Actual source code: ex14.c
1: static const char help[] = "Toy hydrostatic ice flow with multigrid in 3D.\n\
2: \n\
3: Solves the hydrostatic (aka Blatter/Pattyn/First Order) equations for ice sheet flow\n\
4: using multigrid. The ice uses a power-law rheology with \"Glen\" exponent 3 (corresponds\n\
5: to p=4/3 in a p-Laplacian). The focus is on ISMIP-HOM experiments which assume periodic\n\
6: boundary conditions in the x- and y-directions.\n\
7: \n\
8: Equations are rescaled so that the domain size and solution are O(1), details of this scaling\n\
9: can be controlled by the options -units_meter, -units_second, and -units_kilogram.\n\
10: \n\
11: A VTK StructuredGrid output file can be written using the option -o filename.vts\n\
12: \n\n";
14: /*
15: The equations for horizontal velocity (u,v) are
17: - [eta (4 u_x + 2 v_y)]_x - [eta (u_y + v_x)]_y - [eta u_z]_z + rho g s_x = 0
18: - [eta (4 v_y + 2 u_x)]_y - [eta (u_y + v_x)]_x - [eta v_z]_z + rho g s_y = 0
20: where
22: eta = B/2 (epsilon + gamma)^((p-2)/2)
24: is the nonlinear effective viscosity with regularization epsilon and hardness parameter B,
25: written in terms of the second invariant
27: gamma = u_x^2 + v_y^2 + u_x v_y + (1/4) (u_y + v_x)^2 + (1/4) u_z^2 + (1/4) v_z^2
29: The surface boundary conditions are the natural conditions. The basal boundary conditions
30: are either no-slip, or Navier (linear) slip with spatially variant friction coefficient beta^2.
32: In the code, the equations for (u,v) are multiplied through by 1/(rho g) so that residuals are O(1).
34: The discretization is Q1 finite elements, managed by a DMDA. The grid is never distorted in the
35: map (x,y) plane, but the bed and surface may be bumpy. This is handled as usual in FEM, through
36: the Jacobian of the coordinate transformation from a reference element to the physical element.
38: Since ice-flow is tightly coupled in the z-direction (within columns), the DMDA is managed
39: specially so that columns are never distributed, and are always contiguous in memory.
40: This amounts to reversing the meaning of X,Y,Z compared to the DMDA's internal interpretation,
41: and then indexing as vec[i][j][k]. The exotic coarse spaces require 2D DMDAs which are made to
42: use compatible domain decomposition relative to the 3D DMDAs.
44: */
46: #include <petscts.h>
47: #include <petscdm.h>
48: #include <petscdmda.h>
49: #include <petscdmcomposite.h>
50: #include <ctype.h> /* toupper() */
51: #include <petsc/private/petscimpl.h>
53: #if defined __SSE2__
54: #include <emmintrin.h>
55: #endif
57: /* The SSE2 kernels are only for PetscScalar=double on architectures that support it */
58: #define USE_SSE2_KERNELS (!defined NO_SSE2 && !defined PETSC_USE_COMPLEX && !defined PETSC_USE_REAL_SINGLE && defined __SSE2__)
60: #if !defined __STDC_VERSION__ || __STDC_VERSION__ < 199901L
61: #if defined __cplusplus /* C++ restrict is nonstandard and compilers have inconsistent rules about where it can be used */
62: #define restrict
63: #else
64: #define restrict PETSC_RESTRICT
65: #endif
66: #endif
68: static PetscClassId THI_CLASSID;
70: typedef enum {
71: QUAD_GAUSS,
72: QUAD_LOBATTO
73: } QuadratureType;
74: static const char *QuadratureTypes[] = {"gauss", "lobatto", "QuadratureType", "QUAD_", 0};
75: static const PetscReal HexQWeights[8] = {1, 1, 1, 1, 1, 1, 1, 1};
76: static const PetscReal HexQNodes[] = {-0.57735026918962573, 0.57735026918962573};
77: #define G 0.57735026918962573
78: #define H (0.5 * (1. + G))
79: #define L (0.5 * (1. - G))
80: #define M (-0.5)
81: #define P (0.5)
82: /* Special quadrature: Lobatto in horizontal, Gauss in vertical */
83: static const PetscReal HexQInterp_Lobatto[8][8] = {
84: {H, 0, 0, 0, L, 0, 0, 0},
85: {0, H, 0, 0, 0, L, 0, 0},
86: {0, 0, H, 0, 0, 0, L, 0},
87: {0, 0, 0, H, 0, 0, 0, L},
88: {L, 0, 0, 0, H, 0, 0, 0},
89: {0, L, 0, 0, 0, H, 0, 0},
90: {0, 0, L, 0, 0, 0, H, 0},
91: {0, 0, 0, L, 0, 0, 0, H}
92: };
93: static const PetscReal HexQDeriv_Lobatto[8][8][3] = {
94: {{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} },
95: {{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} },
96: {{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} },
97: {{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}},
98: {{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} },
99: {{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} },
100: {{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} },
101: {{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}}
102: };
103: /* Stanndard Gauss */
104: static const PetscReal HexQInterp_Gauss[8][8] = {
105: {H * H * H, L *H *H, L *L *H, H *L *H, H *H *L, L *H *L, L *L *L, H *L *L},
106: {L * H * H, H *H *H, H *L *H, L *L *H, L *H *L, H *H *L, H *L *L, L *L *L},
107: {L * L * H, H *L *H, H *H *H, L *H *H, L *L *L, H *L *L, H *H *L, L *H *L},
108: {H * L * H, L *L *H, L *H *H, H *H *H, H *L *L, L *L *L, L *H *L, H *H *L},
109: {H * H * L, L *H *L, L *L *L, H *L *L, H *H *H, L *H *H, L *L *H, H *L *H},
110: {L * H * L, H *H *L, H *L *L, L *L *L, L *H *H, H *H *H, H *L *H, L *L *H},
111: {L * L * L, H *L *L, H *H *L, L *H *L, L *L *H, H *L *H, H *H *H, L *H *H},
112: {H * L * L, L *L *L, L *H *L, H *H *L, H *L *H, L *L *H, L *H *H, H *H *H}
113: };
114: static const PetscReal HexQDeriv_Gauss[8][8][3] = {
115: {{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}},
116: {{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}},
117: {{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}},
118: {{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}},
119: {{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}},
120: {{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}},
121: {{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}},
122: {{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}}
123: };
124: static const PetscReal (*HexQInterp)[8], (*HexQDeriv)[8][3];
125: /* Standard 2x2 Gauss quadrature for the bottom layer. */
126: static const PetscReal QuadQInterp[4][4] = {
127: {H * H, L *H, L *L, H *L},
128: {L * H, H *H, H *L, L *L},
129: {L * L, H *L, H *H, L *H},
130: {H * L, L *L, L *H, H *H}
131: };
132: static const PetscReal QuadQDeriv[4][4][2] = {
133: {{M * H, M *H}, {P * H, M *L}, {P * L, P *L}, {M * L, P *H}},
134: {{M * H, M *L}, {P * H, M *H}, {P * L, P *H}, {M * L, P *L}},
135: {{M * L, M *L}, {P * L, M *H}, {P * H, P *H}, {M * H, P *L}},
136: {{M * L, M *H}, {P * L, M *L}, {P * H, P *L}, {M * H, P *H}}
137: };
138: #undef G
139: #undef H
140: #undef L
141: #undef M
142: #undef P
144: #define HexExtract(x, i, j, k, n) \
145: 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 HexExtractRef(x, i, j, k, n) \
157: do { \
158: (n)[0] = &(x)[i][j][k]; \
159: (n)[1] = &(x)[i + 1][j][k]; \
160: (n)[2] = &(x)[i + 1][j + 1][k]; \
161: (n)[3] = &(x)[i][j + 1][k]; \
162: (n)[4] = &(x)[i][j][k + 1]; \
163: (n)[5] = &(x)[i + 1][j][k + 1]; \
164: (n)[6] = &(x)[i + 1][j + 1][k + 1]; \
165: (n)[7] = &(x)[i][j + 1][k + 1]; \
166: } while (0)
168: #define QuadExtract(x, i, j, n) \
169: do { \
170: (n)[0] = (x)[i][j]; \
171: (n)[1] = (x)[i + 1][j]; \
172: (n)[2] = (x)[i + 1][j + 1]; \
173: (n)[3] = (x)[i][j + 1]; \
174: } while (0)
176: static PetscScalar Sqr(PetscScalar a)
177: {
178: return a * a;
179: }
181: static void HexGrad(const PetscReal dphi[][3], const PetscReal zn[], PetscReal dz[])
182: {
183: PetscInt i;
184: dz[0] = dz[1] = dz[2] = 0;
185: for (i = 0; i < 8; i++) {
186: dz[0] += dphi[i][0] * zn[i];
187: dz[1] += dphi[i][1] * zn[i];
188: dz[2] += dphi[i][2] * zn[i];
189: }
190: }
192: static void HexComputeGeometry(PetscInt q, PetscReal hx, PetscReal hy, const PetscReal dz[restrict], PetscReal phi[restrict], PetscReal dphi[restrict][3], PetscReal *restrict jw)
193: {
194: const PetscReal jac[3][3] =
195: {
196: {hx / 2, 0, 0 },
197: {0, hy / 2, 0 },
198: {dz[0], dz[1], dz[2]}
199: },
200: 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]}}, jdet = jac[0][0] * jac[1][1] * jac[2][2];
201: PetscInt i;
203: for (i = 0; i < 8; i++) {
204: const PetscReal *dphir = HexQDeriv[q][i];
205: phi[i] = HexQInterp[q][i];
206: dphi[i][0] = dphir[0] * ijac[0][0] + dphir[1] * ijac[1][0] + dphir[2] * ijac[2][0];
207: dphi[i][1] = dphir[0] * ijac[0][1] + dphir[1] * ijac[1][1] + dphir[2] * ijac[2][1];
208: dphi[i][2] = dphir[0] * ijac[0][2] + dphir[1] * ijac[1][2] + dphir[2] * ijac[2][2];
209: }
210: *jw = 1.0 * jdet;
211: }
213: typedef struct _p_THI *THI;
214: typedef struct _n_Units *Units;
216: typedef struct {
217: PetscScalar u, v;
218: } Node;
220: typedef struct {
221: PetscScalar b; /* bed */
222: PetscScalar h; /* thickness */
223: PetscScalar beta2; /* friction */
224: } PrmNode;
226: #define FieldSize(ntype) ((PetscInt)(sizeof(ntype) / sizeof(PetscScalar)))
227: #define FieldOffset(ntype, member) ((PetscInt)(offsetof(ntype, member) / sizeof(PetscScalar)))
228: #define FieldIndex(ntype, i, member) ((PetscInt)((i) * FieldSize(ntype) + FieldOffset(ntype, member)))
229: #define NODE_SIZE FieldSize(Node)
230: #define PRMNODE_SIZE FieldSize(PrmNode)
232: typedef struct {
233: PetscReal min, max, cmin, cmax;
234: } PRange;
236: struct _p_THI {
237: PETSCHEADER(int);
238: void (*initialize)(THI, PetscReal x, PetscReal y, PrmNode *p);
239: PetscInt nlevels;
240: PetscInt zlevels;
241: PetscReal Lx, Ly, Lz; /* Model domain */
242: PetscReal alpha; /* Bed angle */
243: Units units;
244: PetscReal dirichlet_scale;
245: PetscReal ssa_friction_scale;
246: PetscReal inertia;
247: PRange eta;
248: PRange beta2;
249: struct {
250: PetscReal Bd2, eps, exponent, glen_n;
251: } viscosity;
252: struct {
253: PetscReal irefgam, eps2, exponent;
254: } friction;
255: struct {
256: PetscReal rate, exponent, refvel;
257: } erosion;
258: PetscReal rhog;
259: PetscBool no_slip;
260: PetscBool verbose;
261: char *mattype;
262: char *monitor_basename;
263: PetscInt monitor_interval;
264: };
266: struct _n_Units {
267: /* fundamental */
268: PetscReal meter;
269: PetscReal kilogram;
270: PetscReal second;
271: /* derived */
272: PetscReal Pascal;
273: PetscReal year;
274: };
276: static void PrmHexGetZ(const PrmNode pn[], PetscInt k, PetscInt zm, PetscReal zn[])
277: {
278: const PetscScalar zm1 = zm - 1, znl[8] = {pn[0].b + pn[0].h * (PetscScalar)k / zm1, pn[1].b + pn[1].h * (PetscScalar)k / zm1, pn[2].b + pn[2].h * (PetscScalar)k / zm1, pn[3].b + pn[3].h * (PetscScalar)k / zm1,
279: pn[0].b + pn[0].h * (PetscScalar)(k + 1) / zm1, pn[1].b + pn[1].h * (PetscScalar)(k + 1) / zm1, pn[2].b + pn[2].h * (PetscScalar)(k + 1) / zm1, pn[3].b + pn[3].h * (PetscScalar)(k + 1) / zm1};
280: PetscInt i;
281: for (i = 0; i < 8; i++) zn[i] = PetscRealPart(znl[i]);
282: }
284: /* Compute a gradient of all the 2D fields at four quadrature points. Output for [quadrature_point][direction].field_name */
285: static PetscErrorCode QuadComputeGrad4(const PetscReal dphi[][4][2], PetscReal hx, PetscReal hy, const PrmNode pn[4], PrmNode dp[4][2])
286: {
287: PetscInt q, i, f;
288: const PetscScalar(*restrict pg)[PRMNODE_SIZE] = (const PetscScalar(*)[PRMNODE_SIZE])pn; /* Get generic array pointers to the node */
289: PetscScalar(*restrict dpg)[2][PRMNODE_SIZE] = (PetscScalar(*)[2][PRMNODE_SIZE])dp;
291: PetscFunctionBeginUser;
292: PetscCall(PetscArrayzero(dpg, 4));
293: for (q = 0; q < 4; q++) {
294: for (i = 0; i < 4; i++) {
295: for (f = 0; f < PRMNODE_SIZE; f++) {
296: dpg[q][0][f] += dphi[q][i][0] / hx * pg[i][f];
297: dpg[q][1][f] += dphi[q][i][1] / hy * pg[i][f];
298: }
299: }
300: }
301: PetscFunctionReturn(PETSC_SUCCESS);
302: }
304: static inline PetscReal StaggeredMidpoint2D(PetscScalar a, PetscScalar b, PetscScalar c, PetscScalar d)
305: {
306: return 0.5 * PetscRealPart(0.75 * a + 0.75 * b + 0.25 * c + 0.25 * d);
307: }
308: static inline PetscReal UpwindFlux1D(PetscReal u, PetscReal hL, PetscReal hR)
309: {
310: return (u > 0) ? hL * u : hR * u;
311: }
313: #define UpwindFluxXW(x3, x2, h, i, j, k, dj) \
314: 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), 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))
315: #define UpwindFluxXE(x3, x2, h, i, j, k, dj) \
316: 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), 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))
317: #define UpwindFluxYS(x3, x2, h, i, j, k, di) \
318: 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), 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))
319: #define UpwindFluxYN(x3, x2, h, i, j, k, di) \
320: 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), 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))
322: static void PrmNodeGetFaceMeasure(const PrmNode **p, PetscInt i, PetscInt j, PetscScalar h[])
323: {
324: /* West */
325: h[0] = StaggeredMidpoint2D(p[i][j].h, p[i - 1][j].h, p[i - 1][j - 1].h, p[i][j - 1].h);
326: h[1] = StaggeredMidpoint2D(p[i][j].h, p[i - 1][j].h, p[i - 1][j + 1].h, p[i][j + 1].h);
327: /* East */
328: h[2] = StaggeredMidpoint2D(p[i][j].h, p[i + 1][j].h, p[i + 1][j + 1].h, p[i][j + 1].h);
329: h[3] = StaggeredMidpoint2D(p[i][j].h, p[i + 1][j].h, p[i + 1][j - 1].h, p[i][j - 1].h);
330: /* South */
331: h[4] = StaggeredMidpoint2D(p[i][j].h, p[i][j - 1].h, p[i + 1][j - 1].h, p[i + 1][j].h);
332: h[5] = StaggeredMidpoint2D(p[i][j].h, p[i][j - 1].h, p[i - 1][j - 1].h, p[i - 1][j].h);
333: /* North */
334: h[6] = StaggeredMidpoint2D(p[i][j].h, p[i][j + 1].h, p[i - 1][j + 1].h, p[i - 1][j].h);
335: h[7] = StaggeredMidpoint2D(p[i][j].h, p[i][j + 1].h, p[i + 1][j + 1].h, p[i + 1][j].h);
336: }
338: /* Tests A and C are from the ISMIP-HOM paper (Pattyn et al. 2008) */
339: static void THIInitialize_HOM_A(THI thi, PetscReal x, PetscReal y, PrmNode *p)
340: {
341: Units units = thi->units;
342: PetscReal s = -x * PetscSinReal(thi->alpha);
343: p->b = s - 1000 * units->meter + 500 * units->meter * PetscSinReal(x * 2 * PETSC_PI / thi->Lx) * PetscSinReal(y * 2 * PETSC_PI / thi->Ly);
344: p->h = s - p->b;
345: p->beta2 = -1e-10; /* This value is not used, but it should not be huge because that would change the finite difference step size */
346: }
348: static void THIInitialize_HOM_C(THI thi, PetscReal x, PetscReal y, PrmNode *p)
349: {
350: Units units = thi->units;
351: PetscReal s = -x * PetscSinReal(thi->alpha);
352: p->b = s - 1000 * units->meter;
353: p->h = s - p->b;
354: /* tau_b = beta2 v is a stress (Pa).
355: * 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. */
356: 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;
357: }
359: /* These are just toys */
361: /* From Fred Herman */
362: static void THIInitialize_HOM_F(THI thi, PetscReal x, PetscReal y, PrmNode *p)
363: {
364: Units units = thi->units;
365: PetscReal s = -x * PetscSinReal(thi->alpha);
366: p->b = s - 1000 * units->meter + 100 * units->meter * PetscSinReal(x * 2 * PETSC_PI / thi->Lx); /* * sin(y*2*PETSC_PI/thi->Ly); */
367: p->h = s - p->b;
368: p->h = (1 - (atan((x - thi->Lx / 2) / 1.) + PETSC_PI / 2.) / PETSC_PI) * 500 * units->meter + 1 * units->meter;
369: s = PetscRealPart(p->b + p->h);
370: p->beta2 = -1e-10;
371: /* p->beta2 = 1000 * units->Pascal * units->year / units->meter; */
372: }
374: /* Same bed as test A, free slip everywhere except for a discontinuous jump to a circular sticky region in the middle. */
375: static void THIInitialize_HOM_X(THI thi, PetscReal xx, PetscReal yy, PrmNode *p)
376: {
377: Units units = thi->units;
378: PetscReal x = xx * 2 * PETSC_PI / thi->Lx - PETSC_PI, y = yy * 2 * PETSC_PI / thi->Ly - PETSC_PI; /* [-pi,pi] */
379: PetscReal r = PetscSqrtReal(x * x + y * y), s = -x * PetscSinReal(thi->alpha);
380: p->b = s - 1000 * units->meter + 500 * units->meter * PetscSinReal(x + PETSC_PI) * PetscSinReal(y + PETSC_PI);
381: p->h = s - p->b;
382: p->beta2 = 1000 * (r < 1 ? 2 : 0) * units->Pascal * units->year / units->meter / thi->rhog;
383: }
385: /* Like Z, but with 200 meter cliffs */
386: static void THIInitialize_HOM_Y(THI thi, PetscReal xx, PetscReal yy, PrmNode *p)
387: {
388: Units units = thi->units;
389: PetscReal x = xx * 2 * PETSC_PI / thi->Lx - PETSC_PI, y = yy * 2 * PETSC_PI / thi->Ly - PETSC_PI; /* [-pi,pi] */
390: PetscReal r = PetscSqrtReal(x * x + y * y), s = -x * PetscSinReal(thi->alpha);
391: p->b = s - 1000 * units->meter + 500 * units->meter * PetscSinReal(x + PETSC_PI) * PetscSinReal(y + PETSC_PI);
392: if (PetscRealPart(p->b) > -700 * units->meter) p->b += 200 * units->meter;
393: p->h = s - p->b;
394: 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;
395: }
397: /* Same bed as A, smoothly varying slipperiness, similar to MATLAB's "sombrero" (uncorrelated with bathymetry) */
398: static void THIInitialize_HOM_Z(THI thi, PetscReal xx, PetscReal yy, PrmNode *p)
399: {
400: Units units = thi->units;
401: PetscReal x = xx * 2 * PETSC_PI / thi->Lx - PETSC_PI, y = yy * 2 * PETSC_PI / thi->Ly - PETSC_PI; /* [-pi,pi] */
402: PetscReal r = PetscSqrtReal(x * x + y * y), s = -x * PetscSinReal(thi->alpha);
403: p->b = s - 1000 * units->meter + 500 * units->meter * PetscSinReal(x + PETSC_PI) * PetscSinReal(y + PETSC_PI);
404: p->h = s - p->b;
405: 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;
406: }
408: static void THIFriction(THI thi, PetscReal rbeta2, PetscReal gam, PetscReal *beta2, PetscReal *dbeta2)
409: {
410: if (thi->friction.irefgam == 0) {
411: Units units = thi->units;
412: thi->friction.irefgam = 1. / (0.5 * PetscSqr(100 * units->meter / units->year));
413: thi->friction.eps2 = 0.5 * PetscSqr(1.e-4 / thi->friction.irefgam);
414: }
415: if (thi->friction.exponent == 0) {
416: *beta2 = rbeta2;
417: *dbeta2 = 0;
418: } else {
419: *beta2 = rbeta2 * PetscPowReal(thi->friction.eps2 + gam * thi->friction.irefgam, thi->friction.exponent);
420: *dbeta2 = thi->friction.exponent * *beta2 / (thi->friction.eps2 + gam * thi->friction.irefgam) * thi->friction.irefgam;
421: }
422: }
424: static void THIViscosity(THI thi, PetscReal gam, PetscReal *eta, PetscReal *deta)
425: {
426: PetscReal Bd2, eps, exponent;
427: if (thi->viscosity.Bd2 == 0) {
428: Units units = thi->units;
429: const PetscReal n = thi->viscosity.glen_n, /* Glen exponent */
430: p = 1. + 1. / n, /* for Stokes */
431: A = 1.e-16 * PetscPowReal(units->Pascal, -n) / units->year, /* softness parameter (Pa^{-n}/s) */
432: B = PetscPowReal(A, -1. / n); /* hardness parameter */
433: thi->viscosity.Bd2 = B / 2;
434: thi->viscosity.exponent = (p - 2) / 2;
435: thi->viscosity.eps = 0.5 * PetscSqr(1e-5 / units->year);
436: }
437: Bd2 = thi->viscosity.Bd2;
438: exponent = thi->viscosity.exponent;
439: eps = thi->viscosity.eps;
440: *eta = Bd2 * PetscPowReal(eps + gam, exponent);
441: *deta = exponent * (*eta) / (eps + gam);
442: }
444: static void THIErosion(THI thi, const Node *vel, PetscScalar *erate, Node *derate)
445: {
446: const PetscScalar magref2 = 1.e-10 + (PetscSqr(vel->u) + PetscSqr(vel->v)) / PetscSqr(thi->erosion.refvel), rate = -thi->erosion.rate * PetscPowScalar(magref2, 0.5 * thi->erosion.exponent);
447: if (erate) *erate = rate;
448: if (derate) {
449: if (thi->erosion.exponent == 1) {
450: derate->u = 0;
451: derate->v = 0;
452: } else {
453: derate->u = 0.5 * thi->erosion.exponent * rate / magref2 * 2. * vel->u / PetscSqr(thi->erosion.refvel);
454: derate->v = 0.5 * thi->erosion.exponent * rate / magref2 * 2. * vel->v / PetscSqr(thi->erosion.refvel);
455: }
456: }
457: }
459: static void RangeUpdate(PetscReal *min, PetscReal *max, PetscReal x)
460: {
461: if (x < *min) *min = x;
462: if (x > *max) *max = x;
463: }
465: static void PRangeClear(PRange *p)
466: {
467: p->cmin = p->min = 1e100;
468: p->cmax = p->max = -1e100;
469: }
471: static PetscErrorCode PRangeMinMax(PRange *p, PetscReal min, PetscReal max)
472: {
473: PetscFunctionBeginUser;
474: p->cmin = min;
475: p->cmax = max;
476: if (min < p->min) p->min = min;
477: if (max > p->max) p->max = max;
478: PetscFunctionReturn(PETSC_SUCCESS);
479: }
481: static PetscErrorCode THIDestroy(THI *thi)
482: {
483: PetscFunctionBeginUser;
484: if (--((PetscObject)*thi)->refct > 0) PetscFunctionReturn(PETSC_SUCCESS);
485: PetscCall(PetscFree((*thi)->units));
486: PetscCall(PetscFree((*thi)->mattype));
487: PetscCall(PetscFree((*thi)->monitor_basename));
488: PetscCall(PetscHeaderDestroy(thi));
489: PetscFunctionReturn(PETSC_SUCCESS);
490: }
492: static PetscErrorCode THICreate(MPI_Comm comm, THI *inthi)
493: {
494: static PetscBool registered = PETSC_FALSE;
495: THI thi;
496: Units units;
497: char monitor_basename[PETSC_MAX_PATH_LEN] = "thi-";
499: PetscFunctionBeginUser;
500: *inthi = 0;
501: if (!registered) {
502: PetscCall(PetscClassIdRegister("Toy Hydrostatic Ice", &THI_CLASSID));
503: registered = PETSC_TRUE;
504: }
505: PetscCall(PetscHeaderCreate(thi, THI_CLASSID, "THI", "Toy Hydrostatic Ice", "THI", comm, THIDestroy, 0));
507: PetscCall(PetscNew(&thi->units));
509: units = thi->units;
510: units->meter = 1e-2;
511: units->second = 1e-7;
512: units->kilogram = 1e-12;
514: PetscOptionsBegin(comm, NULL, "Scaled units options", "");
515: {
516: PetscCall(PetscOptionsReal("-units_meter", "1 meter in scaled length units", "", units->meter, &units->meter, NULL));
517: PetscCall(PetscOptionsReal("-units_second", "1 second in scaled time units", "", units->second, &units->second, NULL));
518: PetscCall(PetscOptionsReal("-units_kilogram", "1 kilogram in scaled mass units", "", units->kilogram, &units->kilogram, NULL));
519: }
520: PetscOptionsEnd();
521: units->Pascal = units->kilogram / (units->meter * PetscSqr(units->second));
522: units->year = 31556926. * units->second, /* seconds per year */
524: thi->Lx = 10.e3;
525: thi->Ly = 10.e3;
526: thi->Lz = 1000;
527: thi->nlevels = 1;
528: thi->dirichlet_scale = 1;
529: thi->verbose = PETSC_FALSE;
531: thi->viscosity.glen_n = 3.;
532: thi->erosion.rate = 1e-3; /* m/a */
533: thi->erosion.exponent = 1.;
534: thi->erosion.refvel = 1.; /* m/a */
536: PetscOptionsBegin(comm, NULL, "Toy Hydrostatic Ice options", "");
537: {
538: QuadratureType quad = QUAD_GAUSS;
539: char homexp[] = "A";
540: char mtype[256] = MATSBAIJ;
541: PetscReal L, m = 1.0;
542: PetscBool flg;
543: L = thi->Lx;
544: PetscCall(PetscOptionsReal("-thi_L", "Domain size (m)", "", L, &L, &flg));
545: if (flg) thi->Lx = thi->Ly = L;
546: PetscCall(PetscOptionsReal("-thi_Lx", "X Domain size (m)", "", thi->Lx, &thi->Lx, NULL));
547: PetscCall(PetscOptionsReal("-thi_Ly", "Y Domain size (m)", "", thi->Ly, &thi->Ly, NULL));
548: PetscCall(PetscOptionsReal("-thi_Lz", "Z Domain size (m)", "", thi->Lz, &thi->Lz, NULL));
549: PetscCall(PetscOptionsString("-thi_hom", "ISMIP-HOM experiment (A or C)", "", homexp, homexp, sizeof(homexp), NULL));
550: switch (homexp[0] = toupper(homexp[0])) {
551: case 'A':
552: thi->initialize = THIInitialize_HOM_A;
553: thi->no_slip = PETSC_TRUE;
554: thi->alpha = 0.5;
555: break;
556: case 'C':
557: thi->initialize = THIInitialize_HOM_C;
558: thi->no_slip = PETSC_FALSE;
559: thi->alpha = 0.1;
560: break;
561: case 'F':
562: thi->initialize = THIInitialize_HOM_F;
563: thi->no_slip = PETSC_FALSE;
564: thi->alpha = 0.5;
565: break;
566: case 'X':
567: thi->initialize = THIInitialize_HOM_X;
568: thi->no_slip = PETSC_FALSE;
569: thi->alpha = 0.3;
570: break;
571: case 'Y':
572: thi->initialize = THIInitialize_HOM_Y;
573: thi->no_slip = PETSC_FALSE;
574: thi->alpha = 0.5;
575: break;
576: case 'Z':
577: thi->initialize = THIInitialize_HOM_Z;
578: thi->no_slip = PETSC_FALSE;
579: thi->alpha = 0.5;
580: break;
581: default:
582: SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP, "HOM experiment '%c' not implemented", homexp[0]);
583: }
584: PetscCall(PetscOptionsEnum("-thi_quadrature", "Quadrature to use for 3D elements", "", QuadratureTypes, (PetscEnum)quad, (PetscEnum *)&quad, NULL));
585: switch (quad) {
586: case QUAD_GAUSS:
587: HexQInterp = HexQInterp_Gauss;
588: HexQDeriv = HexQDeriv_Gauss;
589: break;
590: case QUAD_LOBATTO:
591: HexQInterp = HexQInterp_Lobatto;
592: HexQDeriv = HexQDeriv_Lobatto;
593: break;
594: }
595: PetscCall(PetscOptionsReal("-thi_alpha", "Bed angle (degrees)", "", thi->alpha, &thi->alpha, NULL));
596: PetscCall(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));
597: PetscCall(PetscOptionsReal("-thi_friction_m", "Friction exponent, 0=Coulomb, 1=Navier", "", m, &m, NULL));
598: thi->friction.exponent = (m - 1) / 2;
599: PetscCall(PetscOptionsReal("-thi_erosion_rate", "Rate of erosion relative to sliding velocity at reference velocity (m/a)", NULL, thi->erosion.rate, &thi->erosion.rate, NULL));
600: PetscCall(PetscOptionsReal("-thi_erosion_exponent", "Power of sliding velocity appearing in erosion relation", NULL, thi->erosion.exponent, &thi->erosion.exponent, NULL));
601: PetscCall(PetscOptionsReal("-thi_erosion_refvel", "Reference sliding velocity for erosion (m/a)", NULL, thi->erosion.refvel, &thi->erosion.refvel, NULL));
602: thi->erosion.rate *= units->meter / units->year;
603: thi->erosion.refvel *= units->meter / units->year;
604: PetscCall(PetscOptionsReal("-thi_dirichlet_scale", "Scale Dirichlet boundary conditions by this factor", "", thi->dirichlet_scale, &thi->dirichlet_scale, NULL));
605: PetscCall(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));
606: PetscCall(PetscOptionsReal("-thi_inertia", "Coefficient of acceleration term in velocity system, physical is almost zero", NULL, thi->inertia, &thi->inertia, NULL));
607: PetscCall(PetscOptionsInt("-thi_nlevels", "Number of levels of refinement", "", thi->nlevels, &thi->nlevels, NULL));
608: PetscCall(PetscOptionsFList("-thi_mat_type", "Matrix type", "MatSetType", MatList, mtype, (char *)mtype, sizeof(mtype), NULL));
609: PetscCall(PetscStrallocpy(mtype, &thi->mattype));
610: PetscCall(PetscOptionsBool("-thi_verbose", "Enable verbose output (like matrix sizes and statistics)", "", thi->verbose, &thi->verbose, NULL));
611: PetscCall(PetscOptionsString("-thi_monitor", "Basename to write state files to", NULL, monitor_basename, monitor_basename, sizeof(monitor_basename), &flg));
612: if (flg) {
613: PetscCall(PetscStrallocpy(monitor_basename, &thi->monitor_basename));
614: thi->monitor_interval = 1;
615: PetscCall(PetscOptionsInt("-thi_monitor_interval", "Frequency at which to write state files", NULL, thi->monitor_interval, &thi->monitor_interval, NULL));
616: }
617: }
618: PetscOptionsEnd();
620: /* dimensionalize */
621: thi->Lx *= units->meter;
622: thi->Ly *= units->meter;
623: thi->Lz *= units->meter;
624: thi->alpha *= PETSC_PI / 180;
626: PRangeClear(&thi->eta);
627: PRangeClear(&thi->beta2);
629: {
630: PetscReal u = 1000 * units->meter / (3e7 * units->second), gradu = u / (100 * units->meter), eta, deta, rho = 910 * units->kilogram / PetscPowRealInt(units->meter, 3), grav = 9.81 * units->meter / PetscSqr(units->second),
631: driving = rho * grav * PetscSinReal(thi->alpha) * 1000 * units->meter;
632: THIViscosity(thi, 0.5 * gradu * gradu, &eta, &deta);
633: thi->rhog = rho * grav;
634: if (thi->verbose) {
635: PetscCall(PetscPrintf(PetscObjectComm((PetscObject)thi), "Units: meter %8.2g second %8.2g kg %8.2g Pa %8.2g\n", (double)units->meter, (double)units->second, (double)units->kilogram, (double)units->Pascal));
636: PetscCall(PetscPrintf(PetscObjectComm((PetscObject)thi), "Domain (%6.2g,%6.2g,%6.2g), pressure %8.2g, driving stress %8.2g\n", (double)thi->Lx, (double)thi->Ly, (double)thi->Lz, (double)(rho * grav * 1e3 * units->meter), (double)driving));
637: PetscCall(PetscPrintf(PetscObjectComm((PetscObject)thi), "Large velocity 1km/a %8.2g, velocity gradient %8.2g, eta %8.2g, stress %8.2g, ratio %8.2g\n", (double)u, (double)gradu, (double)eta, (double)(2 * eta * gradu, 2 * eta * gradu / driving)));
638: THIViscosity(thi, 0.5 * PetscSqr(1e-3 * gradu), &eta, &deta);
639: PetscCall(PetscPrintf(PetscObjectComm((PetscObject)thi), "Small velocity 1m/a %8.2g, velocity gradient %8.2g, eta %8.2g, stress %8.2g, ratio %8.2g\n", (double)(1e-3 * u), (double)(1e-3 * gradu), (double)eta, (double)(2 * eta * 1e-3 * gradu, 2 * eta * 1e-3 * gradu / driving)));
640: }
641: }
643: *inthi = thi;
644: PetscFunctionReturn(PETSC_SUCCESS);
645: }
647: /* Our problem is periodic, but the domain has a mean slope of alpha so the bed does not line up between the upstream
648: * and downstream ends of the domain. This function fixes the ghost values so that the domain appears truly periodic in
649: * the horizontal. */
650: static PetscErrorCode THIFixGhosts(THI thi, DM da3, DM da2, Vec X3, Vec X2)
651: {
652: DMDALocalInfo info;
653: PrmNode **x2;
654: PetscInt i, j;
656: PetscFunctionBeginUser;
657: PetscCall(DMDAGetLocalInfo(da3, &info));
658: /* PetscCall(VecView(X2,PETSC_VIEWER_STDOUT_WORLD)); */
659: PetscCall(DMDAVecGetArray(da2, X2, &x2));
660: for (i = info.gzs; i < info.gzs + info.gzm; i++) {
661: if (i > -1 && i < info.mz) continue;
662: for (j = info.gys; j < info.gys + info.gym; j++) x2[i][j].b += PetscSinReal(thi->alpha) * thi->Lx * (i < 0 ? 1.0 : -1.0);
663: }
664: PetscCall(DMDAVecRestoreArray(da2, X2, &x2));
665: /* PetscCall(VecView(X2,PETSC_VIEWER_STDOUT_WORLD)); */
666: PetscFunctionReturn(PETSC_SUCCESS);
667: }
669: static PetscErrorCode THIInitializePrm(THI thi, DM da2prm, PrmNode **p)
670: {
671: PetscInt i, j, xs, xm, ys, ym, mx, my;
673: PetscFunctionBeginUser;
674: PetscCall(DMDAGetGhostCorners(da2prm, &ys, &xs, 0, &ym, &xm, 0));
675: PetscCall(DMDAGetInfo(da2prm, 0, &my, &mx, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0));
676: for (i = xs; i < xs + xm; i++) {
677: for (j = ys; j < ys + ym; j++) {
678: PetscReal xx = thi->Lx * i / mx, yy = thi->Ly * j / my;
679: thi->initialize(thi, xx, yy, &p[i][j]);
680: }
681: }
682: PetscFunctionReturn(PETSC_SUCCESS);
683: }
685: static PetscErrorCode THIInitial(THI thi, DM pack, Vec X)
686: {
687: DM da3, da2;
688: PetscInt i, j, k, xs, xm, ys, ym, zs, zm, mx, my;
689: PetscReal hx, hy;
690: PrmNode **prm;
691: Node ***x;
692: Vec X3g, X2g, X2;
694: PetscFunctionBeginUser;
695: PetscCall(DMCompositeGetEntries(pack, &da3, &da2));
696: PetscCall(DMCompositeGetAccess(pack, X, &X3g, &X2g));
697: PetscCall(DMGetLocalVector(da2, &X2));
699: PetscCall(DMDAGetInfo(da3, 0, 0, &my, &mx, 0, 0, 0, 0, 0, 0, 0, 0, 0));
700: PetscCall(DMDAGetCorners(da3, &zs, &ys, &xs, &zm, &ym, &xm));
701: PetscCall(DMDAVecGetArray(da3, X3g, &x));
702: PetscCall(DMDAVecGetArray(da2, X2, &prm));
704: PetscCall(THIInitializePrm(thi, da2, prm));
706: hx = thi->Lx / mx;
707: hy = thi->Ly / my;
708: for (i = xs; i < xs + xm; i++) {
709: for (j = ys; j < ys + ym; j++) {
710: for (k = zs; k < zs + zm; k++) {
711: const PetscScalar zm1 = zm - 1, 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), 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);
712: x[i][j][k].u = 0. * drivingx * prm[i][j].h * (PetscScalar)k / zm1;
713: x[i][j][k].v = 0. * drivingy * prm[i][j].h * (PetscScalar)k / zm1;
714: }
715: }
716: }
718: PetscCall(DMDAVecRestoreArray(da3, X3g, &x));
719: PetscCall(DMDAVecRestoreArray(da2, X2, &prm));
721: PetscCall(DMLocalToGlobalBegin(da2, X2, INSERT_VALUES, X2g));
722: PetscCall(DMLocalToGlobalEnd(da2, X2, INSERT_VALUES, X2g));
723: PetscCall(DMRestoreLocalVector(da2, &X2));
725: PetscCall(DMCompositeRestoreAccess(pack, X, &X3g, &X2g));
726: PetscFunctionReturn(PETSC_SUCCESS);
727: }
729: 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)
730: {
731: PetscInt l, ll;
732: PetscScalar gam;
734: du[0] = du[1] = du[2] = 0;
735: dv[0] = dv[1] = dv[2] = 0;
736: *u = 0;
737: *v = 0;
738: for (l = 0; l < 8; l++) {
739: *u += phi[l] * n[l].u;
740: *v += phi[l] * n[l].v;
741: for (ll = 0; ll < 3; ll++) {
742: du[ll] += dphi[l][ll] * n[l].u;
743: dv[ll] += dphi[l][ll] * n[l].v;
744: }
745: }
746: 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]);
747: THIViscosity(thi, PetscRealPart(gam), eta, deta);
748: }
750: static PetscErrorCode THIFunctionLocal_3D(DMDALocalInfo *info, const Node ***x, const PrmNode **prm, const Node ***xdot, Node ***f, THI thi)
751: {
752: PetscInt xs, ys, xm, ym, zm, i, j, k, q, l;
753: PetscReal hx, hy, etamin, etamax, beta2min, beta2max;
755: PetscFunctionBeginUser;
756: xs = info->zs;
757: ys = info->ys;
758: xm = info->zm;
759: ym = info->ym;
760: zm = info->xm;
761: hx = thi->Lx / info->mz;
762: hy = thi->Ly / info->my;
764: etamin = 1e100;
765: etamax = 0;
766: beta2min = 1e100;
767: beta2max = 0;
769: for (i = xs; i < xs + xm; i++) {
770: for (j = ys; j < ys + ym; j++) {
771: PrmNode pn[4], dpn[4][2];
772: QuadExtract(prm, i, j, pn);
773: PetscCall(QuadComputeGrad4(QuadQDeriv, hx, hy, pn, dpn));
774: for (k = 0; k < zm - 1; k++) {
775: PetscInt ls = 0;
776: Node n[8], ndot[8], *fn[8];
777: PetscReal zn[8], etabase = 0;
779: PrmHexGetZ(pn, k, zm, zn);
780: HexExtract(x, i, j, k, n);
781: HexExtract(xdot, i, j, k, ndot);
782: HexExtractRef(f, i, j, k, fn);
783: if (thi->no_slip && k == 0) {
784: for (l = 0; l < 4; l++) n[l].u = n[l].v = 0;
785: /* The first 4 basis functions lie on the bottom layer, so their contribution is exactly 0, hence we can skip them */
786: ls = 4;
787: }
788: for (q = 0; q < 8; q++) {
789: PetscReal dz[3], phi[8], dphi[8][3], jw, eta, deta;
790: PetscScalar du[3], dv[3], u, v, udot = 0, vdot = 0;
791: for (l = ls; l < 8; l++) {
792: udot += HexQInterp[q][l] * ndot[l].u;
793: vdot += HexQInterp[q][l] * ndot[l].v;
794: }
795: HexGrad(HexQDeriv[q], zn, dz);
796: HexComputeGeometry(q, hx, hy, dz, phi, dphi, &jw);
797: PointwiseNonlinearity(thi, n, phi, dphi, &u, &v, du, dv, &eta, &deta);
798: jw /= thi->rhog; /* scales residuals to be O(1) */
799: if (q == 0) etabase = eta;
800: RangeUpdate(&etamin, &etamax, eta);
801: for (l = ls; l < 8; l++) { /* test functions */
802: const PetscScalar ds[2] = {dpn[q % 4][0].h + dpn[q % 4][0].b, dpn[q % 4][1].h + dpn[q % 4][1].b};
803: const PetscReal pp = phi[l], *dp = dphi[l];
804: 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];
805: 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];
806: fn[l]->u += pp * jw * udot * thi->inertia * pp;
807: fn[l]->v += pp * jw * vdot * thi->inertia * pp;
808: }
809: }
810: if (k == 0) { /* we are on a bottom face */
811: if (thi->no_slip) {
812: /* Note: Non-Galerkin coarse grid operators are very sensitive to the scaling of Dirichlet boundary
813: * conditions. After shenanigans above, etabase contains the effective viscosity at the closest quadrature
814: * point to the bed. We want the diagonal entry in the Dirichlet condition to have similar magnitude to the
815: * diagonal entry corresponding to the adjacent node. The fundamental scaling of the viscous part is in
816: * diagu, diagv below. This scaling is easy to recognize by considering the finite difference operator after
817: * scaling by element size. The no-slip Dirichlet condition is scaled by this factor, and also in the
818: * assembled matrix (see the similar block in THIJacobianLocal).
819: *
820: * Note that the residual at this Dirichlet node is linear in the state at this node, but also depends
821: * (nonlinearly in general) on the neighboring interior nodes through the local viscosity. This will make
822: * a matrix-free Jacobian have extra entries in the corresponding row. We assemble only the diagonal part,
823: * so the solution will exactly satisfy the boundary condition after the first linear iteration.
824: */
825: const PetscReal hz = PetscRealPart(pn[0].h) / (zm - 1.);
826: 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);
827: fn[0]->u = thi->dirichlet_scale * diagu * x[i][j][k].u;
828: fn[0]->v = thi->dirichlet_scale * diagv * x[i][j][k].v;
829: } else { /* Integrate over bottom face to apply boundary condition */
830: 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) */
831: const PetscReal jw = 0.25 * hx * hy, *phi = QuadQInterp[q];
832: PetscScalar u = 0, v = 0, rbeta2 = 0;
833: PetscReal beta2, dbeta2;
834: for (l = 0; l < 4; l++) {
835: u += phi[l] * n[l].u;
836: v += phi[l] * n[l].v;
837: rbeta2 += phi[l] * pn[l].beta2;
838: }
839: THIFriction(thi, PetscRealPart(rbeta2), PetscRealPart(u * u + v * v) / 2, &beta2, &dbeta2);
840: RangeUpdate(&beta2min, &beta2max, beta2);
841: for (l = 0; l < 4; l++) {
842: const PetscReal pp = phi[l];
843: fn[ls + l]->u += pp * jw * beta2 * u;
844: fn[ls + l]->v += pp * jw * beta2 * v;
845: }
846: }
847: }
848: }
849: }
850: }
851: }
853: PetscCall(PRangeMinMax(&thi->eta, etamin, etamax));
854: PetscCall(PRangeMinMax(&thi->beta2, beta2min, beta2max));
855: PetscFunctionReturn(PETSC_SUCCESS);
856: }
858: static PetscErrorCode THIFunctionLocal_2D(DMDALocalInfo *info, const Node ***x, const PrmNode **prm, const PrmNode **prmdot, PrmNode **f, THI thi)
859: {
860: PetscInt xs, ys, xm, ym, zm, i, j, k;
862: PetscFunctionBeginUser;
863: xs = info->zs;
864: ys = info->ys;
865: xm = info->zm;
866: ym = info->ym;
867: zm = info->xm;
869: for (i = xs; i < xs + xm; i++) {
870: for (j = ys; j < ys + ym; j++) {
871: PetscScalar div = 0, erate, h[8];
872: PrmNodeGetFaceMeasure(prm, i, j, h);
873: for (k = 0; k < zm; k++) {
874: PetscScalar weight = (k == 0 || k == zm - 1) ? 0.5 / (zm - 1) : 1.0 / (zm - 1);
875: if (0) { /* centered flux */
876: 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) - 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) +
877: 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) + 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) -
878: 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) - 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) +
879: 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) + 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));
880: } else { /* Upwind flux */
881: div += weight * (-UpwindFluxXW(x, prm, h, i, j, k, 1) - UpwindFluxXW(x, prm, h, i, j, k, -1) + UpwindFluxXE(x, prm, h, i, j, k, 1) + UpwindFluxXE(x, prm, h, i, j, k, -1) - UpwindFluxYS(x, prm, h, i, j, k, 1) - UpwindFluxYS(x, prm, h, i, j, k, -1) + UpwindFluxYN(x, prm, h, i, j, k, 1) + UpwindFluxYN(x, prm, h, i, j, k, -1));
882: }
883: }
884: /* printf("div[%d][%d] %g\n",i,j,div); */
885: THIErosion(thi, &x[i][j][0], &erate, NULL);
886: f[i][j].b = prmdot[i][j].b - erate;
887: f[i][j].h = prmdot[i][j].h + div;
888: f[i][j].beta2 = prmdot[i][j].beta2;
889: }
890: }
891: PetscFunctionReturn(PETSC_SUCCESS);
892: }
894: static PetscErrorCode THIFunction(TS ts, PetscReal t, Vec X, Vec Xdot, Vec F, void *ctx)
895: {
896: THI thi = (THI)ctx;
897: DM pack, da3, da2;
898: Vec X3, X2, Xdot3, Xdot2, F3, F2, F3g, F2g;
899: const Node ***x3, ***xdot3;
900: const PrmNode **x2, **xdot2;
901: Node ***f3;
902: PrmNode **f2;
903: DMDALocalInfo info3;
905: PetscFunctionBeginUser;
906: PetscCall(TSGetDM(ts, &pack));
907: PetscCall(DMCompositeGetEntries(pack, &da3, &da2));
908: PetscCall(DMDAGetLocalInfo(da3, &info3));
909: PetscCall(DMCompositeGetLocalVectors(pack, &X3, &X2));
910: PetscCall(DMCompositeGetLocalVectors(pack, &Xdot3, &Xdot2));
911: PetscCall(DMCompositeScatter(pack, X, X3, X2));
912: PetscCall(THIFixGhosts(thi, da3, da2, X3, X2));
913: PetscCall(DMCompositeScatter(pack, Xdot, Xdot3, Xdot2));
915: PetscCall(DMGetLocalVector(da3, &F3));
916: PetscCall(DMGetLocalVector(da2, &F2));
917: PetscCall(VecZeroEntries(F3));
919: PetscCall(DMDAVecGetArray(da3, X3, &x3));
920: PetscCall(DMDAVecGetArray(da2, X2, &x2));
921: PetscCall(DMDAVecGetArray(da3, Xdot3, &xdot3));
922: PetscCall(DMDAVecGetArray(da2, Xdot2, &xdot2));
923: PetscCall(DMDAVecGetArray(da3, F3, &f3));
924: PetscCall(DMDAVecGetArray(da2, F2, &f2));
926: PetscCall(THIFunctionLocal_3D(&info3, x3, x2, xdot3, f3, thi));
927: PetscCall(THIFunctionLocal_2D(&info3, x3, x2, xdot2, f2, thi));
929: PetscCall(DMDAVecRestoreArray(da3, X3, &x3));
930: PetscCall(DMDAVecRestoreArray(da2, X2, &x2));
931: PetscCall(DMDAVecRestoreArray(da3, Xdot3, &xdot3));
932: PetscCall(DMDAVecRestoreArray(da2, Xdot2, &xdot2));
933: PetscCall(DMDAVecRestoreArray(da3, F3, &f3));
934: PetscCall(DMDAVecRestoreArray(da2, F2, &f2));
936: PetscCall(DMCompositeRestoreLocalVectors(pack, &X3, &X2));
937: PetscCall(DMCompositeRestoreLocalVectors(pack, &Xdot3, &Xdot2));
939: PetscCall(VecZeroEntries(F));
940: PetscCall(DMCompositeGetAccess(pack, F, &F3g, &F2g));
941: PetscCall(DMLocalToGlobalBegin(da3, F3, ADD_VALUES, F3g));
942: PetscCall(DMLocalToGlobalEnd(da3, F3, ADD_VALUES, F3g));
943: PetscCall(DMLocalToGlobalBegin(da2, F2, INSERT_VALUES, F2g));
944: PetscCall(DMLocalToGlobalEnd(da2, F2, INSERT_VALUES, F2g));
946: if (thi->verbose) {
947: PetscViewer viewer;
948: PetscCall(PetscViewerASCIIGetStdout(PetscObjectComm((PetscObject)thi), &viewer));
949: PetscCall(PetscViewerASCIIPrintf(viewer, "3D_Velocity residual (bs=2):\n"));
950: PetscCall(PetscViewerASCIIPushTab(viewer));
951: PetscCall(VecView(F3, viewer));
952: PetscCall(PetscViewerASCIIPopTab(viewer));
953: PetscCall(PetscViewerASCIIPrintf(viewer, "2D_Fields residual (bs=3):\n"));
954: PetscCall(PetscViewerASCIIPushTab(viewer));
955: PetscCall(VecView(F2, viewer));
956: PetscCall(PetscViewerASCIIPopTab(viewer));
957: }
959: PetscCall(DMCompositeRestoreAccess(pack, F, &F3g, &F2g));
961: PetscCall(DMRestoreLocalVector(da3, &F3));
962: PetscCall(DMRestoreLocalVector(da2, &F2));
963: PetscFunctionReturn(PETSC_SUCCESS);
964: }
966: static PetscErrorCode THIMatrixStatistics(THI thi, Mat B, PetscViewer viewer)
967: {
968: PetscReal nrm;
969: PetscInt m;
970: PetscMPIInt rank;
972: PetscFunctionBeginUser;
973: PetscCall(MatNorm(B, NORM_FROBENIUS, &nrm));
974: PetscCall(MatGetSize(B, &m, 0));
975: PetscCallMPI(MPI_Comm_rank(PetscObjectComm((PetscObject)B), &rank));
976: if (rank == 0) {
977: PetscScalar val0, val2;
978: PetscCall(MatGetValue(B, 0, 0, &val0));
979: PetscCall(MatGetValue(B, 2, 2, &val2));
980: PetscCall(PetscViewerASCIIPrintf(viewer, "Matrix dim %8" PetscInt_FMT " norm %8.2e, (0,0) %8.2e (2,2) %8.2e, eta [%8.2e,%8.2e] beta2 [%8.2e,%8.2e]\n", m, (double)nrm, (double)PetscRealPart(val0), (double)PetscRealPart(val2), (double)thi->eta.cmin,
981: (double)thi->eta.cmax, (double)thi->beta2.cmin, (double)thi->beta2.cmax));
982: }
983: PetscFunctionReturn(PETSC_SUCCESS);
984: }
986: static PetscErrorCode THISurfaceStatistics(DM pack, Vec X, PetscReal *min, PetscReal *max, PetscReal *mean)
987: {
988: DM da3, da2;
989: Vec X3, X2;
990: Node ***x;
991: PetscInt i, j, xs, ys, zs, xm, ym, zm, mx, my, mz;
992: PetscReal umin = 1e100, umax = -1e100;
993: PetscScalar usum = 0.0, gusum;
995: PetscFunctionBeginUser;
996: PetscCall(DMCompositeGetEntries(pack, &da3, &da2));
997: PetscCall(DMCompositeGetAccess(pack, X, &X3, &X2));
998: *min = *max = *mean = 0;
999: PetscCall(DMDAGetInfo(da3, 0, &mz, &my, &mx, 0, 0, 0, 0, 0, 0, 0, 0, 0));
1000: PetscCall(DMDAGetCorners(da3, &zs, &ys, &xs, &zm, &ym, &xm));
1001: PetscCheck(zs == 0 && zm == mz, PETSC_COMM_WORLD, PETSC_ERR_PLIB, "Unexpected decomposition");
1002: PetscCall(DMDAVecGetArray(da3, X3, &x));
1003: for (i = xs; i < xs + xm; i++) {
1004: for (j = ys; j < ys + ym; j++) {
1005: PetscReal u = PetscRealPart(x[i][j][zm - 1].u);
1006: RangeUpdate(&umin, &umax, u);
1007: usum += u;
1008: }
1009: }
1010: PetscCall(DMDAVecRestoreArray(da3, X3, &x));
1011: PetscCall(DMCompositeRestoreAccess(pack, X, &X3, &X2));
1013: PetscCallMPI(MPIU_Allreduce(&umin, min, 1, MPIU_REAL, MPIU_MIN, PetscObjectComm((PetscObject)da3)));
1014: PetscCallMPI(MPIU_Allreduce(&umax, max, 1, MPIU_REAL, MPIU_MAX, PetscObjectComm((PetscObject)da3)));
1015: PetscCallMPI(MPIU_Allreduce(&usum, &gusum, 1, MPIU_SCALAR, MPIU_SUM, PetscObjectComm((PetscObject)da3)));
1016: *mean = PetscRealPart(gusum) / (mx * my);
1017: PetscFunctionReturn(PETSC_SUCCESS);
1018: }
1020: static PetscErrorCode THISolveStatistics(THI thi, TS ts, PetscInt coarsened, const char name[])
1021: {
1022: MPI_Comm comm;
1023: DM pack;
1024: Vec X, X3, X2;
1026: PetscFunctionBeginUser;
1027: PetscCall(PetscObjectGetComm((PetscObject)thi, &comm));
1028: PetscCall(TSGetDM(ts, &pack));
1029: PetscCall(TSGetSolution(ts, &X));
1030: PetscCall(DMCompositeGetAccess(pack, X, &X3, &X2));
1031: PetscCall(PetscPrintf(comm, "Solution statistics after solve: %s\n", name));
1032: {
1033: PetscInt its, lits;
1034: SNESConvergedReason reason;
1035: SNES snes;
1036: PetscCall(TSGetSNES(ts, &snes));
1037: PetscCall(SNESGetIterationNumber(snes, &its));
1038: PetscCall(SNESGetConvergedReason(snes, &reason));
1039: PetscCall(SNESGetLinearSolveIterations(snes, &lits));
1040: PetscCall(PetscPrintf(comm, "%s: Number of SNES iterations = %" PetscInt_FMT ", total linear iterations = %" PetscInt_FMT "\n", SNESConvergedReasons[reason], its, lits));
1041: }
1042: {
1043: PetscReal nrm2, tmin[3] = {1e100, 1e100, 1e100}, tmax[3] = {-1e100, -1e100, -1e100}, min[3], max[3];
1044: PetscInt i, j, m;
1045: PetscScalar *x;
1046: PetscCall(VecNorm(X3, NORM_2, &nrm2));
1047: PetscCall(VecGetLocalSize(X3, &m));
1048: PetscCall(VecGetArray(X3, &x));
1049: for (i = 0; i < m; i += 2) {
1050: PetscReal u = PetscRealPart(x[i]), v = PetscRealPart(x[i + 1]), c = PetscSqrtReal(u * u + v * v);
1051: tmin[0] = PetscMin(u, tmin[0]);
1052: tmin[1] = PetscMin(v, tmin[1]);
1053: tmin[2] = PetscMin(c, tmin[2]);
1054: tmax[0] = PetscMax(u, tmax[0]);
1055: tmax[1] = PetscMax(v, tmax[1]);
1056: tmax[2] = PetscMax(c, tmax[2]);
1057: }
1058: PetscCall(VecRestoreArray(X, &x));
1059: PetscCallMPI(MPIU_Allreduce(tmin, min, 3, MPIU_REAL, MPIU_MIN, PetscObjectComm((PetscObject)thi)));
1060: PetscCallMPI(MPIU_Allreduce(tmax, max, 3, MPIU_REAL, MPIU_MAX, PetscObjectComm((PetscObject)thi)));
1061: /* Dimensionalize to meters/year */
1062: nrm2 *= thi->units->year / thi->units->meter;
1063: for (j = 0; j < 3; j++) {
1064: min[j] *= thi->units->year / thi->units->meter;
1065: max[j] *= thi->units->year / thi->units->meter;
1066: }
1067: PetscCall(PetscPrintf(comm, "|X|_2 %g u in [%g, %g] v in [%g, %g] c in [%g, %g] \n", (double)nrm2, (double)min[0], (double)max[0], (double)min[1], (double)max[1], (double)min[2], (double)max[2]));
1068: {
1069: PetscReal umin, umax, umean;
1070: PetscCall(THISurfaceStatistics(pack, X, &umin, &umax, &umean));
1071: umin *= thi->units->year / thi->units->meter;
1072: umax *= thi->units->year / thi->units->meter;
1073: umean *= thi->units->year / thi->units->meter;
1074: PetscCall(PetscPrintf(comm, "Surface statistics: u in [%12.6e, %12.6e] mean %12.6e\n", (double)umin, (double)umax, (double)umean));
1075: }
1076: /* These values stay nondimensional */
1077: PetscCall(PetscPrintf(comm, "Global eta range [%g, %g], converged range [%g, %g]\n", (double)thi->eta.min, (double)thi->eta.max, (double)thi->eta.cmin, (double)thi->eta.cmax));
1078: PetscCall(PetscPrintf(comm, "Global beta2 range [%g, %g], converged range [%g, %g]\n", (double)thi->beta2.min, (double)thi->beta2.max, (double)thi->beta2.cmin, (double)thi->beta2.cmax));
1079: }
1080: PetscCall(PetscPrintf(comm, "\n"));
1081: PetscCall(DMCompositeRestoreAccess(pack, X, &X3, &X2));
1082: PetscFunctionReturn(PETSC_SUCCESS);
1083: }
1085: static inline PetscInt DMDALocalIndex3D(DMDALocalInfo *info, PetscInt i, PetscInt j, PetscInt k)
1086: {
1087: return ((i - info->gzs) * info->gym + (j - info->gys)) * info->gxm + (k - info->gxs);
1088: }
1089: static inline PetscInt DMDALocalIndex2D(DMDALocalInfo *info, PetscInt i, PetscInt j)
1090: {
1091: return (i - info->gzs) * info->gym + (j - info->gys);
1092: }
1094: static PetscErrorCode THIJacobianLocal_Momentum(DMDALocalInfo *info, const Node ***x, const PrmNode **prm, Mat B, Mat Bcpl, THI thi)
1095: {
1096: PetscInt xs, ys, xm, ym, zm, i, j, k, q, l, ll;
1097: PetscReal hx, hy;
1099: PetscFunctionBeginUser;
1100: xs = info->zs;
1101: ys = info->ys;
1102: xm = info->zm;
1103: ym = info->ym;
1104: zm = info->xm;
1105: hx = thi->Lx / info->mz;
1106: hy = thi->Ly / info->my;
1108: for (i = xs; i < xs + xm; i++) {
1109: for (j = ys; j < ys + ym; j++) {
1110: PrmNode pn[4], dpn[4][2];
1111: QuadExtract(prm, i, j, pn);
1112: PetscCall(QuadComputeGrad4(QuadQDeriv, hx, hy, pn, dpn));
1113: for (k = 0; k < zm - 1; k++) {
1114: Node n[8];
1115: PetscReal zn[8], etabase = 0;
1116: PetscScalar Ke[8 * NODE_SIZE][8 * NODE_SIZE], Kcpl[8 * NODE_SIZE][4 * PRMNODE_SIZE];
1117: PetscInt ls = 0;
1119: PrmHexGetZ(pn, k, zm, zn);
1120: HexExtract(x, i, j, k, n);
1121: PetscCall(PetscMemzero(Ke, sizeof(Ke)));
1122: PetscCall(PetscMemzero(Kcpl, sizeof(Kcpl)));
1123: if (thi->no_slip && k == 0) {
1124: for (l = 0; l < 4; l++) n[l].u = n[l].v = 0;
1125: ls = 4;
1126: }
1127: for (q = 0; q < 8; q++) {
1128: PetscReal dz[3], phi[8], dphi[8][3], jw, eta, deta;
1129: PetscScalar du[3], dv[3], u, v;
1130: HexGrad(HexQDeriv[q], zn, dz);
1131: HexComputeGeometry(q, hx, hy, dz, phi, dphi, &jw);
1132: PointwiseNonlinearity(thi, n, phi, dphi, &u, &v, du, dv, &eta, &deta);
1133: jw /= thi->rhog; /* residuals are scaled by this factor */
1134: if (q == 0) etabase = eta;
1135: for (l = ls; l < 8; l++) { /* test functions */
1136: const PetscReal pp = phi[l], *restrict dp = dphi[l];
1137: for (ll = ls; ll < 8; ll++) { /* trial functions */
1138: const PetscReal *restrict dpl = dphi[ll];
1139: PetscScalar dgdu, dgdv;
1140: dgdu = 2. * du[0] * dpl[0] + dv[1] * dpl[0] + 0.5 * (du[1] + dv[0]) * dpl[1] + 0.5 * du[2] * dpl[2];
1141: dgdv = 2. * dv[1] * dpl[1] + du[0] * dpl[1] + 0.5 * (du[1] + dv[0]) * dpl[0] + 0.5 * dv[2] * dpl[2];
1142: /* Picard part */
1143: 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];
1144: Ke[l * 2 + 0][ll * 2 + 1] += dp[0] * jw * eta * 2. * dpl[1] + dp[1] * jw * eta * dpl[0];
1145: Ke[l * 2 + 1][ll * 2 + 0] += dp[1] * jw * eta * 2. * dpl[0] + dp[0] * jw * eta * dpl[1];
1146: 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];
1147: /* extra Newton terms */
1148: 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];
1149: 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];
1150: 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];
1151: 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];
1152: /* inertial part */
1153: Ke[l * 2 + 0][ll * 2 + 0] += pp * jw * thi->inertia * pp;
1154: Ke[l * 2 + 1][ll * 2 + 1] += pp * jw * thi->inertia * pp;
1155: }
1156: for (ll = 0; ll < 4; ll++) { /* Trial functions for surface/bed */
1157: const PetscReal dpl[] = {QuadQDeriv[q % 4][ll][0] / hx, QuadQDeriv[q % 4][ll][1] / hy}; /* surface = h + b */
1158: Kcpl[FieldIndex(Node, l, u)][FieldIndex(PrmNode, ll, h)] += pp * jw * thi->rhog * dpl[0];
1159: Kcpl[FieldIndex(Node, l, u)][FieldIndex(PrmNode, ll, b)] += pp * jw * thi->rhog * dpl[0];
1160: Kcpl[FieldIndex(Node, l, v)][FieldIndex(PrmNode, ll, h)] += pp * jw * thi->rhog * dpl[1];
1161: Kcpl[FieldIndex(Node, l, v)][FieldIndex(PrmNode, ll, b)] += pp * jw * thi->rhog * dpl[1];
1162: }
1163: }
1164: }
1165: if (k == 0) { /* on a bottom face */
1166: if (thi->no_slip) {
1167: const PetscReal hz = PetscRealPart(pn[0].h) / (zm - 1);
1168: 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);
1169: Ke[0][0] = thi->dirichlet_scale * diagu;
1170: Ke[0][1] = 0;
1171: Ke[1][0] = 0;
1172: Ke[1][1] = thi->dirichlet_scale * diagv;
1173: } else {
1174: for (q = 0; q < 4; q++) { /* We remove the explicit scaling by 1/rhog because beta2 already has that scaling to be O(1) */
1175: const PetscReal jw = 0.25 * hx * hy, *phi = QuadQInterp[q];
1176: PetscScalar u = 0, v = 0, rbeta2 = 0;
1177: PetscReal beta2, dbeta2;
1178: for (l = 0; l < 4; l++) {
1179: u += phi[l] * n[l].u;
1180: v += phi[l] * n[l].v;
1181: rbeta2 += phi[l] * pn[l].beta2;
1182: }
1183: THIFriction(thi, PetscRealPart(rbeta2), PetscRealPart(u * u + v * v) / 2, &beta2, &dbeta2);
1184: for (l = 0; l < 4; l++) {
1185: const PetscReal pp = phi[l];
1186: for (ll = 0; ll < 4; ll++) {
1187: const PetscReal ppl = phi[ll];
1188: Ke[l * 2 + 0][ll * 2 + 0] += pp * jw * beta2 * ppl + pp * jw * dbeta2 * u * u * ppl;
1189: Ke[l * 2 + 0][ll * 2 + 1] += pp * jw * dbeta2 * u * v * ppl;
1190: Ke[l * 2 + 1][ll * 2 + 0] += pp * jw * dbeta2 * v * u * ppl;
1191: Ke[l * 2 + 1][ll * 2 + 1] += pp * jw * beta2 * ppl + pp * jw * dbeta2 * v * v * ppl;
1192: }
1193: }
1194: }
1195: }
1196: }
1197: {
1198: const PetscInt rc3blocked[8] = {DMDALocalIndex3D(info, i + 0, j + 0, k + 0), DMDALocalIndex3D(info, i + 1, j + 0, k + 0), DMDALocalIndex3D(info, i + 1, j + 1, k + 0), DMDALocalIndex3D(info, i + 0, j + 1, k + 0),
1199: DMDALocalIndex3D(info, i + 0, j + 0, k + 1), DMDALocalIndex3D(info, i + 1, j + 0, k + 1), DMDALocalIndex3D(info, i + 1, j + 1, k + 1), DMDALocalIndex3D(info, i + 0, j + 1, k + 1)},
1200: col2blocked[PRMNODE_SIZE * 4] = {DMDALocalIndex2D(info, i + 0, j + 0), DMDALocalIndex2D(info, i + 1, j + 0), DMDALocalIndex2D(info, i + 1, j + 1), DMDALocalIndex2D(info, i + 0, j + 1)};
1201: #if !defined COMPUTE_LOWER_TRIANGULAR /* fill in lower-triangular part, this is really cheap compared to computing the entries */
1202: for (l = 0; l < 8; l++) {
1203: for (ll = l + 1; ll < 8; ll++) {
1204: Ke[ll * 2 + 0][l * 2 + 0] = Ke[l * 2 + 0][ll * 2 + 0];
1205: Ke[ll * 2 + 1][l * 2 + 0] = Ke[l * 2 + 0][ll * 2 + 1];
1206: Ke[ll * 2 + 0][l * 2 + 1] = Ke[l * 2 + 1][ll * 2 + 0];
1207: Ke[ll * 2 + 1][l * 2 + 1] = Ke[l * 2 + 1][ll * 2 + 1];
1208: }
1209: }
1210: #endif
1211: PetscCall(MatSetValuesBlockedLocal(B, 8, rc3blocked, 8, rc3blocked, &Ke[0][0], ADD_VALUES)); /* velocity-velocity coupling can use blocked insertion */
1212: { /* The off-diagonal part cannot (yet) */
1213: PetscInt row3scalar[NODE_SIZE * 8], col2scalar[PRMNODE_SIZE * 4];
1214: for (l = 0; l < 8; l++)
1215: for (ll = 0; ll < NODE_SIZE; ll++) row3scalar[l * NODE_SIZE + ll] = rc3blocked[l] * NODE_SIZE + ll;
1216: for (l = 0; l < 4; l++)
1217: for (ll = 0; ll < PRMNODE_SIZE; ll++) col2scalar[l * PRMNODE_SIZE + ll] = col2blocked[l] * PRMNODE_SIZE + ll;
1218: PetscCall(MatSetValuesLocal(Bcpl, 8 * NODE_SIZE, row3scalar, 4 * PRMNODE_SIZE, col2scalar, &Kcpl[0][0], ADD_VALUES));
1219: }
1220: }
1221: }
1222: }
1223: }
1224: PetscFunctionReturn(PETSC_SUCCESS);
1225: }
1227: static PetscErrorCode THIJacobianLocal_2D(DMDALocalInfo *info, const Node ***x3, const PrmNode **x2, const PrmNode **xdot2, PetscReal a, Mat B22, Mat B21, THI thi)
1228: {
1229: PetscInt xs, ys, xm, ym, zm, i, j, k;
1231: PetscFunctionBeginUser;
1232: xs = info->zs;
1233: ys = info->ys;
1234: xm = info->zm;
1235: ym = info->ym;
1236: zm = info->xm;
1238: PetscCheck(zm <= 1024, ((PetscObject)info->da)->comm, PETSC_ERR_SUP, "Need to allocate more space");
1239: for (i = xs; i < xs + xm; i++) {
1240: for (j = ys; j < ys + ym; j++) {
1241: { /* Self-coupling */
1242: const PetscInt row[] = {DMDALocalIndex2D(info, i, j)};
1243: const PetscInt col[] = {DMDALocalIndex2D(info, i, j)};
1244: const PetscScalar vals[] = {a, 0, 0, 0, a, 0, 0, 0, a};
1245: PetscCall(MatSetValuesBlockedLocal(B22, 1, row, 1, col, vals, INSERT_VALUES));
1246: }
1247: for (k = 0; k < zm; k++) { /* Coupling to velocity problem */
1248: /* Use a cheaper quadrature than for residual evaluation, because it is much sparser */
1249: const PetscInt row[] = {FieldIndex(PrmNode, DMDALocalIndex2D(info, i, j), h)};
1250: const PetscInt cols[] = {FieldIndex(Node, DMDALocalIndex3D(info, i - 1, j, k), u), FieldIndex(Node, DMDALocalIndex3D(info, i, j, k), u), FieldIndex(Node, DMDALocalIndex3D(info, i + 1, j, k), u),
1251: FieldIndex(Node, DMDALocalIndex3D(info, i, j - 1, k), v), FieldIndex(Node, DMDALocalIndex3D(info, i, j, k), v), FieldIndex(Node, DMDALocalIndex3D(info, i, j + 1, k), v)};
1252: const PetscScalar w = (k && k < zm - 1) ? 0.5 : 0.25, hW = w * (x2[i - 1][j].h + x2[i][j].h) / (zm - 1.), hE = w * (x2[i][j].h + x2[i + 1][j].h) / (zm - 1.), hS = w * (x2[i][j - 1].h + x2[i][j].h) / (zm - 1.),
1253: hN = w * (x2[i][j].h + x2[i][j + 1].h) / (zm - 1.);
1254: PetscScalar *vals, vals_upwind[] = {((PetscRealPart(x3[i][j][k].u) > 0) ? -hW : 0), (PetscRealPart(x3[i][j][k].u) > 0) ? +hE : -hW, (PetscRealPart(x3[i][j][k].u) > 0) ? 0 : +hE,
1255: (PetscRealPart(x3[i][j][k].v) > 0) ? -hS : 0, (PetscRealPart(x3[i][j][k].v) > 0) ? +hN : -hS, ((PetscRealPart(x3[i][j][k].v) > 0) ? 0 : +hN)},
1256: vals_centered[] = {-0.5 * hW, 0.5 * (-hW + hE), 0.5 * hE, -0.5 * hS, 0.5 * (-hS + hN), 0.5 * hN};
1257: vals = 1 ? vals_upwind : vals_centered;
1258: if (k == 0) {
1259: Node derate;
1260: THIErosion(thi, &x3[i][j][0], NULL, &derate);
1261: vals[1] -= derate.u;
1262: vals[4] -= derate.v;
1263: }
1264: PetscCall(MatSetValuesLocal(B21, 1, row, 6, cols, vals, INSERT_VALUES));
1265: }
1266: }
1267: }
1268: PetscFunctionReturn(PETSC_SUCCESS);
1269: }
1271: static PetscErrorCode THIJacobian(TS ts, PetscReal t, Vec X, Vec Xdot, PetscReal a, Mat A, Mat B, void *ctx)
1272: {
1273: THI thi = (THI)ctx;
1274: DM pack, da3, da2;
1275: Vec X3, X2, Xdot2;
1276: Mat B11, B12, B21, B22;
1277: DMDALocalInfo info3;
1278: IS *isloc;
1279: const Node ***x3;
1280: const PrmNode **x2, **xdot2;
1282: PetscFunctionBeginUser;
1283: PetscCall(TSGetDM(ts, &pack));
1284: PetscCall(DMCompositeGetEntries(pack, &da3, &da2));
1285: PetscCall(DMDAGetLocalInfo(da3, &info3));
1286: PetscCall(DMCompositeGetLocalVectors(pack, &X3, &X2));
1287: PetscCall(DMCompositeGetLocalVectors(pack, NULL, &Xdot2));
1288: PetscCall(DMCompositeScatter(pack, X, X3, X2));
1289: PetscCall(THIFixGhosts(thi, da3, da2, X3, X2));
1290: PetscCall(DMCompositeScatter(pack, Xdot, NULL, Xdot2));
1292: PetscCall(MatZeroEntries(B));
1294: PetscCall(DMCompositeGetLocalISs(pack, &isloc));
1295: PetscCall(MatGetLocalSubMatrix(B, isloc[0], isloc[0], &B11));
1296: PetscCall(MatGetLocalSubMatrix(B, isloc[0], isloc[1], &B12));
1297: PetscCall(MatGetLocalSubMatrix(B, isloc[1], isloc[0], &B21));
1298: PetscCall(MatGetLocalSubMatrix(B, isloc[1], isloc[1], &B22));
1300: PetscCall(DMDAVecGetArray(da3, X3, &x3));
1301: PetscCall(DMDAVecGetArray(da2, X2, &x2));
1302: PetscCall(DMDAVecGetArray(da2, Xdot2, &xdot2));
1304: PetscCall(THIJacobianLocal_Momentum(&info3, x3, x2, B11, B12, thi));
1306: /* Need to switch from ADD_VALUES to INSERT_VALUES */
1307: PetscCall(MatAssemblyBegin(B, MAT_FLUSH_ASSEMBLY));
1308: PetscCall(MatAssemblyEnd(B, MAT_FLUSH_ASSEMBLY));
1310: PetscCall(THIJacobianLocal_2D(&info3, x3, x2, xdot2, a, B22, B21, thi));
1312: PetscCall(DMDAVecRestoreArray(da3, X3, &x3));
1313: PetscCall(DMDAVecRestoreArray(da2, X2, &x2));
1314: PetscCall(DMDAVecRestoreArray(da2, Xdot2, &xdot2));
1316: PetscCall(MatRestoreLocalSubMatrix(B, isloc[0], isloc[0], &B11));
1317: PetscCall(MatRestoreLocalSubMatrix(B, isloc[0], isloc[1], &B12));
1318: PetscCall(MatRestoreLocalSubMatrix(B, isloc[1], isloc[0], &B21));
1319: PetscCall(MatRestoreLocalSubMatrix(B, isloc[1], isloc[1], &B22));
1320: PetscCall(ISDestroy(&isloc[0]));
1321: PetscCall(ISDestroy(&isloc[1]));
1322: PetscCall(PetscFree(isloc));
1324: PetscCall(DMCompositeRestoreLocalVectors(pack, &X3, &X2));
1325: PetscCall(DMCompositeRestoreLocalVectors(pack, 0, &Xdot2));
1327: PetscCall(MatAssemblyBegin(B, MAT_FINAL_ASSEMBLY));
1328: PetscCall(MatAssemblyEnd(B, MAT_FINAL_ASSEMBLY));
1329: if (A != B) {
1330: PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY));
1331: PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY));
1332: }
1333: if (thi->verbose) PetscCall(THIMatrixStatistics(thi, B, PETSC_VIEWER_STDOUT_WORLD));
1334: PetscFunctionReturn(PETSC_SUCCESS);
1335: }
1337: /* VTK's XML formats are so brain-dead that they can't handle multiple grids in the same file. Since the communication
1338: * can be shared between the two grids, we write two files at once, one for velocity (living on a 3D grid defined by
1339: * h=thickness and b=bed) and another for all properties living on the 2D grid.
1340: */
1341: static PetscErrorCode THIDAVecView_VTK_XML(THI thi, DM pack, Vec X, const char filename[], const char filename2[])
1342: {
1343: const PetscInt dof = NODE_SIZE, dof2 = PRMNODE_SIZE;
1344: Units units = thi->units;
1345: MPI_Comm comm;
1346: PetscViewer viewer3, viewer2;
1347: PetscMPIInt rank, size, tag, nn, nmax, nn2, nmax2;
1348: PetscInt mx, my, mz, r, range[6];
1349: PetscScalar *x, *x2;
1350: DM da3, da2;
1351: Vec X3, X2;
1353: PetscFunctionBeginUser;
1354: PetscCall(PetscObjectGetComm((PetscObject)thi, &comm));
1355: PetscCall(DMCompositeGetEntries(pack, &da3, &da2));
1356: PetscCall(DMCompositeGetAccess(pack, X, &X3, &X2));
1357: PetscCall(DMDAGetInfo(da3, 0, &mz, &my, &mx, 0, 0, 0, 0, 0, 0, 0, 0, 0));
1358: PetscCallMPI(MPI_Comm_size(comm, &size));
1359: PetscCallMPI(MPI_Comm_rank(comm, &rank));
1360: PetscCall(PetscViewerASCIIOpen(comm, filename, &viewer3));
1361: PetscCall(PetscViewerASCIIOpen(comm, filename2, &viewer2));
1362: PetscCall(PetscViewerASCIIPrintf(viewer3, "<VTKFile type=\"StructuredGrid\" version=\"0.1\" byte_order=\"LittleEndian\">\n"));
1363: PetscCall(PetscViewerASCIIPrintf(viewer2, "<VTKFile type=\"StructuredGrid\" version=\"0.1\" byte_order=\"LittleEndian\">\n"));
1364: PetscCall(PetscViewerASCIIPrintf(viewer3, " <StructuredGrid WholeExtent=\"%d %" PetscInt_FMT " %d %" PetscInt_FMT " %d %" PetscInt_FMT "\">\n", 0, mz - 1, 0, my - 1, 0, mx - 1));
1365: PetscCall(PetscViewerASCIIPrintf(viewer2, " <StructuredGrid WholeExtent=\"%d %d %d %" PetscInt_FMT " %d %" PetscInt_FMT "\">\n", 0, 0, 0, my - 1, 0, mx - 1));
1367: PetscCall(DMDAGetCorners(da3, range, range + 1, range + 2, range + 3, range + 4, range + 5));
1368: PetscCall(PetscMPIIntCast(range[3] * range[4] * range[5] * dof, &nn));
1369: PetscCallMPI(MPI_Reduce(&nn, &nmax, 1, MPI_INT, MPI_MAX, 0, comm));
1370: PetscCall(PetscMPIIntCast(range[4] * range[5] * dof2, &nn2));
1371: PetscCallMPI(MPI_Reduce(&nn2, &nmax2, 1, MPI_INT, MPI_MAX, 0, comm));
1372: tag = ((PetscObject)viewer3)->tag;
1373: PetscCall(VecGetArrayRead(X3, (const PetscScalar **)&x));
1374: PetscCall(VecGetArrayRead(X2, (const PetscScalar **)&x2));
1375: if (rank == 0) {
1376: PetscScalar *array, *array2;
1377: PetscCall(PetscMalloc2(nmax, &array, nmax2, &array2));
1378: for (r = 0; r < size; r++) {
1379: PetscInt i, j, k, f, xs, xm, ys, ym, zs, zm;
1380: Node *y3;
1381: PetscScalar(*y2)[PRMNODE_SIZE];
1382: MPI_Status status;
1384: if (r) PetscCallMPI(MPI_Recv(range, 6, MPIU_INT, r, tag, comm, MPI_STATUS_IGNORE));
1385: zs = range[0];
1386: ys = range[1];
1387: xs = range[2];
1388: zm = range[3];
1389: ym = range[4];
1390: xm = range[5];
1391: PetscCheck(xm * ym * zm * dof <= nmax, PETSC_COMM_SELF, PETSC_ERR_PLIB, "should not happen");
1392: if (r) {
1393: PetscCallMPI(MPI_Recv(array, nmax, MPIU_SCALAR, r, tag, comm, &status));
1394: PetscCallMPI(MPI_Get_count(&status, MPIU_SCALAR, &nn));
1395: PetscCheck(nn == xm * ym * zm * dof, PETSC_COMM_SELF, PETSC_ERR_PLIB, "corrupt da3 send");
1396: y3 = (Node *)array;
1397: PetscCallMPI(MPI_Recv(array2, nmax2, MPIU_SCALAR, r, tag, comm, &status));
1398: PetscCallMPI(MPI_Get_count(&status, MPIU_SCALAR, &nn2));
1399: PetscCheck(nn2 == xm * ym * dof2, PETSC_COMM_SELF, PETSC_ERR_PLIB, "corrupt da2 send");
1400: y2 = (PetscScalar(*)[PRMNODE_SIZE])array2;
1401: } else {
1402: y3 = (Node *)x;
1403: y2 = (PetscScalar(*)[PRMNODE_SIZE])x2;
1404: }
1405: PetscCall(PetscViewerASCIIPrintf(viewer3, " <Piece Extent=\"%" PetscInt_FMT " %" PetscInt_FMT " %" PetscInt_FMT " %" PetscInt_FMT " %" PetscInt_FMT " %" PetscInt_FMT "\">\n", zs, zs + zm - 1, ys, ys + ym - 1, xs, xs + xm - 1));
1406: PetscCall(PetscViewerASCIIPrintf(viewer2, " <Piece Extent=\"%d %d %" PetscInt_FMT " %" PetscInt_FMT " %" PetscInt_FMT " %" PetscInt_FMT "\">\n", 0, 0, ys, ys + ym - 1, xs, xs + xm - 1));
1408: PetscCall(PetscViewerASCIIPrintf(viewer3, " <Points>\n"));
1409: PetscCall(PetscViewerASCIIPrintf(viewer2, " <Points>\n"));
1410: PetscCall(PetscViewerASCIIPrintf(viewer3, " <DataArray type=\"Float32\" NumberOfComponents=\"3\" format=\"ascii\">\n"));
1411: PetscCall(PetscViewerASCIIPrintf(viewer2, " <DataArray type=\"Float32\" NumberOfComponents=\"3\" format=\"ascii\">\n"));
1412: for (i = xs; i < xs + xm; i++) {
1413: for (j = ys; j < ys + ym; j++) {
1414: PetscReal xx = thi->Lx * i / mx, yy = thi->Ly * j / my, b = PetscRealPart(y2[i * ym + j][FieldOffset(PrmNode, b)]), h = PetscRealPart(y2[i * ym + j][FieldOffset(PrmNode, h)]);
1415: for (k = zs; k < zs + zm; k++) {
1416: PetscReal zz = b + h * k / (mz - 1.);
1417: PetscCall(PetscViewerASCIIPrintf(viewer3, "%f %f %f\n", (double)xx, (double)yy, (double)zz));
1418: }
1419: PetscCall(PetscViewerASCIIPrintf(viewer2, "%f %f %f\n", (double)xx, (double)yy, (double)0.0));
1420: }
1421: }
1422: PetscCall(PetscViewerASCIIPrintf(viewer3, " </DataArray>\n"));
1423: PetscCall(PetscViewerASCIIPrintf(viewer2, " </DataArray>\n"));
1424: PetscCall(PetscViewerASCIIPrintf(viewer3, " </Points>\n"));
1425: PetscCall(PetscViewerASCIIPrintf(viewer2, " </Points>\n"));
1427: { /* Velocity and rank (3D) */
1428: PetscCall(PetscViewerASCIIPrintf(viewer3, " <PointData>\n"));
1429: PetscCall(PetscViewerASCIIPrintf(viewer3, " <DataArray type=\"Float32\" Name=\"velocity\" NumberOfComponents=\"3\" format=\"ascii\">\n"));
1430: for (i = 0; i < nn / dof; i++) PetscCall(PetscViewerASCIIPrintf(viewer3, "%f %f %f\n", (double)(PetscRealPart(y3[i].u) * units->year / units->meter), (double)(PetscRealPart(y3[i].v) * units->year / units->meter), 0.0));
1431: PetscCall(PetscViewerASCIIPrintf(viewer3, " </DataArray>\n"));
1433: PetscCall(PetscViewerASCIIPrintf(viewer3, " <DataArray type=\"Int32\" Name=\"rank\" NumberOfComponents=\"1\" format=\"ascii\">\n"));
1434: for (i = 0; i < nn; i += dof) PetscCall(PetscViewerASCIIPrintf(viewer3, "%" PetscInt_FMT "\n", r));
1435: PetscCall(PetscViewerASCIIPrintf(viewer3, " </DataArray>\n"));
1436: PetscCall(PetscViewerASCIIPrintf(viewer3, " </PointData>\n"));
1437: }
1439: { /* 2D */
1440: PetscCall(PetscViewerASCIIPrintf(viewer2, " <PointData>\n"));
1441: for (f = 0; f < PRMNODE_SIZE; f++) {
1442: const char *fieldname;
1443: PetscCall(DMDAGetFieldName(da2, f, &fieldname));
1444: PetscCall(PetscViewerASCIIPrintf(viewer2, " <DataArray type=\"Float32\" Name=\"%s\" format=\"ascii\">\n", fieldname));
1445: for (i = 0; i < nn2 / PRMNODE_SIZE; i++) PetscCall(PetscViewerASCIIPrintf(viewer2, "%g\n", (double)y2[i][f]));
1446: PetscCall(PetscViewerASCIIPrintf(viewer2, " </DataArray>\n"));
1447: }
1448: PetscCall(PetscViewerASCIIPrintf(viewer2, " </PointData>\n"));
1449: }
1451: PetscCall(PetscViewerASCIIPrintf(viewer3, " </Piece>\n"));
1452: PetscCall(PetscViewerASCIIPrintf(viewer2, " </Piece>\n"));
1453: }
1454: PetscCall(PetscFree2(array, array2));
1455: } else {
1456: PetscCallMPI(MPI_Send(range, 6, MPIU_INT, 0, tag, comm));
1457: PetscCallMPI(MPI_Send(x, nn, MPIU_SCALAR, 0, tag, comm));
1458: PetscCallMPI(MPI_Send(x2, nn2, MPIU_SCALAR, 0, tag, comm));
1459: }
1460: PetscCall(VecRestoreArrayRead(X3, (const PetscScalar **)&x));
1461: PetscCall(VecRestoreArrayRead(X2, (const PetscScalar **)&x2));
1462: PetscCall(PetscViewerASCIIPrintf(viewer3, " </StructuredGrid>\n"));
1463: PetscCall(PetscViewerASCIIPrintf(viewer2, " </StructuredGrid>\n"));
1465: PetscCall(DMCompositeRestoreAccess(pack, X, &X3, &X2));
1466: PetscCall(PetscViewerASCIIPrintf(viewer3, "</VTKFile>\n"));
1467: PetscCall(PetscViewerASCIIPrintf(viewer2, "</VTKFile>\n"));
1468: PetscCall(PetscViewerDestroy(&viewer3));
1469: PetscCall(PetscViewerDestroy(&viewer2));
1470: PetscFunctionReturn(PETSC_SUCCESS);
1471: }
1473: static PetscErrorCode THITSMonitor(TS ts, PetscInt step, PetscReal t, Vec X, void *ctx)
1474: {
1475: THI thi = (THI)ctx;
1476: DM pack;
1477: char filename3[PETSC_MAX_PATH_LEN], filename2[PETSC_MAX_PATH_LEN];
1479: PetscFunctionBeginUser;
1480: if (step < 0) PetscFunctionReturn(PETSC_SUCCESS); /* negative one is used to indicate an interpolated solution */
1481: PetscCall(PetscPrintf(PetscObjectComm((PetscObject)ts), "%3" PetscInt_FMT ": t=%g\n", step, (double)t));
1482: if (thi->monitor_interval && step % thi->monitor_interval) PetscFunctionReturn(PETSC_SUCCESS);
1483: PetscCall(TSGetDM(ts, &pack));
1484: PetscCall(PetscSNPrintf(filename3, sizeof(filename3), "%s-3d-%03" PetscInt_FMT ".vts", thi->monitor_basename, step));
1485: PetscCall(PetscSNPrintf(filename2, sizeof(filename2), "%s-2d-%03" PetscInt_FMT ".vts", thi->monitor_basename, step));
1486: PetscCall(THIDAVecView_VTK_XML(thi, pack, X, filename3, filename2));
1487: PetscFunctionReturn(PETSC_SUCCESS);
1488: }
1490: static PetscErrorCode THICreateDM3d(THI thi, DM *dm3d)
1491: {
1492: MPI_Comm comm;
1493: PetscInt M = 3, N = 3, P = 2;
1494: DM da;
1496: PetscFunctionBeginUser;
1497: PetscCall(PetscObjectGetComm((PetscObject)thi, &comm));
1498: PetscOptionsBegin(comm, NULL, "Grid resolution options", "");
1499: {
1500: PetscCall(PetscOptionsInt("-M", "Number of elements in x-direction on coarse level", "", M, &M, NULL));
1501: N = M;
1502: PetscCall(PetscOptionsInt("-N", "Number of elements in y-direction on coarse level (if different from M)", "", N, &N, NULL));
1503: PetscCall(PetscOptionsInt("-P", "Number of elements in z-direction on coarse level", "", P, &P, NULL));
1504: }
1505: PetscOptionsEnd();
1506: PetscCall(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));
1507: PetscCall(DMSetFromOptions(da));
1508: PetscCall(DMSetUp(da));
1509: PetscCall(DMDASetFieldName(da, 0, "x-velocity"));
1510: PetscCall(DMDASetFieldName(da, 1, "y-velocity"));
1511: *dm3d = da;
1512: PetscFunctionReturn(PETSC_SUCCESS);
1513: }
1515: int main(int argc, char *argv[])
1516: {
1517: MPI_Comm comm;
1518: DM pack, da3, da2;
1519: TS ts;
1520: THI thi;
1521: Vec X;
1522: Mat B;
1523: PetscInt i, steps;
1524: PetscReal ftime;
1526: PetscFunctionBeginUser;
1527: PetscCall(PetscInitialize(&argc, &argv, 0, help));
1528: comm = PETSC_COMM_WORLD;
1530: PetscCall(THICreate(comm, &thi));
1531: PetscCall(THICreateDM3d(thi, &da3));
1532: {
1533: PetscInt Mx, My, mx, my, s;
1534: DMDAStencilType st;
1535: PetscCall(DMDAGetInfo(da3, 0, 0, &My, &Mx, 0, &my, &mx, 0, &s, 0, 0, 0, &st));
1536: PetscCall(DMDACreate2d(PetscObjectComm((PetscObject)thi), DM_BOUNDARY_PERIODIC, DM_BOUNDARY_PERIODIC, st, My, Mx, my, mx, sizeof(PrmNode) / sizeof(PetscScalar), s, 0, 0, &da2));
1537: PetscCall(DMSetUp(da2));
1538: }
1540: PetscCall(PetscObjectSetName((PetscObject)da3, "3D_Velocity"));
1541: PetscCall(DMSetOptionsPrefix(da3, "f3d_"));
1542: PetscCall(DMDASetFieldName(da3, 0, "u"));
1543: PetscCall(DMDASetFieldName(da3, 1, "v"));
1544: PetscCall(PetscObjectSetName((PetscObject)da2, "2D_Fields"));
1545: PetscCall(DMSetOptionsPrefix(da2, "f2d_"));
1546: PetscCall(DMDASetFieldName(da2, 0, "b"));
1547: PetscCall(DMDASetFieldName(da2, 1, "h"));
1548: PetscCall(DMDASetFieldName(da2, 2, "beta2"));
1549: PetscCall(DMCompositeCreate(comm, &pack));
1550: PetscCall(DMCompositeAddDM(pack, da3));
1551: PetscCall(DMCompositeAddDM(pack, da2));
1552: PetscCall(DMDestroy(&da3));
1553: PetscCall(DMDestroy(&da2));
1554: PetscCall(DMSetUp(pack));
1555: PetscCall(DMCreateMatrix(pack, &B));
1556: PetscCall(MatSetOption(B, MAT_NEW_NONZERO_LOCATION_ERR, PETSC_FALSE));
1557: PetscCall(MatSetOptionsPrefix(B, "thi_"));
1559: for (i = 0; i < thi->nlevels; i++) {
1560: PetscReal Lx = thi->Lx / thi->units->meter, Ly = thi->Ly / thi->units->meter, Lz = thi->Lz / thi->units->meter;
1561: PetscInt Mx, My, Mz;
1562: PetscCall(DMCompositeGetEntries(pack, &da3, &da2));
1563: PetscCall(DMDAGetInfo(da3, 0, &Mz, &My, &Mx, 0, 0, 0, 0, 0, 0, 0, 0, 0));
1564: PetscCall(PetscPrintf(PetscObjectComm((PetscObject)thi), "Level %" PetscInt_FMT " 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)));
1565: }
1567: PetscCall(DMCreateGlobalVector(pack, &X));
1568: PetscCall(THIInitial(thi, pack, X));
1570: PetscCall(TSCreate(comm, &ts));
1571: PetscCall(TSSetDM(ts, pack));
1572: PetscCall(TSSetProblemType(ts, TS_NONLINEAR));
1573: PetscCall(TSMonitorSet(ts, THITSMonitor, thi, NULL));
1574: PetscCall(TSSetType(ts, TSTHETA));
1575: PetscCall(TSSetIFunction(ts, NULL, THIFunction, thi));
1576: PetscCall(TSSetIJacobian(ts, B, B, THIJacobian, thi));
1577: PetscCall(TSSetMaxTime(ts, 10.0));
1578: PetscCall(TSSetExactFinalTime(ts, TS_EXACTFINALTIME_STEPOVER));
1579: PetscCall(TSSetSolution(ts, X));
1580: PetscCall(TSSetTimeStep(ts, 1e-3));
1581: PetscCall(TSSetFromOptions(ts));
1583: PetscCall(TSSolve(ts, X));
1584: PetscCall(TSGetSolveTime(ts, &ftime));
1585: PetscCall(TSGetStepNumber(ts, &steps));
1586: PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Steps %" PetscInt_FMT " final time %g\n", steps, (double)ftime));
1588: if (0) PetscCall(THISolveStatistics(thi, ts, 0, "Full"));
1590: {
1591: PetscBool flg;
1592: char filename[PETSC_MAX_PATH_LEN] = "";
1593: PetscCall(PetscOptionsGetString(NULL, NULL, "-o", filename, sizeof(filename), &flg));
1594: if (flg) PetscCall(THIDAVecView_VTK_XML(thi, pack, X, filename, NULL));
1595: }
1597: PetscCall(VecDestroy(&X));
1598: PetscCall(MatDestroy(&B));
1599: PetscCall(DMDestroy(&pack));
1600: PetscCall(TSDestroy(&ts));
1601: PetscCall(THIDestroy(&thi));
1602: PetscCall(PetscFinalize());
1603: return 0;
1604: }