal dphi[][3],const PetscReal zn[],PetscReal dz[])
166: {
167: PetscInt i;
168: dz[0] = dz[1] = dz[2] = 0;
169: for (i=0; i<8; i++) {
170: dz[0] += dphi[i][0] * zn[i];
171: dz[1] += dphi[i][1] * zn[i];
172: dz[2] += dphi[i][2] * zn[i];
173: }
174: }
176: static void HexComputeGeometry(PetscInt q,PetscReal hx,PetscReal hy,const PetscReal dz[restrict],PetscReal phi[restrict],PetscReal dphi[restrict][3],PetscReal *restrict jw)
177: {
178: const PetscReal
179: jac[3][3] = {{hx/2,0,0}, {0,hy/2,0}, {dz[0],dz[1],dz[2]}}
180: ,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]}}
181: ,jdet = jac[0][0]*jac[1][1]*jac[2][2];
182: PetscInt i;
184: for (i=0; i<8; i++) {
185: const PetscReal *dphir = HexQDeriv[q][i];
186: phi[i] = HexQInterp[q][i];
187: dphi[i][0] = dphir[0]*ijac[0][0] + dphir[1]*ijac[1][0] + dphir[2]*ijac[2][0];
188: dphi[i][1] = dphir[0]*ijac[0][1] + dphir[1]*ijac[1][1] + dphir[2]*ijac[2][1];
189: dphi[i][2] = dphir[0]*ijac[0][2] + dphir[1]*ijac[1][2] + dphir[2]*ijac[2][2];
190: }
191: *jw = 1.0 * jdet;
192: }
194: typedef struct _p_THI *THI;
195: typedef struct _n_Units *Units;
197: typedef struct {
198: PetscScalar u,v;
199: } Node;
201: typedef struct {
202: PetscScalar b; /* bed */
203: PetscScalar h; /* thickness */
204: PetscScalar beta2; /* friction */
205: } PrmNode;
207: #define FieldSize(ntype) ((PetscInt)(sizeof(ntype)/sizeof(PetscScalar)))
208: #define FieldOffset(ntype,member) ((PetscInt)(offsetof(ntype,member)/sizeof(PetscScalar)))
209: #define FieldIndex(ntype,i,member) ((PetscInt)((i)*FieldSize(ntype) + FieldOffset(ntype,member)))
210: #define NODE_SIZE FieldSize(Node)
211: #define PRMNODE_SIZE FieldSize(PrmNode)
213: typedef struct {
214: PetscReal min,max,cmin,cmax;
215: } PRange;
217: struct _p_THI {
218: PETSCHEADER(int);
219: void (*initialize)(THI,PetscReal x,PetscReal y,PrmNode *p);
220: PetscInt nlevels;
221: PetscInt zlevels;
222: PetscReal Lx,Ly,Lz; /* Model domain */
223: PetscReal alpha; /* Bed angle */
224: Units units;
225: PetscReal dirichlet_scale;
226: PetscReal ssa_friction_scale;
227: PetscReal inertia;
228: PRange eta;
229: PRange beta2;
230: struct {
231: PetscReal Bd2,eps,exponent,glen_n;
232: } viscosity;
233: struct {
234: PetscReal irefgam,eps2,exponent;
235: } friction;
236: struct {
237: PetscReal rate,exponent,refvel;
238: } erosion;
239: PetscReal rhog;
240: PetscBool no_slip;
241: PetscBool verbose;
242: MatType mattype;
243: char *monitor_basename;
244: PetscInt monitor_interval;
245: };
247: struct _n_Units {
248: /* fundamental */
249: PetscReal meter;
250: PetscReal kilogram;
251: PetscReal second;
252: /* derived */
253: PetscReal Pascal;
254: PetscReal year;
255: };
257: static void PrmHexGetZ(const PrmNode pn[],PetscInt k,PetscInt zm,PetscReal zn[])
258: {
259: const PetscScalar zm1 = zm-1,
260: znl[8] = {pn[0].b + pn[0].h*(PetscScalar)k/zm1,
261: pn[1].b + pn[1].h*(PetscScalar)k/zm1,
262: pn[2].b + pn[2].h*(PetscScalar)k/zm1,
263: pn[3].b + pn[3].h*(PetscScalar)k/zm1,
264: pn[0].b + pn[0].h*(PetscScalar)(k+1)/zm1,
265: pn[1].b + pn[1].h*(PetscScalar)(k+1)/zm1,
266: pn[2].b + pn[2].h*(PetscScalar)(k+1)/zm1,
267: pn[3].b + pn[3].h*(PetscScalar)(k+1)/zm1};
268: PetscInt i;
269: for (i=0; i<8; i++) zn[i] = PetscRealPart(znl[i]);
270: }
274: /* Compute a gradient of all the 2D fields at four quadrature points. Output for [quadrature_point][direction].field_name */
275: static PetscErrorCode QuadComputeGrad4(const PetscReal dphi[][4][2],PetscReal hx,PetscReal hy,const PrmNode pn[4],PrmNode dp[4][2])
276: {
278: PetscInt q,i,f;
279: const PetscScalar (*restrict pg)[PRMNODE_SIZE] = (const PetscScalar(*)[PRMNODE_SIZE])pn; /* Get generic array pointers to the node */
280: PetscScalar (*restrict dpg)[2][PRMNODE_SIZE] = (PetscScalar(*)[2][PRMNODE_SIZE])dp;
283: PetscMemzero(dpg,4*sizeof(dpg[0]));
284: for (q=0; q<4; q++) {
285: for (i=0; i<4; i++) {
286: for (f=0; f<PRMNODE_SIZE; f++) {
287: dpg[q][0][f] += dphi[q][i][0]/hx * pg[i][f];
288: dpg[q][1][f] += dphi[q][i][1]/hy * pg[i][f];
289: }
290: }
291: }
292: return(0);
293: }
295: static inline PetscReal StaggeredMidpoint2D(PetscScalar a,PetscScalar b,PetscScalar c,PetscScalar d)
296: {return 0.5*PetscRealPart(0.75*a + 0.75*b + 0.25*c + 0.25*d);}
297: static inline PetscReal UpwindFlux1D(PetscReal u,PetscReal hL,PetscReal hR)
298: {return (u > 0) ? hL*u : hR*u;}
300: #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), \
301: 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))
302: #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), \
303: 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))
304: #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), \
305: 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))
306: #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), \
307: 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))
309: static void PrmNodeGetFaceMeasure(const PrmNode **p,PetscInt i,PetscInt j,PetscScalar h[])
310: {
311: /* West */
312: h[0] = StaggeredMidpoint2D(p[i][j].h,p[i-1][j].h,p[i-1][j-1].h,p[i][j-1].h);
313: h[1] = StaggeredMidpoint2D(p[i][j].h,p[i-1][j].h,p[i-1][j+1].h,p[i][j+1].h);
314: /* East */
315: h[2] = StaggeredMidpoint2D(p[i][j].h,p[i+1][j].h,p[i+1][j+1].h,p[i][j+1].h);
316: h[3] = StaggeredMidpoint2D(p[i][j].h,p[i+1][j].h,p[i+1][j-1].h,p[i][j-1].h);
317: /* South */
318: h[4] = StaggeredMidpoint2D(p[i][j].h,p[i][j-1].h,p[i+1][j-1].h,p[i+1][j].h);
319: h[5] = StaggeredMidpoint2D(p[i][j].h,p[i][j-1].h,p[i-1][j-1].h,p[i-1][j].h);
320: /* North */
321: h[6] = StaggeredMidpoint2D(p[i][j].h,p[i][j+1].h,p[i-1][j+1].h,p[i-1][j].h);
322: h[7] = StaggeredMidpoint2D(p[i][j].h,p[i][j+1].h,p[i+1][j+1].h,p[i+1][j].h);
323: }
325: /* Tests A and C are from the ISMIP-HOM paper (Pattyn et al. 2008) */
326: static void THIInitialize_HOM_A(THI thi,PetscReal x,PetscReal y,PrmNode *p)
327: {
328: Units units = thi->units;
329: PetscReal s = -x*PetscSinReal(thi->alpha);
330: p->b = s - 1000*units->meter + 500*units->meter * PetscSinReal(x*2*PETSC_PI/thi->Lx) * PetscSinReal(y*2*PETSC_PI/thi->Ly);
331: p->h = s - p->b;
332: p->beta2 = -1e-10; /* This value is not used, but it should not be huge because that would change the finite difference step size */
333: }
335: static void THIInitialize_HOM_C(THI thi,PetscReal x,PetscReal y,PrmNode *p)
336: {
337: Units units = thi->units;
338: PetscReal s = -x*PetscSinReal(thi->alpha);
339: p->b = s - 1000*units->meter;
340: p->h = s - p->b;
341: /* tau_b = beta2 v is a stress (Pa).
342: * 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. */
343: 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;
344: }
346: /* These are just toys */
348: /* From Fred Herman */
349: static void THIInitialize_HOM_F(THI thi,PetscReal x,PetscReal y,PrmNode *p)
350: {
351: Units units = thi->units;
352: PetscReal s = -x*PetscSinReal(thi->alpha);
353: p->b = s - 1000*units->meter + 100*units->meter * PetscSinReal(x*2*PETSC_PI/thi->Lx);/* * sin(y*2*PETSC_PI/thi->Ly); */
354: p->h = s - p->b;
355: p->h = (1-(atan((x-thi->Lx/2)/1.)+PETSC_PI/2.)/PETSC_PI)*500*units->meter+1*units->meter;
356: s = PetscRealPart(p->b + p->h);
357: p->beta2 = -1e-10;
358: /* p->beta2 = 1000 * units->Pascal * units->year / units->meter; */
359: }
361: /* Same bed as test A, free slip everywhere except for a discontinuous jump to a circular sticky region in the middle. */
362: static void THIInitialize_HOM_X(THI thi,PetscReal xx,PetscReal yy,PrmNode *p)
363: {
364: Units units = thi->units;
365: PetscReal x = xx*2*PETSC_PI/thi->Lx - PETSC_PI,y = yy*2*PETSC_PI/thi->Ly - PETSC_PI; /* [-pi,pi] */
366: PetscReal r = PetscSqrtReal(x*x + y*y),s = -x*PetscSinReal(thi->alpha);
367: p->b = s - 1000*units->meter + 500*units->meter * PetscSinReal(x + PETSC_PI) * PetscSinReal(y + PETSC_PI);
368: p->h = s - p->b;
369: p->beta2 = 1000 * (r < 1 ? 2 : 0) * units->Pascal * units->year / units->meter / thi->rhog;
370: }
372: /* Like Z, but with 200 meter cliffs */
373: static void THIInitialize_HOM_Y(THI thi,PetscReal xx,PetscReal yy,PrmNode *p)
374: {
375: Units units = thi->units;
376: PetscReal x = xx*2*PETSC_PI/thi->Lx - PETSC_PI,y = yy*2*PETSC_PI/thi->Ly - PETSC_PI; /* [-pi,pi] */
377: PetscReal r = PetscSqrtReal(x*x + y*y),s = -x*PetscSinReal(thi->alpha);
378: p->b = s - 1000*units->meter + 500*units->meter * PetscSinReal(x + PETSC_PI) * PetscSinReal(y + PETSC_PI);
379: if (PetscRealPart(p->b) > -700*units->meter) p->b += 200*units->meter;
380: p->h = s - p->b;
381: 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;
382: }
384: /* Same bed as A, smoothly varying slipperiness, similar to MATLAB's "sombrero" (uncorrelated with bathymetry) */
385: static void THIInitialize_HOM_Z(THI thi,PetscReal xx,PetscReal yy,PrmNode *p)
386: {
387: Units units = thi->units;
388: PetscReal x = xx*2*PETSC_PI/thi->Lx - PETSC_PI,y = yy*2*PETSC_PI/thi->Ly - PETSC_PI; /* [-pi,pi] */
389: PetscReal r = PetscSqrtReal(x*x + y*y),s = -x*PetscSinReal(thi->alpha);
390: p->b = s - 1000*units->meter + 500*units->meter * PetscSinReal(x + PETSC_PI) * PetscSinReal(y + PETSC_PI);
391: p->h = s - p->b;
392: 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;
393: }
395: static void THIFriction(THI thi,PetscReal rbeta2,PetscReal gam,PetscReal *beta2,PetscReal *dbeta2)
396: {
397: if (thi->friction.irefgam == 0) {
398: Units units = thi->units;
399: thi->friction.irefgam = 1./(0.5*PetscSqr(100 * units->meter / units->year));
400: thi->friction.eps2 = 0.5*PetscSqr(1.e-4 / thi->friction.irefgam);
401: }
402: if (thi->friction.exponent == 0) {
403: *beta2 = rbeta2;
404: *dbeta2 = 0;
405: } else {
406: *beta2 = rbeta2 * PetscPowReal(thi->friction.eps2 + gam*thi->friction.irefgam,thi->friction.exponent);
407: *dbeta2 = thi->friction.exponent * *beta2 / (thi->friction.eps2 + gam*thi->friction.irefgam) * thi->friction.irefgam;
408: }
409: }
411: static void THIViscosity(THI thi,PetscReal gam,PetscReal *eta,PetscReal *deta)
412: {
413: PetscReal Bd2,eps,exponent;
414: if (thi->viscosity.Bd2 == 0) {
415: Units units = thi->units;
416: const PetscReal
417: n = thi->viscosity.glen_n, /* Glen exponent */
418: p = 1. + 1./n, /* for Stokes */
419: A = 1.e-16 * PetscPowReal(units->Pascal,-n) / units->year, /* softness parameter (Pa^{-n}/s) */
420: B = PetscPowReal(A,-1./n); /* hardness parameter */
421: thi->viscosity.Bd2 = B/2;
422: thi->viscosity.exponent = (p-2)/2;
423: thi->viscosity.eps = 0.5*PetscSqr(1e-5 / units->year);
424: }
425: Bd2 = thi->viscosity.Bd2;
426: exponent = thi->viscosity.exponent;
427: eps = thi->viscosity.eps;
428: *eta = Bd2 * PetscPowReal(eps + gam,exponent);
429: *deta = exponent * (*eta) / (eps + gam);
430: }
432: static void THIErosion(THI thi,const Node *vel,PetscScalar *erate,Node *derate)
433: {
434: const PetscScalar magref2 = 1.e-10 + (PetscSqr(vel->u) + PetscSqr(vel->v)) / PetscSqr(thi->erosion.refvel),
435: rate = -thi->erosion.rate*PetscPowScalar(magref2, 0.5*thi->erosion.exponent);
436: if (erate) *erate = rate;
437: if (derate) {
438: if (thi->erosion.exponent == 1) {
439: derate->u = 0;
440: derate->v = 0;
441: } else {
442: derate->u = 0.5*thi->erosion.exponent * rate / magref2 * 2. * vel->u / PetscSqr(thi->erosion.refvel);
443: derate->v = 0.5*thi->erosion.exponent * rate / magref2 * 2. * vel->v / PetscSqr(thi->erosion.refvel);
444: }
445: }
446: }
448: static void RangeUpdate(PetscReal *min,PetscReal *max,PetscReal x)
449: {
450: if (x < *min) *min = x;
451: if (x > *max) *max = x;
452: }
454: static void PRangeClear(PRange *p)
455: {
456: p->cmin = p->min = 1e100;
457: p->cmax = p->max = -1e100;
458: }
462: static PetscErrorCode PRangeMinMax(PRange *p,PetscReal min,PetscReal max)
463: {
466: p->cmin = min;
467: p->cmax = max;
468: if (min < p->min) p->min = min;
469: if (max > p->max) p->max = max;
470: return(0);
471: }
475: static PetscErrorCode THIDestroy(THI *thi)
476: {
480: if (--((PetscObject)(*thi))->refct > 0) return(0);
481: PetscFree((*thi)->units);
482: PetscFree((*thi)->mattype);
483: PetscFree((*thi)->monitor_basename);
484: PetscHeaderDestroy(thi);
485: return(0);
486: }
490: static PetscErrorCode THICreate(MPI_Comm comm,THI *inthi)
491: {
492: static PetscBool registered = PETSC_FALSE;
493: THI thi;
494: Units units;
495: char monitor_basename[PETSC_MAX_PATH_LEN] = "thi-";
496: PetscErrorCode ierr;
499: *inthi = 0;
500: if (!registered) {
501: PetscClassIdRegister("Toy Hydrostatic Ice",&THI_CLASSID);
502: registered = PETSC_TRUE;
503: }
504: PetscHeaderCreate(thi,_p_THI,0,THI_CLASSID,"THI","Toy Hydrostatic Ice","THI",comm,THIDestroy,0);
506: PetscNew(&thi->units);
508: units = thi->units;
509: units->meter = 1e-2;
510: units->second = 1e-7;
511: units->kilogram = 1e-12;
513: PetscOptionsBegin(comm,NULL,"Scaled units options","");
514: {
515: PetscOptionsReal("-units_meter","1 meter in scaled length units","",units->meter,&units->meter,NULL);
516: PetscOptionsReal("-units_second","1 second in scaled time units","",units->second,&units->second,NULL);
517: PetscOptionsReal("-units_kilogram","1 kilogram in scaled mass units","",units->kilogram,&units->kilogram,NULL);
518: }
519: PetscOptionsEnd();
520: units->Pascal = units->kilogram / (units->meter * PetscSqr(units->second));
521: units->year = 31556926. * units->second, /* seconds per year */
523: thi->Lx = 10.e3;
524: thi->Ly = 10.e3;
525: thi->Lz = 1000;
526: thi->nlevels = 1;
527: thi->dirichlet_scale = 1;
528: thi->verbose = PETSC_FALSE;
530: thi->viscosity.glen_n = 3.;
531: thi->erosion.rate = 1e-3; /* m/a */
532: thi->erosion.exponent = 1.;
533: thi->erosion.refvel = 1.; /* m/a */
535: PetscOptionsBegin(comm,NULL,"Toy Hydrostatic Ice options","");
536: {
537: QuadratureType quad = QUAD_GAUSS;
538: char homexp[] = "A";
539: char mtype[256] = MATSBAIJ;
540: PetscReal L,m = 1.0;
541: PetscBool flg;
542: L = thi->Lx;
543: PetscOptionsReal("-thi_L","Domain size (m)","",L,&L,&flg);
544: if (flg) thi->Lx = thi->Ly = L;
545: PetscOptionsReal("-thi_Lx","X Domain size (m)","",thi->Lx,&thi->Lx,NULL);
546: PetscOptionsReal("-thi_Ly","Y Domain size (m)","",thi->Ly,&thi->Ly,NULL);
547: PetscOptionsReal("-thi_Lz","Z Domain size (m)","",thi->Lz,&thi->Lz,NULL);
548: PetscOptionsString("-thi_hom","ISMIP-HOM experiment (A or C)","",homexp,homexp,sizeof(homexp),NULL);
549: switch (homexp[0] = toupper(homexp[0])) {
550: case 'A':
551: thi->initialize = THIInitialize_HOM_A;
552: thi->no_slip = PETSC_TRUE;
553: thi->alpha = 0.5;
554: break;
555: case 'C':
556: thi->initialize = THIInitialize_HOM_C;
557: thi->no_slip = PETSC_FALSE;
558: thi->alpha = 0.1;
559: break;
560: case 'F':
561: thi->initialize = THIInitialize_HOM_F;
562: thi->no_slip = PETSC_FALSE;
563: thi->alpha = 0.5;
564: break;
565: case 'X':
566: thi->initialize = THIInitialize_HOM_X;
567: thi->no_slip = PETSC_FALSE;
568: thi->alpha = 0.3;
569: break;
570: case 'Y':
571: thi->initialize = THIInitialize_HOM_Y;
572: thi->no_slip = PETSC_FALSE;
573: thi->alpha = 0.5;
574: break;
575: case 'Z':
576: thi->initialize = THIInitialize_HOM_Z;
577: thi->no_slip = PETSC_FALSE;
578: thi->alpha = 0.5;
579: break;
580: default:
581: SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"HOM experiment '%c' not implemented",homexp[0]);
582: }
583: PetscOptionsEnum("-thi_quadrature","Quadrature to use for 3D elements","",QuadratureTypes,(PetscEnum)quad,(PetscEnum*)&quad,NULL);
584: switch (quad) {
585: case QUAD_GAUSS:
586: HexQInterp = HexQInterp_Gauss;
587: HexQDeriv = HexQDeriv_Gauss;
588: break;
589: case QUAD_LOBATTO:
590: HexQInterp = HexQInterp_Lobatto;
591: HexQDeriv = HexQDeriv_Lobatto;
592: break;
593: }
594: PetscOptionsReal("-thi_alpha","Bed angle (degrees)","",thi->alpha,&thi->alpha,NULL);
595: 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);
596: PetscOptionsReal("-thi_friction_m","Friction exponent, 0=Coulomb, 1=Navier","",m,&m,NULL);
597: thi->friction.exponent = (m-1)/2;
598: PetscOptionsReal("-thi_erosion_rate","Rate of erosion relative to sliding velocity at reference velocity (m/a)",NULL,thi->erosion.rate,&thi->erosion.rate,NULL);
599: PetscOptionsReal("-thi_erosion_exponent","Power of sliding velocity appearing in erosion relation",NULL,thi->erosion.exponent,&thi->erosion.exponent,NULL);
600: PetscOptionsReal("-thi_erosion_refvel","Reference sliding velocity for erosion (m/a)",NULL,thi->erosion.refvel,&thi->erosion.refvel,NULL);
601: thi->erosion.rate *= units->meter / units->year;
602: thi->erosion.refvel *= units->meter / units->year;
603: PetscOptionsReal("-thi_dirichlet_scale","Scale Dirichlet boundary conditions by this factor","",thi->dirichlet_scale,&thi->dirichlet_scale,NULL);
604: 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);
605: PetscOptionsReal("-thi_inertia","Coefficient of accelaration term in velocity system, physical is almost zero",NULL,thi->inertia,&thi->inertia,NULL);
606: PetscOptionsInt("-thi_nlevels","Number of levels of refinement","",thi->nlevels,&thi->nlevels,NULL);
607: PetscOptionsFList("-thi_mat_type","Matrix type","MatSetType",MatList,mtype,(char*)mtype,sizeof(mtype),NULL);
608: PetscStrallocpy(mtype,&thi->mattype);
609: PetscOptionsBool("-thi_verbose","Enable verbose output (like matrix sizes and statistics)","",thi->verbose,&thi->verbose,NULL);
610: PetscOptionsString("-thi_monitor","Basename to write state files to",NULL,monitor_basename,monitor_basename,sizeof(monitor_basename),&flg);
611: if (flg) {
612: PetscStrallocpy(monitor_basename,&thi->monitor_basename);
613: thi->monitor_interval = 1;
614: PetscOptionsInt("-thi_monitor_interval","Frequency at which to write state files",NULL,thi->monitor_interval,&thi->monitor_interval,NULL);
615: }
616: }
617: PetscOptionsEnd();
619: /* dimensionalize */
620: thi->Lx *= units->meter;
621: thi->Ly *= units->meter;
622: thi->Lz *= units->meter;
623: thi->alpha *= PETSC_PI / 180;
625: PRangeClear(&thi->eta);
626: PRangeClear(&thi->beta2);
628: {
629: PetscReal u = 1000*units->meter/(3e7*units->second),
630: gradu = u / (100*units->meter),eta,deta,
631: rho = 910 * units->kilogram/PetscPowRealInt(units->meter,3),
632: grav = 9.81 * units->meter/PetscSqr(units->second),
633: driving = rho * grav * PetscSinReal(thi->alpha) * 1000*units->meter;
634: THIViscosity(thi,0.5*gradu*gradu,&eta,&deta);
635: thi->rhog = rho * grav;
636: if (thi->verbose) {
637: 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);
638: 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);
639: 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);
640: THIViscosity(thi,0.5*PetscSqr(1e-3*gradu),&eta,&deta);
641: 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);
642: }
643: }
645: *inthi = thi;
646: return(0);
647: }
651: /* Our problem is periodic, but the domain has a mean slope of alpha so the bed does not line up between the upstream
652: * and downstream ends of the domain. This function fixes the ghost values so that the domain appears truly periodic in
653: * the horizontal. */
654: static PetscErrorCode THIFixGhosts(THI thi,DM da3,DM da2,Vec X3,Vec X2)
655: {
657: DMDALocalInfo info;
658: PrmNode **x2;
659: PetscInt i,j;
662: DMDAGetLocalInfo(da3,&info);
663: /* VecView(X2,PETSC_VIEWER_STDOUT_WORLD); */
664: DMDAVecGetArray(da2,X2,&x2);
665: for (i=info.gzs; i<info.gzs+info.gzm; i++) {
666: if (i > -1 && i < info.mz) continue;
667: for (j=info.gys; j<info.gys+info.gym; j++) {
668: x2[i][j].b += PetscSinReal(thi->alpha) * thi->Lx * (i<0 ? 1.0 : -1.0);
669: }
670: }
671: DMDAVecRestoreArray(da2,X2,&x2);
672: /* VecView(X2,PETSC_VIEWER_STDOUT_WORLD); */
673: return(0);
674: }
678: static PetscErrorCode THIInitializePrm(THI thi,DM da2prm,PrmNode **p)
679: {
680: PetscInt i,j,xs,xm,ys,ym,mx,my;
684: DMDAGetGhostCorners(da2prm,&ys,&xs,0,&ym,&xm,0);
685: DMDAGetInfo(da2prm,0, &my,&mx,0, 0,0,0, 0,0,0,0,0,0);
686: for (i=xs; i<xs+xm; i++) {
687: for (j=ys; j<ys+ym; j++) {
688: PetscReal xx = thi->Lx*i/mx,yy = thi->Ly*j/my;
689: thi->initialize(thi,xx,yy,&p[i][j]);
690: }
691: }
692: return(0);
693: }
697: static PetscErrorCode THIInitial(THI thi,DM pack,Vec X)
698: {
699: DM da3,da2;
700: PetscInt i,j,k,xs,xm,ys,ym,zs,zm,mx,my;
701: PetscReal hx,hy;
702: PrmNode **prm;
703: Node ***x;
704: Vec X3g,X2g,X2;
708: DMCompositeGetEntries(pack,&da3,&da2);
709: DMCompositeGetAccess(pack,X,&X3g,&X2g);
710: DMGetLocalVector(da2,&X2);
712: DMDAGetInfo(da3,0, 0,&my,&mx, 0,0,0, 0,0,0,0,0,0);
713: DMDAGetCorners(da3,&zs,&ys,&xs,&zm,&ym,&xm);
714: DMDAVecGetArray(da3,X3g,&x);
715: DMDAVecGetArray(da2,X2,&prm);
717: THIInitializePrm(thi,da2,prm);
719: hx = thi->Lx / mx;
720: hy = thi->Ly / my;
721: for (i=xs; i<xs+xm; i++) {
722: for (j=ys; j<ys+ym; j++) {
723: for (k=zs; k<zs+zm; k++) {
724: const PetscScalar zm1 = zm-1,
725: 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),
726: 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);
727: x[i][j][k].u = 0. * drivingx * prm[i][j].h*(PetscScalar)k/zm1;
728: x[i][j][k].v = 0. * drivingy * prm[i][j].h*(PetscScalar)k/zm1;
729: }
730: }
731: }
733: DMDAVecRestoreArray(da3,X3g,&x);
734: DMDAVecRestoreArray(da2,X2,&prm);
736: DMLocalToGlobalBegin(da2,X2,INSERT_VALUES,X2g);
737: DMLocalToGlobalEnd (da2,X2,INSERT_VALUES,X2g);
738: DMRestoreLocalVector(da2,&X2);
740: DMCompositeRestoreAccess(pack,X,&X3g,&X2g);
741: return(0);
742: }
744: 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)
745: {
746: PetscInt l,ll;
747: PetscScalar gam;
749: du[0] = du[1] = du[2] = 0;
750: dv[0] = dv[1] = dv[2] = 0;
751: *u = 0;
752: *v = 0;
753: for (l=0; l<8; l++) {
754: *u += phi[l] * n[l].u;
755: *v += phi[l] * n[l].v;
756: for (ll=0; ll<3; ll++) {
757: du[ll] += dphi[l][ll] * n[l].u;
758: dv[ll] += dphi[l][ll] * n[l].v;
759: }
760: }
761: 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]);
762: THIViscosity(thi,PetscRealPart(gam),eta,deta);
763: }
767: static PetscErrorCode THIFunctionLocal_3D(DMDALocalInfo *info,const Node ***x,const PrmNode **prm,const Node ***xdot,Node ***f,THI thi)
768: {
769: PetscInt xs,ys,xm,ym,zm,i,j,k,q,l;
770: PetscReal hx,hy,etamin,etamax,beta2min,beta2max;
774: xs = info->zs;
775: ys = info->ys;
776: xm = info->zm;
777: ym = info->ym;
778: zm = info->xm;
779: hx = thi->Lx / info->mz;
780: hy = thi->Ly / info->my;
782: etamin = 1e100;
783: etamax = 0;
784: beta2min = 1e100;
785: beta2max = 0;
787: for (i=xs; i<xs+xm; i++) {
788: for (j=ys; j<ys+ym; j++) {
789: PrmNode pn[4],dpn[4][2];
790: QuadExtract(prm,i,j,pn);
791: QuadComputeGrad4(QuadQDeriv,hx,hy,pn,dpn);
792: for (k=0; k<zm-1; k++) {
793: PetscInt ls = 0;
794: Node n[8],ndot[8],*fn[8];
795: PetscReal zn[8],etabase = 0;
796: PrmHexGetZ(pn,k,zm,zn);
797: HexExtract(x,i,j,k,n);
798: HexExtract(xdot,i,j,k,ndot);
799: HexExtractRef(f,i,j,k,fn);
800: if (thi->no_slip && k == 0) {
801: for (l=0; l<4; l++) n[l].u = n[l].v = 0;
802: /* The first 4 basis functions lie on the bottom layer, so their contribution is exactly 0, hence we can skip them */
803: ls = 4;
804: }
805: for (q=0; q<8; q++) {
806: PetscReal dz[3],phi[8],dphi[8][3],jw,eta,deta;
807: PetscScalar du[3],dv[3],u,v,udot=0,vdot=0;
808: for (l=ls; l<8; l++) {
809: udot += HexQInterp[q][l]*ndot[l].u;
810: vdot += HexQInterp[q][l]*ndot[l].v;
811: }
812: HexGrad(HexQDeriv[q],zn,dz);
813: HexComputeGeometry(q,hx,hy,dz,phi,dphi,&jw);
814: PointwiseNonlinearity(thi,n,phi,dphi,&u,&v,du,dv,&eta,&deta);
815: jw /= thi->rhog; /* scales residuals to be O(1) */
816: if (q == 0) etabase = eta;
817: RangeUpdate(&etamin,&etamax,eta);
818: for (l=ls; l<8; l++) { /* test functions */
819: const PetscScalar ds[2] = {dpn[q%4][0].h+dpn[q%4][0].b, dpn[q%4][1].h+dpn[q%4][1].b};
820: const PetscReal pp = phi[l],*dp = dphi[l];
821: 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];
822: 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];
823: fn[l]->u += pp*jw*udot*thi->inertia*pp;
824: fn[l]->v += pp*jw*vdot*thi->inertia*pp;
825: }
826: }
827: if (k == 0) { /* we are on a bottom face */
828: if (thi->no_slip) {
829: /* Note: Non-Galerkin coarse grid operators are very sensitive to the scaling of Dirichlet boundary
830: * conditions. After shenanigans above, etabase contains the effective viscosity at the closest quadrature
831: * point to the bed. We want the diagonal entry in the Dirichlet condition to have similar magnitude to the
832: * diagonal entry corresponding to the adjacent node. The fundamental scaling of the viscous part is in
833: * diagu, diagv below. This scaling is easy to recognize by considering the finite difference operator after
834: * scaling by element size. The no-slip Dirichlet condition is scaled by this factor, and also in the
835: * assembled matrix (see the similar block in THIJacobianLocal).
836: *
837: * Note that the residual at this Dirichlet node is linear in the state at this node, but also depends
838: * (nonlinearly in general) on the neighboring interior nodes through the local viscosity. This will make
839: * a matrix-free Jacobian have extra entries in the corresponding row. We assemble only the diagonal part,
840: * so the solution will exactly satisfy the boundary condition after the first linear iteration.
841: */
842: const PetscReal hz = PetscRealPart(pn[0].h)/(zm-1.);
843: 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);
844: fn[0]->u = thi->dirichlet_scale*diagu*x[i][j][k].u;
845: fn[0]->v = thi->dirichlet_scale*diagv*x[i][j][k].v;
846: } else { /* Integrate over bottom face to apply boundary condition */
847: 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) */
848: const PetscReal jw = 0.25*hx*hy,*phi = QuadQInterp[q];
849: PetscScalar u =0,v=0,rbeta2=0;
850: PetscReal beta2,dbeta2;
851: for (l=0; l<4; l++) {
852: u += phi[l]*n[l].u;
853: v += phi[l]*n[l].v;
854: rbeta2 += phi[l]*pn[l].beta2;
855: }
856: THIFriction(thi,PetscRealPart(rbeta2),PetscRealPart(u*u+v*v)/2,&beta2,&dbeta2);
857: RangeUpdate(&beta2min,&beta2max,beta2);
858: for (l=0; l<4; l++) {
859: const PetscReal pp = phi[l];
860: fn[ls+l]->u += pp*jw*beta2*u;
861: fn[ls+l]->v += pp*jw*beta2*v;
862: }
863: }
864: }
865: }
866: }
867: }
868: }
870: PRangeMinMax(&thi->eta,etamin,etamax);
871: PRangeMinMax(&thi->beta2,beta2min,beta2max);
872: return(0);
873: }
877: static PetscErrorCode THIFunctionLocal_2D(DMDALocalInfo *info,const Node ***x,const PrmNode **prm,const PrmNode **prmdot,PrmNode **f,THI thi)
878: {
879: PetscInt xs,ys,xm,ym,zm,i,j,k;
882: xs = info->zs;
883: ys = info->ys;
884: xm = info->zm;
885: ym = info->ym;
886: zm = info->xm;
888: for (i=xs; i<xs+xm; i++) {
889: for (j=ys; j<ys+ym; j++) {
890: PetscScalar div = 0,erate,h[8];
891: PrmNodeGetFaceMeasure(prm,i,j,h);
892: for (k=0; k<zm; k++) {
893: PetscScalar weight = (k==0 || k == zm-1) ? 0.5/(zm-1) : 1.0/(zm-1);
894: if (0) { /* centered flux */
895: 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)
896: - 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)
897: + 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)
898: + 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)
899: - 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)
900: - 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)
901: + 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)
902: + 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));
903: } else { /* Upwind flux */
904: div += weight*(-UpwindFluxXW(x,prm,h,i,j,k, 1)
905: -UpwindFluxXW(x,prm,h,i,j,k,-1)
906: +UpwindFluxXE(x,prm,h,i,j,k, 1)
907: +UpwindFluxXE(x,prm,h,i,j,k,-1)
908: -UpwindFluxYS(x,prm,h,i,j,k, 1)
909: -UpwindFluxYS(x,prm,h,i,j,k,-1)
910: +UpwindFluxYN(x,prm,h,i,j,k, 1)
911: +UpwindFluxYN(x,prm,h,i,j,k,-1));
912: }
913: }
914: /* printf("div[%d][%d] %g\n",i,j,div); */
915: THIErosion(thi,&x[i][j][0],&erate,NULL);
916: f[i][j].b = prmdot[i][j].b - erate;
917: f[i][j].h = prmdot[i][j].h + div;
918: f[i][j].beta2 = prmdot[i][j].beta2;
919: }
920: }
921: return(0);
922: }
926: static PetscErrorCode THIFunction(TS ts,PetscReal t,Vec X,Vec Xdot,Vec F,void *ctx)
927: {
929: THI thi = (THI)ctx;
930: DM pack,da3,da2;
931: Vec X3,X2,Xdot3,Xdot2,F3,F2,F3g,F2g;
932: const Node ***x3,***xdot3;
933: const PrmNode **x2,**xdot2;
934: Node ***f3;
935: PrmNode **f2;
936: DMDALocalInfo info3;
939: TSGetDM(ts,&pack);
940: DMCompositeGetEntries(pack,&da3,&da2);
941: DMDAGetLocalInfo(da3,&info3);
942: DMCompositeGetLocalVectors(pack,&X3,&X2);
943: DMCompositeGetLocalVectors(pack,&Xdot3,&Xdot2);
944: DMCompositeScatter(pack,X,X3,X2);
945: THIFixGhosts(thi,da3,da2,X3,X2);
946: DMCompositeScatter(pack,Xdot,Xdot3,Xdot2);
948: DMGetLocalVector(da3,&F3);
949: DMGetLocalVector(da2,&F2);
950: VecZeroEntries(F3);
952: DMDAVecGetArray(da3,X3,&x3);
953: DMDAVecGetArray(da2,X2,&x2);
954: DMDAVecGetArray(da3,Xdot3,&xdot3);
955: DMDAVecGetArray(da2,Xdot2,&xdot2);
956: DMDAVecGetArray(da3,F3,&f3);
957: DMDAVecGetArray(da2,F2,&f2);
959: THIFunctionLocal_3D(&info3,x3,x2,xdot3,f3,thi);
960: THIFunctionLocal_2D(&info3,x3,x2,xdot2,f2,thi);
962: DMDAVecRestoreArray(da3,X3,&x3);
963: DMDAVecRestoreArray(da2,X2,&x2);
964: DMDAVecRestoreArray(da3,Xdot3,&xdot3);
965: DMDAVecRestoreArray(da2,Xdot2,&xdot2);
966: DMDAVecRestoreArray(da3,F3,&f3);
967: DMDAVecRestoreArray(da2,F2,&f2);
969: DMCompositeRestoreLocalVectors(pack,&X3,&X2);
970: DMCompositeRestoreLocalVectors(pack,&Xdot3,&Xdot2);
972: VecZeroEntries(F);
973: DMCompositeGetAccess(pack,F,&F3g,&F2g);
974: DMLocalToGlobalBegin(da3,F3,ADD_VALUES,F3g);
975: DMLocalToGlobalEnd (da3,F3,ADD_VALUES,F3g);
976: DMLocalToGlobalBegin(da2,F2,INSERT_VALUES,F2g);
977: DMLocalToGlobalEnd (da2,F2,INSERT_VALUES,F2g);
979: if (thi->verbose) {
980: PetscViewer viewer;
981: PetscViewerASCIIGetStdout(PetscObjectComm((PetscObject)thi),&viewer);
982: PetscViewerASCIIPrintf(viewer,"3D_Velocity residual (bs=2):\n");
983: PetscViewerASCIIPushTab(viewer);
984: VecView(F3,viewer);
985: PetscViewerASCIIPopTab(viewer);
986: PetscViewerASCIIPrintf(viewer,"2D_Fields residual (bs=3):\n");
987: PetscViewerASCIIPushTab(viewer);
988: VecView(F2,viewer);
989: PetscViewerASCIIPopTab(viewer);
990: }
992: DMCompositeRestoreAccess(pack,F,&F3g,&F2g);
994: DMRestoreLocalVector(da3,&F3);
995: DMRestoreLocalVector(da2,&F2);
996: return(0);
997: }
1001: static PetscErrorCode THIMatrixStatistics(THI thi,Mat B,PetscViewer viewer)
1002: {
1004: PetscReal nrm;
1005: PetscInt m;
1006: PetscMPIInt rank;
1009: MatNorm(B,NORM_FROBENIUS,&nrm);
1010: MatGetSize(B,&m,0);
1011: MPI_Comm_rank(PetscObjectComm((PetscObject)B),&rank);
1012: if (!rank) {
1013: PetscScalar val0,val2;
1014: MatGetValue(B,0,0,&val0);
1015: MatGetValue(B,2,2,&val2);
1016: 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);
1017: }
1018: return(0);
1019: }
1023: static PetscErrorCode THISurfaceStatistics(DM pack,Vec X,PetscReal *min,PetscReal *max,PetscReal *mean)
1024: {
1026: DM da3,da2;
1027: Vec X3,X2;
1028: Node ***x;
1029: PetscInt i,j,xs,ys,zs,xm,ym,zm,mx,my,mz;
1030: PetscReal umin = 1e100,umax=-1e100;
1031: PetscScalar usum =0.0,gusum;
1034: DMCompositeGetEntries(pack,&da3,&da2);
1035: DMCompositeGetAccess(pack,X,&X3,&X2);
1036: *min = *max = *mean = 0;
1037: DMDAGetInfo(da3,0, &mz,&my,&mx, 0,0,0, 0,0,0,0,0,0);
1038: DMDAGetCorners(da3,&zs,&ys,&xs,&zm,&ym,&xm);
1039: if (zs != 0 || zm != mz) SETERRQ(PETSC_COMM_SELF,1,"Unexpected decomposition");
1040: DMDAVecGetArray(da3,X3,&x);
1041: for (i=xs; i<xs+xm; i++) {
1042: for (j=ys; j<ys+ym; j++) {
1043: PetscReal u = PetscRealPart(x[i][j][zm-1].u);
1044: RangeUpdate(&umin,&umax,u);
1045: usum += u;
1046: }
1047: }
1048: DMDAVecRestoreArray(da3,X3,&x);
1049: DMCompositeRestoreAccess(pack,X,&X3,&X2);
1051: MPI_Allreduce(&umin,min,1,MPIU_REAL,MPIU_MIN,PetscObjectComm((PetscObject)da3));
1052: MPI_Allreduce(&umax,max,1,MPIU_REAL,MPIU_MAX,PetscObjectComm((PetscObject)da3));
1053: MPI_Allreduce(&usum,&gusum,1,MPIU_SCALAR,MPIU_SUM,PetscObjectComm((PetscObject)da3));
1054: *mean = PetscRealPart(gusum) / (mx*my);
1055: return(0);
1056: }
1060: static PetscErrorCode THISolveStatistics(THI thi,TS ts,PetscInt coarsened,const char name[])
1061: {
1062: MPI_Comm comm;
1063: DM pack;
1064: Vec X,X3,X2;
1068: PetscObjectGetComm((PetscObject)thi,&comm);
1069: TSGetDM(ts,&pack);
1070: TSGetSolution(ts,&X);
1071: DMCompositeGetAccess(pack,X,&X3,&X2);
1072: PetscPrintf(comm,"Solution statistics after solve: %s\n",name);
1073: {
1074: PetscInt its,lits;
1075: SNESConvergedReason reason;
1076: SNES snes;
1077: TSGetSNES(ts,&snes);
1078: SNESGetIterationNumber(snes,&its);
1079: SNESGetConvergedReason(snes,&reason);
1080: SNESGetLinearSolveIterations(snes,&lits);
1081: PetscPrintf(comm,"%s: Number of SNES iterations = %d, total linear iterations = %d\n",SNESConvergedReasons[reason],its,lits);
1082: }
1083: {
1084: PetscReal nrm2,tmin[3]={1e100,1e100,1e100},tmax[3]={-1e100,-1e100,-1e100},min[3],max[3];
1085: PetscInt i,j,m;
1086: PetscScalar *x;
1087: VecNorm(X3,NORM_2,&nrm2);
1088: VecGetLocalSize(X3,&m);
1089: VecGetArray(X3,&x);
1090: for (i=0; i<m; i+=2) {
1091: PetscReal u = PetscRealPart(x[i]),v = PetscRealPart(x[i+1]),c = PetscSqrtReal(u*u+v*v);
1092: tmin[0] = PetscMin(u,tmin[0]);
1093: tmin[1] = PetscMin(v,tmin[1]);
1094: tmin[2] = PetscMin(c,tmin[2]);
1095: tmax[0] = PetscMax(u,tmax[0]);
1096: tmax[1] = PetscMax(v,tmax[1]);
1097: tmax[2] = PetscMax(c,tmax[2]);
1098: }
1099: VecRestoreArray(X,&x);
1100: MPI_Allreduce(tmin,min,3,MPIU_REAL,MPIU_MIN,PetscObjectComm((PetscObject)thi));
1101: MPI_Allreduce(tmax,max,3,MPIU_REAL,MPIU_MAX,PetscObjectComm((PetscObject)thi));
1102: /* Dimensionalize to meters/year */
1103: nrm2 *= thi->units->year / thi->units->meter;
1104: for (j=0; j<3; j++) {
1105: min[j] *= thi->units->year / thi->units->meter;
1106: max[j] *= thi->units->year / thi->units->meter;
1107: }
1108: 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]);
1109: {
1110: PetscReal umin,umax,umean;
1111: THISurfaceStatistics(pack,X,&umin,&umax,&umean);
1112: umin *= thi->units->year / thi->units->meter;
1113: umax *= thi->units->year / thi->units->meter;
1114: umean *= thi->units->year / thi->units->meter;
1115: PetscPrintf(comm,"Surface statistics: u in [%12.6e, %12.6e] mean %12.6e\n",umin,umax,umean);
1116: }
1117: /* These values stay nondimensional */
1118: PetscPrintf(comm,"Global eta range [%g, %g], converged range [%g, %g]\n",thi->eta.min,thi->eta.max,thi->eta.cmin,thi->eta.cmax);
1119: PetscPrintf(comm,"Global beta2 range [%g, %g], converged range [%g, %g]\n",thi->beta2.min,thi->beta2.max,thi->beta2.cmin,thi->beta2.cmax);
1120: }
1121: PetscPrintf(comm,"\n");
1122: DMCompositeRestoreAccess(pack,X,&X3,&X2);
1123: return(0);
1124: }
1126: static inline PetscInt DMDALocalIndex3D(DMDALocalInfo *info,PetscInt i,PetscInt j,PetscInt k)
1127: {return ((i-info->gzs)*info->gym + (j-info->gys))*info->gxm + (k-info->gxs);}
1128: static inline PetscInt DMDALocalIndex2D(DMDALocalInfo *info,PetscInt i,PetscInt j)
1129: {return (i-info->gzs)*info->gym + (j-info->gys);}
1133: static PetscErrorCode THIJacobianLocal_Momentum(DMDALocalInfo *info,const Node ***x,const PrmNode **prm,Mat B,Mat Bcpl,THI thi)
1134: {
1135: PetscInt xs,ys,xm,ym,zm,i,j,k,q,l,ll;
1136: PetscReal hx,hy;
1140: xs = info->zs;
1141: ys = info->ys;
1142: xm = info->zm;
1143: ym = info->ym;
1144: zm = info->xm;
1145: hx = thi->Lx / info->mz;
1146: hy = thi->Ly / info->my;
1148: for (i=xs; i<xs+xm; i++) {
1149: for (j=ys; j<ys+ym; j++) {
1150: PrmNode pn[4],dpn[4][2];
1151: QuadExtract(prm,i,j,pn);
1152: QuadComputeGrad4(QuadQDeriv,hx,hy,pn,dpn);
1153: for (k=0; k<zm-1; k++) {
1154: Node n[8];
1155: PetscReal zn[8],etabase = 0;
1156: PetscScalar Ke[8*NODE_SIZE][8*NODE_SIZE],Kcpl[8*NODE_SIZE][4*PRMNODE_SIZE];
1157: PetscInt ls = 0;
1159: PrmHexGetZ(pn,k,zm,zn);
1160: HexExtract(x,i,j,k,n);
1161: PetscMemzero(Ke,sizeof(Ke));
1162: PetscMemzero(Kcpl,sizeof(Kcpl));
1163: if (thi->no_slip && k == 0) {
1164: for (l=0; l<4; l++) n[l].u = n[l].v = 0;
1165: ls = 4;
1166: }
1167: for (q=0; q<8; q++) {
1168: PetscReal dz[3],phi[8],dphi[8][3],jw,eta,deta;
1169: PetscScalar du[3],dv[3],u,v;
1170: HexGrad(HexQDeriv[q],zn,dz);
1171: HexComputeGeometry(q,hx,hy,dz,phi,dphi,&jw);
1172: PointwiseNonlinearity(thi,n,phi,dphi,&u,&v,du,dv,&eta,&deta);
1173: jw /= thi->rhog; /* residuals are scaled by this factor */
1174: if (q == 0) etabase = eta;
1175: for (l=ls; l<8; l++) { /* test functions */
1176: const PetscReal pp=phi[l],*restrict dp = dphi[l];
1177: for (ll=ls; ll<8; ll++) { /* trial functions */
1178: const PetscReal *restrict dpl = dphi[ll];
1179: PetscScalar dgdu,dgdv;
1180: dgdu = 2.*du[0]*dpl[0] + dv[1]*dpl[0] + 0.5*(du[1]+dv[0])*dpl[1] + 0.5*du[2]*dpl[2];
1181: dgdv = 2.*dv[1]*dpl[1] + du[0]*dpl[1] + 0.5*(du[1]+dv[0])*dpl[0] + 0.5*dv[2]*dpl[2];
1182: /* Picard part */
1183: 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];
1184: Ke[l*2+0][ll*2+1] += dp[0]*jw*eta*2.*dpl[1] + dp[1]*jw*eta*dpl[0];
1185: Ke[l*2+1][ll*2+0] += dp[1]*jw*eta*2.*dpl[0] + dp[0]*jw*eta*dpl[1];
1186: 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];
1187: /* extra Newton terms */
1188: 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];
1189: 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];
1190: 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];
1191: 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];
1192: /* inertial part */
1193: Ke[l*2+0][ll*2+0] += pp*jw*thi->inertia*pp;
1194: Ke[l*2+1][ll*2+1] += pp*jw*thi->inertia*pp;
1195: }
1196: for (ll=0; ll<4; ll++) { /* Trial functions for surface/bed */
1197: const PetscReal dpl[] = {QuadQDeriv[q%4][ll][0]/hx, QuadQDeriv[q%4][ll][1]/hy}; /* surface = h + b */
1198: Kcpl[FieldIndex(Node,l,u)][FieldIndex(PrmNode,ll,h)] += pp*jw*thi->rhog*dpl[0];
1199: Kcpl[FieldIndex(Node,l,u)][FieldIndex(PrmNode,ll,b)] += pp*jw*thi->rhog*dpl[0];
1200: Kcpl[FieldIndex(Node,l,v)][FieldIndex(PrmNode,ll,h)] += pp*jw*thi->rhog*dpl[1];
1201: Kcpl[FieldIndex(Node,l,v)][FieldIndex(PrmNode,ll,b)] += pp*jw*thi->rhog*dpl[1];
1202: }
1203: }
1204: }
1205: if (k == 0) { /* on a bottom face */
1206: if (thi->no_slip) {
1207: const PetscReal hz = PetscRealPart(pn[0].h)/(zm-1);
1208: 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);
1209: Ke[0][0] = thi->dirichlet_scale*diagu;
1210: Ke[0][1] = 0;
1211: Ke[1][0] = 0;
1212: Ke[1][1] = thi->dirichlet_scale*diagv;
1213: } else {
1214: for (q=0; q<4; q++) { /* We remove the explicit scaling by 1/rhog because beta2 already has that scaling to be O(1) */
1215: const PetscReal jw = 0.25*hx*hy,*phi = QuadQInterp[q];
1216: PetscScalar u =0,v=0,rbeta2=0;
1217: PetscReal beta2,dbeta2;
1218: for (l=0; l<4; l++) {
1219: u += phi[l]*n[l].u;
1220: v += phi[l]*n[l].v;
1221: rbeta2 += phi[l]*pn[l].beta2;
1222: }
1223: THIFriction(thi,PetscRealPart(rbeta2),PetscRealPart(u*u+v*v)/2,&beta2,&dbeta2);
1224: for (l=0; l<4; l++) {
1225: const PetscReal pp = phi[l];
1226: for (ll=0; ll<4; ll++) {
1227: const PetscReal ppl = phi[ll];
1228: Ke[l*2+0][ll*2+0] += pp*jw*beta2*ppl + pp*jw*dbeta2*u*u*ppl;
1229: Ke[l*2+0][ll*2+1] += pp*jw*dbeta2*u*v*ppl;
1230: Ke[l*2+1][ll*2+0] += pp*jw*dbeta2*v*u*ppl;
1231: Ke[l*2+1][ll*2+1] += pp*jw*beta2*ppl + pp*jw*dbeta2*v*v*ppl;
1232: }
1233: }
1234: }
1235: }
1236: }
1237: {
1238: const PetscInt rc3blocked[8] = {
1239: DMDALocalIndex3D(info,i+0,j+0,k+0),
1240: DMDALocalIndex3D(info,i+1,j+0,k+0),
1241: DMDALocalIndex3D(info,i+1,j+1,k+0),
1242: DMDALocalIndex3D(info,i+0,j+1,k+0),
1243: DMDALocalIndex3D(info,i+0,j+0,k+1),
1244: DMDALocalIndex3D(info,i+1,j+0,k+1),
1245: DMDALocalIndex3D(info,i+1,j+1,k+1),
1246: DMDALocalIndex3D(info,i+0,j+1,k+1)
1247: },col2blocked[PRMNODE_SIZE*4] = {
1248: DMDALocalIndex2D(info,i+0,j+0),
1249: DMDALocalIndex2D(info,i+1,j+0),
1250: DMDALocalIndex2D(info,i+1,j+1),
1251: DMDALocalIndex2D(info,i+0,j+1)
1252: };
1253: #if !defined COMPUTE_LOWER_TRIANGULAR /* fill in lower-triangular part, this is really cheap compared to computing the entries */
1254: for (l=0; l<8; l++) {
1255: for (ll=l+1; ll<8; ll++) {
1256: Ke[ll*2+0][l*2+0] = Ke[l*2+0][ll*2+0];
1257: Ke[ll*2+1][l*2+0] = Ke[l*2+0][ll*2+1];
1258: Ke[ll*2+0][l*2+1] = Ke[l*2+1][ll*2+0];
1259: Ke[ll*2+1][l*2+1] = Ke[l*2+1][ll*2+1];
1260: }
1261: }
1262: #endif
1263: MatSetValuesBlockedLocal(B,8,rc3blocked,8,rc3blocked,&Ke[0][0],ADD_VALUES); /* velocity-velocity coupling can use blocked insertion */
1264: { /* The off-diagonal part cannot (yet) */
1265: PetscInt row3scalar[NODE_SIZE*8],col2scalar[PRMNODE_SIZE*4];
1266: for (l=0; l<8; l++) for (ll=0; ll<NODE_SIZE; ll++) row3scalar[l*NODE_SIZE+ll] = rc3blocked[l]*NODE_SIZE+ll;
1267: for (l=0; l<4; l++) for (ll=0; ll<PRMNODE_SIZE; ll++) col2scalar[l*PRMNODE_SIZE+ll] = col2blocked[l]*PRMNODE_SIZE+ll;
1268: MatSetValuesLocal(Bcpl,8*NODE_SIZE,row3scalar,4*PRMNODE_SIZE,col2scalar,&Kcpl[0][0],ADD_VALUES);
1269: }
1270: }
1271: }
1272: }
1273: }
1274: return(0);
1275: }
1279: static PetscErrorCode THIJacobianLocal_2D(DMDALocalInfo *info,const Node ***x3,const PrmNode **x2,const PrmNode **xdot2,PetscReal a,Mat B22,Mat B21,THI thi)
1280: {
1282: PetscInt xs,ys,xm,ym,zm,i,j,k;
1285: xs = info->zs;
1286: ys = info->ys;
1287: xm = info->zm;
1288: ym = info->ym;
1289: zm = info->xm;
1291: if (zm > 1024) SETERRQ(((PetscObject)info->da)->comm,PETSC_ERR_SUP,"Need to allocate more space");
1292: for (i=xs; i<xs+xm; i++) {
1293: for (j=ys; j<ys+ym; j++) {
1294: { /* Self-coupling */
1295: const PetscInt row[] = {DMDALocalIndex2D(info,i,j)};
1296: const PetscInt col[] = {DMDALocalIndex2D(info,i,j)};
1297: const PetscScalar vals[] = {
1298: a,0,0,
1299: 0,a,0,
1300: 0,0,a
1301: };
1302: MatSetValuesBlockedLocal(B22,1,row,1,col,vals,INSERT_VALUES);
1303: }
1304: for (k=0; k<zm; k++) { /* Coupling to velocity problem */
1305: /* Use a cheaper quadrature than for residual evaluation, because it is much sparser */
1306: const PetscInt row[] = {FieldIndex(PrmNode,DMDALocalIndex2D(info,i,j),h)};
1307: const PetscInt cols[] = {
1308: FieldIndex(Node,DMDALocalIndex3D(info,i-1,j,k),u),
1309: FieldIndex(Node,DMDALocalIndex3D(info,i ,j,k),u),
1310: FieldIndex(Node,DMDALocalIndex3D(info,i+1,j,k),u),
1311: FieldIndex(Node,DMDALocalIndex3D(info,i,j-1,k),v),
1312: FieldIndex(Node,DMDALocalIndex3D(info,i,j ,k),v),
1313: FieldIndex(Node,DMDALocalIndex3D(info,i,j+1,k),v)
1314: };
1315: const PetscScalar
1316: w = (k && k<zm-1) ? 0.5 : 0.25,
1317: hW = w*(x2[i-1][j ].h+x2[i ][j ].h)/(zm-1.),
1318: hE = w*(x2[i ][j ].h+x2[i+1][j ].h)/(zm-1.),
1319: hS = w*(x2[i ][j-1].h+x2[i ][j ].h)/(zm-1.),
1320: hN = w*(x2[i ][j ].h+x2[i ][j+1].h)/(zm-1.);
1321: PetscScalar *vals,
1322: vals_upwind[] = {((PetscRealPart(x3[i][j][k].u) > 0) ? -hW : 0),
1323: ((PetscRealPart(x3[i][j][k].u) > 0) ? +hE : -hW),
1324: ((PetscRealPart(x3[i][j][k].u) > 0) ? 0 : +hE),
1325: ((PetscRealPart(x3[i][j][k].v) > 0) ? -hS : 0),
1326: ((PetscRealPart(x3[i][j][k].v) > 0) ? +hN : -hS),
1327: ((PetscRealPart(x3[i][j][k].v) > 0) ? 0 : +hN)},
1328: vals_centered[] = {-0.5*hW, 0.5*(-hW+hE), 0.5*hE,
1329: -0.5*hS, 0.5*(-hS+hN), 0.5*hN};
1330: vals = 1 ? vals_upwind : vals_centered;
1331: if (k == 0) {
1332: Node derate;
1333: THIErosion(thi,&x3[i][j][0],NULL,&derate);
1334: vals[1] -= derate.u;
1335: vals[4] -= derate.v;
1336: }
1337: MatSetValuesLocal(B21,1,row,6,cols,vals,INSERT_VALUES);
1338: }
1339: }
1340: }
1341: return(0);
1342: }
1346: static PetscErrorCode THIJacobian(TS ts,PetscReal t,Vec X,Vec Xdot,PetscReal a,Mat A,Mat B,void *ctx)
1347: {
1349: THI thi = (THI)ctx;
1350: DM pack,da3,da2;
1351: Vec X3,X2,Xdot2;
1352: Mat B11,B12,B21,B22;
1353: DMDALocalInfo info3;
1354: IS *isloc;
1355: const Node ***x3;
1356: const PrmNode **x2,**xdot2;
1359: TSGetDM(ts,&pack);
1360: DMCompositeGetEntries(pack,&da3,&da2);
1361: DMDAGetLocalInfo(da3,&info3);
1362: DMCompositeGetLocalVectors(pack,&X3,&X2);
1363: DMCompositeGetLocalVectors(pack,NULL,&Xdot2);
1364: DMCompositeScatter(pack,X,X3,X2);
1365: THIFixGhosts(thi,da3,da2,X3,X2);
1366: DMCompositeScatter(pack,Xdot,NULL,Xdot2);
1368: MatZeroEntries(B);
1370: DMCompositeGetLocalISs(pack,&isloc);
1371: MatGetLocalSubMatrix(B,isloc[0],isloc[0],&B11);
1372: MatGetLocalSubMatrix(B,isloc[0],isloc[1],&B12);
1373: MatGetLocalSubMatrix(B,isloc[1],isloc[0],&B21);
1374: MatGetLocalSubMatrix(B,isloc[1],isloc[1],&B22);
1376: DMDAVecGetArray(da3,X3,&x3);
1377: DMDAVecGetArray(da2,X2,&x2);
1378: DMDAVecGetArray(da2,Xdot2,&xdot2);
1380: THIJacobianLocal_Momentum(&info3,x3,x2,B11,B12,thi);
1382: /* Need to switch from ADD_VALUES to INSERT_VALUES */
1383: MatAssemblyBegin(*B,MAT_FLUSH_ASSEMBLY);
1384: MatAssemblyEnd(*B,MAT_FLUSH_ASSEMBLY);
1386: THIJacobianLocal_2D(&info3,x3,x2,xdot2,a,B22,B21,thi);
1388: DMDAVecRestoreArray(da3,X3,&x3);
1389: DMDAVecRestoreArray(da2,X2,&x2);
1390: DMDAVecRestoreArray(da2,Xdot2,&xdot2);
1392: MatRestoreLocalSubMatrix(B,isloc[0],isloc[0],&B11);
1393: MatRestoreLocalSubMatrix(B,isloc[0],isloc[1],&B12);
1394: MatRestoreLocalSubMatrix(B,isloc[1],isloc[0],&B21);
1395: MatRestoreLocalSubMatrix(B,isloc[1],isloc[1],&B22);
1396: ISDestroy(&isloc[0]);
1397: ISDestroy(&isloc[1]);
1398: PetscFree(isloc);
1400: DMCompositeRestoreLocalVectors(pack,&X3,&X2);
1401: DMCompositeRestoreLocalVectors(pack,0,&Xdot2);
1403: MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
1404: MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
1405: if (A != B) {
1406: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
1407: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
1408: }
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,&array,nmax2,&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,(double)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,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);
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),DM_BOUNDARY_PERIODIC,DM_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,&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,(double)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: }