Actual source code: ex48.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: There are two compile-time options:
46: NO_SSE2:
47: If the host supports SSE2, we use integration code that has been vectorized with SSE2
48: intrinsics, unless this macro is defined. The intrinsics speed up integration by about
49: 30% on my architecture (P8700, gcc-4.5 snapshot).
51: COMPUTE_LOWER_TRIANGULAR:
52: The element matrices we assemble are lower-triangular so it is not necessary to compute
53: all entries explicitly. If this macro is defined, the lower-triangular entries are
54: computed explicitly.
56: */
58: #if defined(PETSC_APPLE_FRAMEWORK)
59: #import <PETSc/petscsnes.h>
60: #import <PETSc/petsc/private/dmdaimpl.h> /* There is not yet a public interface to manipulate dm->ops */
61: #else
63: #include <petscsnes.h>
64: #include <petsc/private/dmdaimpl.h>
65: #endif
66: #include <ctype.h> /* toupper() */
68: #if defined(__cplusplus) || defined (PETSC_HAVE_WINDOWS_COMPILERS) || defined (__PGI)
69: /* c++ cannot handle [_restrict_] notation like C does */
70: #undef PETSC_RESTRICT
71: #define PETSC_RESTRICT
72: #endif
74: #if defined __SSE2__
75: # include <emmintrin.h>
76: #endif
78: /* The SSE2 kernels are only for PetscScalar=double on architectures that support it */
79: #if !defined NO_SSE2 \
80: && !defined PETSC_USE_COMPLEX \
81: && !defined PETSC_USE_REAL_SINGLE \
82: && !defined PETSC_USE_REAL___FLOAT128 \
83: && !defined PETSC_USE_REAL___FP16 \
84: && defined __SSE2__
85: #define USE_SSE2_KERNELS 1
86: #else
87: #define USE_SSE2_KERNELS 0
88: #endif
90: static PetscClassId THI_CLASSID;
92: typedef enum {QUAD_GAUSS,QUAD_LOBATTO} QuadratureType;
93: static const char *QuadratureTypes[] = {"gauss","lobatto","QuadratureType","QUAD_",0};
94: PETSC_UNUSED static const PetscReal HexQWeights[8] = {1,1,1,1,1,1,1,1};
95: PETSC_UNUSED static const PetscReal HexQNodes[] = {-0.57735026918962573, 0.57735026918962573};
96: #define G 0.57735026918962573
97: #define H (0.5*(1.+G))
98: #define L (0.5*(1.-G))
99: #define M (-0.5)
100: #define P (0.5)
101: /* Special quadrature: Lobatto in horizontal, Gauss in vertical */
102: static const PetscReal HexQInterp_Lobatto[8][8] = {{H,0,0,0,L,0,0,0},
103: {0,H,0,0,0,L,0,0},
104: {0,0,H,0,0,0,L,0},
105: {0,0,0,H,0,0,0,L},
106: {L,0,0,0,H,0,0,0},
107: {0,L,0,0,0,H,0,0},
108: {0,0,L,0,0,0,H,0},
109: {0,0,0,L,0,0,0,H}};
110: static const PetscReal HexQDeriv_Lobatto[8][8][3] = {
111: {{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} },
112: {{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} },
113: {{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} },
114: {{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}},
115: {{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} },
116: {{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} },
117: {{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} },
118: {{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}}};
119: /* Stanndard Gauss */
120: 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},
121: {L*H*H,H*H*H,H*L*H,L*L*H, L*H*L,H*H*L,H*L*L,L*L*L},
122: {L*L*H,H*L*H,H*H*H,L*H*H, L*L*L,H*L*L,H*H*L,L*H*L},
123: {H*L*H,L*L*H,L*H*H,H*H*H, H*L*L,L*L*L,L*H*L,H*H*L},
124: {H*H*L,L*H*L,L*L*L,H*L*L, H*H*H,L*H*H,L*L*H,H*L*H},
125: {L*H*L,H*H*L,H*L*L,L*L*L, L*H*H,H*H*H,H*L*H,L*L*H},
126: {L*L*L,H*L*L,H*H*L,L*H*L, L*L*H,H*L*H,H*H*H,L*H*H},
127: {H*L*L,L*L*L,L*H*L,H*H*L, H*L*H,L*L*H,L*H*H,H*H*H}};
128: static const PetscReal HexQDeriv_Gauss[8][8][3] = {
129: {{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}},
130: {{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}},
131: {{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}},
132: {{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}},
133: {{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}},
134: {{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}},
135: {{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}},
136: {{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}}};
137: static const PetscReal (*HexQInterp)[8],(*HexQDeriv)[8][3];
138: /* Standard 2x2 Gauss quadrature for the bottom layer. */
139: static const PetscReal QuadQInterp[4][4] = {{H*H,L*H,L*L,H*L},
140: {L*H,H*H,H*L,L*L},
141: {L*L,H*L,H*H,L*H},
142: {H*L,L*L,L*H,H*H}};
143: static const PetscReal QuadQDeriv[4][4][2] = {
144: {{M*H,M*H},{P*H,M*L},{P*L,P*L},{M*L,P*H}},
145: {{M*H,M*L},{P*H,M*H},{P*L,P*H},{M*L,P*L}},
146: {{M*L,M*L},{P*L,M*H},{P*H,P*H},{M*H,P*L}},
147: {{M*L,M*H},{P*L,M*L},{P*H,P*L},{M*H,P*H}}};
148: #undef G
149: #undef H
150: #undef L
151: #undef M
152: #undef P
154: #define HexExtract(x,i,j,k,n) do { \
155: (n)[0] = (x)[i][j][k]; \
156: (n)[1] = (x)[i+1][j][k]; \
157: (n)[2] = (x)[i+1][j+1][k]; \
158: (n)[3] = (x)[i][j+1][k]; \
159: (n)[4] = (x)[i][j][k+1]; \
160: (n)[5] = (x)[i+1][j][k+1]; \
161: (n)[6] = (x)[i+1][j+1][k+1]; \
162: (n)[7] = (x)[i][j+1][k+1]; \
163: } while (0)
165: #define HexExtractRef(x,i,j,k,n) do { \
166: (n)[0] = &(x)[i][j][k]; \
167: (n)[1] = &(x)[i+1][j][k]; \
168: (n)[2] = &(x)[i+1][j+1][k]; \
169: (n)[3] = &(x)[i][j+1][k]; \
170: (n)[4] = &(x)[i][j][k+1]; \
171: (n)[5] = &(x)[i+1][j][k+1]; \
172: (n)[6] = &(x)[i+1][j+1][k+1]; \
173: (n)[7] = &(x)[i][j+1][k+1]; \
174: } while (0)
176: #define QuadExtract(x,i,j,n) do { \
177: (n)[0] = (x)[i][j]; \
178: (n)[1] = (x)[i+1][j]; \
179: (n)[2] = (x)[i+1][j+1]; \
180: (n)[3] = (x)[i][j+1]; \
181: } while (0)
183: static void HexGrad(const PetscReal dphi[][3],const PetscReal zn[],PetscReal dz[])
184: {
185: PetscInt i;
186: dz[0] = dz[1] = dz[2] = 0;
187: for (i=0; i<8; i++) {
188: dz[0] += dphi[i][0] * zn[i];
189: dz[1] += dphi[i][1] * zn[i];
190: dz[2] += dphi[i][2] * zn[i];
191: }
192: }
194: static void HexComputeGeometry(PetscInt q,PetscReal hx,PetscReal hy,const PetscReal dz[PETSC_RESTRICT],PetscReal phi[PETSC_RESTRICT],PetscReal dphi[PETSC_RESTRICT][3],PetscReal *PETSC_RESTRICT jw)
195: {
196: const PetscReal jac[3][3] = {{hx/2,0,0}, {0,hy/2,0}, {dz[0],dz[1],dz[2]}};
197: const PetscReal 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]}};
198: const PetscReal jdet = jac[0][0]*jac[1][1]*jac[2][2];
199: PetscInt i;
201: for (i=0; i<8; i++) {
202: const PetscReal *dphir = HexQDeriv[q][i];
203: phi[i] = HexQInterp[q][i];
204: dphi[i][0] = dphir[0]*ijac[0][0] + dphir[1]*ijac[1][0] + dphir[2]*ijac[2][0];
205: dphi[i][1] = dphir[0]*ijac[0][1] + dphir[1]*ijac[1][1] + dphir[2]*ijac[2][1];
206: dphi[i][2] = dphir[0]*ijac[0][2] + dphir[1]*ijac[1][2] + dphir[2]*ijac[2][2];
207: }
208: *jw = 1.0 * jdet;
209: }
211: typedef struct _p_THI *THI;
212: typedef struct _n_Units *Units;
214: typedef struct {
215: PetscScalar u,v;
216: } Node;
218: typedef struct {
219: PetscScalar b; /* bed */
220: PetscScalar h; /* thickness */
221: PetscScalar beta2; /* friction */
222: } PrmNode;
224: typedef struct {
225: PetscReal min,max,cmin,cmax;
226: } PRange;
228: typedef enum {THIASSEMBLY_TRIDIAGONAL,THIASSEMBLY_FULL} THIAssemblyMode;
230: struct _p_THI {
231: PETSCHEADER(int);
232: void (*initialize)(THI,PetscReal x,PetscReal y,PrmNode *p);
233: PetscInt zlevels;
234: PetscReal Lx,Ly,Lz; /* Model domain */
235: PetscReal alpha; /* Bed angle */
236: Units units;
237: PetscReal dirichlet_scale;
238: PetscReal ssa_friction_scale;
239: PRange eta;
240: PRange beta2;
241: struct {
242: PetscReal Bd2,eps,exponent;
243: } viscosity;
244: struct {
245: PetscReal irefgam,eps2,exponent,refvel,epsvel;
246: } friction;
247: PetscReal rhog;
248: PetscBool no_slip;
249: PetscBool tridiagonal;
250: PetscBool coarse2d;
251: PetscBool verbose;
252: MatType mattype;
253: };
255: struct _n_Units {
256: /* fundamental */
257: PetscReal meter;
258: PetscReal kilogram;
259: PetscReal second;
260: /* derived */
261: PetscReal Pascal;
262: PetscReal year;
263: };
265: static PetscErrorCode THIJacobianLocal_3D_Full(DMDALocalInfo*,Node***,Mat,Mat,THI);
266: static PetscErrorCode THIJacobianLocal_3D_Tridiagonal(DMDALocalInfo*,Node***,Mat,Mat,THI);
267: static PetscErrorCode THIJacobianLocal_2D(DMDALocalInfo*,Node**,Mat,Mat,THI);
269: static void PrmHexGetZ(const PrmNode pn[],PetscInt k,PetscInt zm,PetscReal zn[])
270: {
271: const PetscScalar zm1 = zm-1,
272: znl[8] = {pn[0].b + pn[0].h*(PetscScalar)k/zm1,
273: pn[1].b + pn[1].h*(PetscScalar)k/zm1,
274: pn[2].b + pn[2].h*(PetscScalar)k/zm1,
275: pn[3].b + pn[3].h*(PetscScalar)k/zm1,
276: pn[0].b + pn[0].h*(PetscScalar)(k+1)/zm1,
277: pn[1].b + pn[1].h*(PetscScalar)(k+1)/zm1,
278: pn[2].b + pn[2].h*(PetscScalar)(k+1)/zm1,
279: 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: /* Tests A and C are from the ISMIP-HOM paper (Pattyn et al. 2008) */
285: static void THIInitialize_HOM_A(THI thi,PetscReal x,PetscReal y,PrmNode *p)
286: {
287: Units units = thi->units;
288: PetscReal s = -x*PetscSinReal(thi->alpha);
290: p->b = s - 1000*units->meter + 500*units->meter * PetscSinReal(x*2*PETSC_PI/thi->Lx) * PetscSinReal(y*2*PETSC_PI/thi->Ly);
291: p->h = s - p->b;
292: p->beta2 = 1e30;
293: }
295: static void THIInitialize_HOM_C(THI thi,PetscReal x,PetscReal y,PrmNode *p)
296: {
297: Units units = thi->units;
298: PetscReal s = -x*PetscSinReal(thi->alpha);
300: p->b = s - 1000*units->meter;
301: p->h = s - p->b;
302: /* tau_b = beta2 v is a stress (Pa) */
303: p->beta2 = 1000 * (1 + PetscSinReal(x*2*PETSC_PI/thi->Lx)*PetscSinReal(y*2*PETSC_PI/thi->Ly)) * units->Pascal * units->year / units->meter;
304: }
306: /* These are just toys */
308: /* Same bed as test A, free slip everywhere except for a discontinuous jump to a circular sticky region in the middle. */
309: static void THIInitialize_HOM_X(THI thi,PetscReal xx,PetscReal yy,PrmNode *p)
310: {
311: Units units = thi->units;
312: PetscReal x = xx*2*PETSC_PI/thi->Lx - PETSC_PI,y = yy*2*PETSC_PI/thi->Ly - PETSC_PI; /* [-pi,pi] */
313: PetscReal r = PetscSqrtReal(x*x + y*y),s = -x*PetscSinReal(thi->alpha);
314: p->b = s - 1000*units->meter + 500*units->meter*PetscSinReal(x + PETSC_PI) * PetscSinReal(y + PETSC_PI);
315: p->h = s - p->b;
316: p->beta2 = 1000 * (r < 1 ? 2 : 0) * units->Pascal * units->year / units->meter;
317: }
319: /* Like Z, but with 200 meter cliffs */
320: static void THIInitialize_HOM_Y(THI thi,PetscReal xx,PetscReal yy,PrmNode *p)
321: {
322: Units units = thi->units;
323: PetscReal x = xx*2*PETSC_PI/thi->Lx - PETSC_PI,y = yy*2*PETSC_PI/thi->Ly - PETSC_PI; /* [-pi,pi] */
324: PetscReal r = PetscSqrtReal(x*x + y*y),s = -x*PetscSinReal(thi->alpha);
326: p->b = s - 1000*units->meter + 500*units->meter * PetscSinReal(x + PETSC_PI) * PetscSinReal(y + PETSC_PI);
327: if (PetscRealPart(p->b) > -700*units->meter) p->b += 200*units->meter;
328: p->h = s - p->b;
329: 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;
330: }
332: /* Same bed as A, smoothly varying slipperiness, similar to MATLAB's "sombrero" (uncorrelated with bathymetry) */
333: static void THIInitialize_HOM_Z(THI thi,PetscReal xx,PetscReal yy,PrmNode *p)
334: {
335: Units units = thi->units;
336: PetscReal x = xx*2*PETSC_PI/thi->Lx - PETSC_PI,y = yy*2*PETSC_PI/thi->Ly - PETSC_PI; /* [-pi,pi] */
337: PetscReal r = PetscSqrtReal(x*x + y*y),s = -x*PetscSinReal(thi->alpha);
339: p->b = s - 1000*units->meter + 500*units->meter * PetscSinReal(x + PETSC_PI) * PetscSinReal(y + PETSC_PI);
340: p->h = s - p->b;
341: 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;
342: }
344: static void THIFriction(THI thi,PetscReal rbeta2,PetscReal gam,PetscReal *beta2,PetscReal *dbeta2)
345: {
346: if (thi->friction.irefgam == 0) {
347: Units units = thi->units;
348: thi->friction.irefgam = 1./(0.5*PetscSqr(thi->friction.refvel * units->meter / units->year));
349: thi->friction.eps2 = 0.5*PetscSqr(thi->friction.epsvel * units->meter / units->year) * thi->friction.irefgam;
350: }
351: if (thi->friction.exponent == 0) {
352: *beta2 = rbeta2;
353: *dbeta2 = 0;
354: } else {
355: *beta2 = rbeta2 * PetscPowReal(thi->friction.eps2 + gam*thi->friction.irefgam,thi->friction.exponent);
356: *dbeta2 = thi->friction.exponent * *beta2 / (thi->friction.eps2 + gam*thi->friction.irefgam) * thi->friction.irefgam;
357: }
358: }
360: static void THIViscosity(THI thi,PetscReal gam,PetscReal *eta,PetscReal *deta)
361: {
362: PetscReal Bd2,eps,exponent;
363: if (thi->viscosity.Bd2 == 0) {
364: Units units = thi->units;
365: const PetscReal
366: n = 3., /* Glen exponent */
367: p = 1. + 1./n, /* for Stokes */
368: A = 1.e-16 * PetscPowReal(units->Pascal,-n) / units->year, /* softness parameter (Pa^{-n}/s) */
369: B = PetscPowReal(A,-1./n); /* hardness parameter */
370: thi->viscosity.Bd2 = B/2;
371: thi->viscosity.exponent = (p-2)/2;
372: thi->viscosity.eps = 0.5*PetscSqr(1e-5 / units->year);
373: }
374: Bd2 = thi->viscosity.Bd2;
375: exponent = thi->viscosity.exponent;
376: eps = thi->viscosity.eps;
377: *eta = Bd2 * PetscPowReal(eps + gam,exponent);
378: *deta = exponent * (*eta) / (eps + gam);
379: }
381: static void RangeUpdate(PetscReal *min,PetscReal *max,PetscReal x)
382: {
383: if (x < *min) *min = x;
384: if (x > *max) *max = x;
385: }
387: static void PRangeClear(PRange *p)
388: {
389: p->cmin = p->min = 1e100;
390: p->cmax = p->max = -1e100;
391: }
393: static PetscErrorCode PRangeMinMax(PRange *p,PetscReal min,PetscReal max)
394: {
397: p->cmin = min;
398: p->cmax = max;
399: if (min < p->min) p->min = min;
400: if (max > p->max) p->max = max;
401: return(0);
402: }
404: static PetscErrorCode THIDestroy(THI *thi)
405: {
409: if (!*thi) return(0);
410: if (--((PetscObject)(*thi))->refct > 0) {*thi = 0; return(0);}
411: PetscFree((*thi)->units);
412: PetscFree((*thi)->mattype);
413: PetscHeaderDestroy(thi);
414: return(0);
415: }
417: static PetscErrorCode THICreate(MPI_Comm comm,THI *inthi)
418: {
419: static PetscBool registered = PETSC_FALSE;
420: THI thi;
421: Units units;
422: PetscErrorCode ierr;
425: *inthi = 0;
426: if (!registered) {
427: PetscClassIdRegister("Toy Hydrostatic Ice",&THI_CLASSID);
428: registered = PETSC_TRUE;
429: }
430: PetscHeaderCreate(thi,THI_CLASSID,"THI","Toy Hydrostatic Ice","",comm,THIDestroy,0);
432: PetscNew(&thi->units);
433: units = thi->units;
434: units->meter = 1e-2;
435: units->second = 1e-7;
436: units->kilogram = 1e-12;
438: PetscOptionsBegin(comm,NULL,"Scaled units options","");
439: {
440: PetscOptionsReal("-units_meter","1 meter in scaled length units","",units->meter,&units->meter,NULL);
441: PetscOptionsReal("-units_second","1 second in scaled time units","",units->second,&units->second,NULL);
442: PetscOptionsReal("-units_kilogram","1 kilogram in scaled mass units","",units->kilogram,&units->kilogram,NULL);
443: }
444: PetscOptionsEnd();
445: units->Pascal = units->kilogram / (units->meter * PetscSqr(units->second));
446: units->year = 31556926. * units->second; /* seconds per year */
448: thi->Lx = 10.e3;
449: thi->Ly = 10.e3;
450: thi->Lz = 1000;
451: thi->dirichlet_scale = 1;
452: thi->verbose = PETSC_FALSE;
454: PetscOptionsBegin(comm,NULL,"Toy Hydrostatic Ice options","");
455: {
456: QuadratureType quad = QUAD_GAUSS;
457: char homexp[] = "A";
458: char mtype[256] = MATSBAIJ;
459: PetscReal L,m = 1.0;
460: PetscBool flg;
461: L = thi->Lx;
462: PetscOptionsReal("-thi_L","Domain size (m)","",L,&L,&flg);
463: if (flg) thi->Lx = thi->Ly = L;
464: PetscOptionsReal("-thi_Lx","X Domain size (m)","",thi->Lx,&thi->Lx,NULL);
465: PetscOptionsReal("-thi_Ly","Y Domain size (m)","",thi->Ly,&thi->Ly,NULL);
466: PetscOptionsReal("-thi_Lz","Z Domain size (m)","",thi->Lz,&thi->Lz,NULL);
467: PetscOptionsString("-thi_hom","ISMIP-HOM experiment (A or C)","",homexp,homexp,sizeof(homexp),NULL);
468: switch (homexp[0] = toupper(homexp[0])) {
469: case 'A':
470: thi->initialize = THIInitialize_HOM_A;
471: thi->no_slip = PETSC_TRUE;
472: thi->alpha = 0.5;
473: break;
474: case 'C':
475: thi->initialize = THIInitialize_HOM_C;
476: thi->no_slip = PETSC_FALSE;
477: thi->alpha = 0.1;
478: break;
479: case 'X':
480: thi->initialize = THIInitialize_HOM_X;
481: thi->no_slip = PETSC_FALSE;
482: thi->alpha = 0.3;
483: break;
484: case 'Y':
485: thi->initialize = THIInitialize_HOM_Y;
486: thi->no_slip = PETSC_FALSE;
487: thi->alpha = 0.5;
488: break;
489: case 'Z':
490: thi->initialize = THIInitialize_HOM_Z;
491: thi->no_slip = PETSC_FALSE;
492: thi->alpha = 0.5;
493: break;
494: default:
495: SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"HOM experiment '%c' not implemented",homexp[0]);
496: }
497: PetscOptionsEnum("-thi_quadrature","Quadrature to use for 3D elements","",QuadratureTypes,(PetscEnum)quad,(PetscEnum*)&quad,NULL);
498: switch (quad) {
499: case QUAD_GAUSS:
500: HexQInterp = HexQInterp_Gauss;
501: HexQDeriv = HexQDeriv_Gauss;
502: break;
503: case QUAD_LOBATTO:
504: HexQInterp = HexQInterp_Lobatto;
505: HexQDeriv = HexQDeriv_Lobatto;
506: break;
507: }
508: PetscOptionsReal("-thi_alpha","Bed angle (degrees)","",thi->alpha,&thi->alpha,NULL);
510: thi->friction.refvel = 100.;
511: thi->friction.epsvel = 1.;
513: PetscOptionsReal("-thi_friction_refvel","Reference velocity for sliding","",thi->friction.refvel,&thi->friction.refvel,NULL);
514: PetscOptionsReal("-thi_friction_epsvel","Regularization velocity for sliding","",thi->friction.epsvel,&thi->friction.epsvel,NULL);
515: PetscOptionsReal("-thi_friction_m","Friction exponent, 0=Coulomb, 1=Navier","",m,&m,NULL);
517: thi->friction.exponent = (m-1)/2;
519: PetscOptionsReal("-thi_dirichlet_scale","Scale Dirichlet boundary conditions by this factor","",thi->dirichlet_scale,&thi->dirichlet_scale,NULL);
520: 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);
521: PetscOptionsBool("-thi_coarse2d","Use a 2D coarse space corresponding to SSA","",thi->coarse2d,&thi->coarse2d,NULL);
522: PetscOptionsBool("-thi_tridiagonal","Assemble a tridiagonal system (column coupling only) on the finest level","",thi->tridiagonal,&thi->tridiagonal,NULL);
523: PetscOptionsFList("-thi_mat_type","Matrix type","MatSetType",MatList,mtype,(char*)mtype,sizeof(mtype),NULL);
524: PetscStrallocpy(mtype,(char**)&thi->mattype);
525: PetscOptionsBool("-thi_verbose","Enable verbose output (like matrix sizes and statistics)","",thi->verbose,&thi->verbose,NULL);
526: }
527: PetscOptionsEnd();
529: /* dimensionalize */
530: thi->Lx *= units->meter;
531: thi->Ly *= units->meter;
532: thi->Lz *= units->meter;
533: thi->alpha *= PETSC_PI / 180;
535: PRangeClear(&thi->eta);
536: PRangeClear(&thi->beta2);
538: {
539: PetscReal u = 1000*units->meter/(3e7*units->second),
540: gradu = u / (100*units->meter),eta,deta,
541: rho = 910 * units->kilogram/PetscPowReal(units->meter,3),
542: grav = 9.81 * units->meter/PetscSqr(units->second),
543: driving = rho * grav * PetscSinReal(thi->alpha) * 1000*units->meter;
544: THIViscosity(thi,0.5*gradu*gradu,&eta,&deta);
545: thi->rhog = rho * grav;
546: if (thi->verbose) {
547: 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);
548: 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);
549: 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),(double)(2*eta*gradu/driving));
550: THIViscosity(thi,0.5*PetscSqr(1e-3*gradu),&eta,&deta);
551: 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),(double)(2*eta*1e-3*gradu/driving));
552: }
553: }
555: *inthi = thi;
556: return(0);
557: }
559: static PetscErrorCode THIInitializePrm(THI thi,DM da2prm,Vec prm)
560: {
561: PrmNode **p;
562: PetscInt i,j,xs,xm,ys,ym,mx,my;
566: DMDAGetGhostCorners(da2prm,&ys,&xs,0,&ym,&xm,0);
567: DMDAGetInfo(da2prm,0, &my,&mx,0, 0,0,0, 0,0,0,0,0,0);
568: DMDAVecGetArray(da2prm,prm,&p);
569: for (i=xs; i<xs+xm; i++) {
570: for (j=ys; j<ys+ym; j++) {
571: PetscReal xx = thi->Lx*i/mx,yy = thi->Ly*j/my;
572: thi->initialize(thi,xx,yy,&p[i][j]);
573: }
574: }
575: DMDAVecRestoreArray(da2prm,prm,&p);
576: return(0);
577: }
579: static PetscErrorCode THISetUpDM(THI thi,DM dm)
580: {
581: PetscErrorCode ierr;
582: PetscInt refinelevel,coarsenlevel,level,dim,Mx,My,Mz,mx,my,s;
583: DMDAStencilType st;
584: DM da2prm;
585: Vec X;
588: DMDAGetInfo(dm,&dim, &Mz,&My,&Mx, 0,&my,&mx, 0,&s,0,0,0,&st);
589: if (dim == 2) {
590: DMDAGetInfo(dm,&dim, &My,&Mx,0, &my,&mx,0, 0,&s,0,0,0,&st);
591: }
592: DMGetRefineLevel(dm,&refinelevel);
593: DMGetCoarsenLevel(dm,&coarsenlevel);
594: level = refinelevel - coarsenlevel;
595: DMDACreate2d(PetscObjectComm((PetscObject)thi),DM_BOUNDARY_PERIODIC,DM_BOUNDARY_PERIODIC,st,My,Mx,my,mx,sizeof(PrmNode)/sizeof(PetscScalar),s,0,0,&da2prm);
596: DMSetUp(da2prm);
597: DMCreateLocalVector(da2prm,&X);
598: {
599: PetscReal Lx = thi->Lx / thi->units->meter,Ly = thi->Ly / thi->units->meter,Lz = thi->Lz / thi->units->meter;
600: if (dim == 2) {
601: PetscPrintf(PetscObjectComm((PetscObject)thi),"Level %D domain size (m) %8.2g x %8.2g, num elements %D x %D (%D), size (m) %g x %g\n",level,(double)Lx,(double)Ly,Mx,My,Mx*My,(double)(Lx/Mx),(double)(Ly/My));
602: } else {
603: PetscPrintf(PetscObjectComm((PetscObject)thi),"Level %D domain size (m) %8.2g x %8.2g x %8.2g, num elements %D x %D x %D (%D), size (m) %g x %g x %g\n",level,(double)Lx,(double)Ly,(double)Lz,Mx,My,Mz,Mx*My*Mz,(double)(Lx/Mx),(double)(Ly/My),(double)(1000./(Mz-1)));
604: }
605: }
606: THIInitializePrm(thi,da2prm,X);
607: if (thi->tridiagonal) { /* Reset coarse Jacobian evaluation */
608: DMDASNESSetJacobianLocal(dm,(DMDASNESJacobian)THIJacobianLocal_3D_Full,thi);
609: }
610: if (thi->coarse2d) {
611: DMDASNESSetJacobianLocal(dm,(DMDASNESJacobian)THIJacobianLocal_2D,thi);
612: }
613: PetscObjectCompose((PetscObject)dm,"DMDA2Prm",(PetscObject)da2prm);
614: PetscObjectCompose((PetscObject)dm,"DMDA2Prm_Vec",(PetscObject)X);
615: DMDestroy(&da2prm);
616: VecDestroy(&X);
617: return(0);
618: }
620: static PetscErrorCode DMCoarsenHook_THI(DM dmf,DM dmc,void *ctx)
621: {
622: THI thi = (THI)ctx;
624: PetscInt rlevel,clevel;
627: THISetUpDM(thi,dmc);
628: DMGetRefineLevel(dmc,&rlevel);
629: DMGetCoarsenLevel(dmc,&clevel);
630: if (rlevel-clevel == 0) {DMSetMatType(dmc,MATAIJ);}
631: DMCoarsenHookAdd(dmc,DMCoarsenHook_THI,NULL,thi);
632: return(0);
633: }
635: static PetscErrorCode DMRefineHook_THI(DM dmc,DM dmf,void *ctx)
636: {
637: THI thi = (THI)ctx;
641: THISetUpDM(thi,dmf);
642: DMSetMatType(dmf,thi->mattype);
643: DMRefineHookAdd(dmf,DMRefineHook_THI,NULL,thi);
644: /* With grid sequencing, a formerly-refined DM will later be coarsened by PCSetUp_MG */
645: DMCoarsenHookAdd(dmf,DMCoarsenHook_THI,NULL,thi);
646: return(0);
647: }
649: static PetscErrorCode THIDAGetPrm(DM da,PrmNode ***prm)
650: {
652: DM da2prm;
653: Vec X;
656: PetscObjectQuery((PetscObject)da,"DMDA2Prm",(PetscObject*)&da2prm);
657: if (!da2prm) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"No DMDA2Prm composed with given DMDA");
658: PetscObjectQuery((PetscObject)da,"DMDA2Prm_Vec",(PetscObject*)&X);
659: if (!X) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"No DMDA2Prm_Vec composed with given DMDA");
660: DMDAVecGetArray(da2prm,X,prm);
661: return(0);
662: }
664: static PetscErrorCode THIDARestorePrm(DM da,PrmNode ***prm)
665: {
667: DM da2prm;
668: Vec X;
671: PetscObjectQuery((PetscObject)da,"DMDA2Prm",(PetscObject*)&da2prm);
672: if (!da2prm) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"No DMDA2Prm composed with given DMDA");
673: PetscObjectQuery((PetscObject)da,"DMDA2Prm_Vec",(PetscObject*)&X);
674: if (!X) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"No DMDA2Prm_Vec composed with given DMDA");
675: DMDAVecRestoreArray(da2prm,X,prm);
676: return(0);
677: }
679: static PetscErrorCode THIInitial(SNES snes,Vec X,void *ctx)
680: {
681: THI thi;
682: PetscInt i,j,k,xs,xm,ys,ym,zs,zm,mx,my;
683: PetscReal hx,hy;
684: PrmNode **prm;
685: Node ***x;
687: DM da;
690: SNESGetDM(snes,&da);
691: DMGetApplicationContext(da,&thi);
692: DMDAGetInfo(da,0, 0,&my,&mx, 0,0,0, 0,0,0,0,0,0);
693: DMDAGetCorners(da,&zs,&ys,&xs,&zm,&ym,&xm);
694: DMDAVecGetArray(da,X,&x);
695: THIDAGetPrm(da,&prm);
696: hx = thi->Lx / mx;
697: hy = thi->Ly / my;
698: for (i=xs; i<xs+xm; i++) {
699: for (j=ys; j<ys+ym; j++) {
700: for (k=zs; k<zs+zm; k++) {
701: const PetscScalar zm1 = zm-1,
702: 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),
703: 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);
704: x[i][j][k].u = 0. * drivingx * prm[i][j].h*(PetscScalar)k/zm1;
705: x[i][j][k].v = 0. * drivingy * prm[i][j].h*(PetscScalar)k/zm1;
706: }
707: }
708: }
709: DMDAVecRestoreArray(da,X,&x);
710: THIDARestorePrm(da,&prm);
711: return(0);
712: }
714: static void PointwiseNonlinearity(THI thi,const Node n[PETSC_RESTRICT],const PetscReal phi[PETSC_RESTRICT],PetscReal dphi[PETSC_RESTRICT][3],PetscScalar *PETSC_RESTRICT u,PetscScalar *PETSC_RESTRICT v,PetscScalar du[PETSC_RESTRICT],PetscScalar dv[PETSC_RESTRICT],PetscReal *eta,PetscReal *deta)
715: {
716: PetscInt l,ll;
717: PetscScalar gam;
719: du[0] = du[1] = du[2] = 0;
720: dv[0] = dv[1] = dv[2] = 0;
721: *u = 0;
722: *v = 0;
723: for (l=0; l<8; l++) {
724: *u += phi[l] * n[l].u;
725: *v += phi[l] * n[l].v;
726: for (ll=0; ll<3; ll++) {
727: du[ll] += dphi[l][ll] * n[l].u;
728: dv[ll] += dphi[l][ll] * n[l].v;
729: }
730: }
731: gam = PetscSqr(du[0]) + PetscSqr(dv[1]) + du[0]*dv[1] + 0.25*PetscSqr(du[1]+dv[0]) + 0.25*PetscSqr(du[2]) + 0.25*PetscSqr(dv[2]);
732: THIViscosity(thi,PetscRealPart(gam),eta,deta);
733: }
735: static void PointwiseNonlinearity2D(THI thi,Node n[],PetscReal phi[],PetscReal dphi[4][2],PetscScalar *u,PetscScalar *v,PetscScalar du[],PetscScalar dv[],PetscReal *eta,PetscReal *deta)
736: {
737: PetscInt l,ll;
738: PetscScalar gam;
740: du[0] = du[1] = 0;
741: dv[0] = dv[1] = 0;
742: *u = 0;
743: *v = 0;
744: for (l=0; l<4; l++) {
745: *u += phi[l] * n[l].u;
746: *v += phi[l] * n[l].v;
747: for (ll=0; ll<2; ll++) {
748: du[ll] += dphi[l][ll] * n[l].u;
749: dv[ll] += dphi[l][ll] * n[l].v;
750: }
751: }
752: gam = PetscSqr(du[0]) + PetscSqr(dv[1]) + du[0]*dv[1] + 0.25*PetscSqr(du[1]+dv[0]);
753: THIViscosity(thi,PetscRealPart(gam),eta,deta);
754: }
756: static PetscErrorCode THIFunctionLocal(DMDALocalInfo *info,Node ***x,Node ***f,THI thi)
757: {
758: PetscInt xs,ys,xm,ym,zm,i,j,k,q,l;
759: PetscReal hx,hy,etamin,etamax,beta2min,beta2max;
760: PrmNode **prm;
764: xs = info->zs;
765: ys = info->ys;
766: xm = info->zm;
767: ym = info->ym;
768: zm = info->xm;
769: hx = thi->Lx / info->mz;
770: hy = thi->Ly / info->my;
772: etamin = 1e100;
773: etamax = 0;
774: beta2min = 1e100;
775: beta2max = 0;
777: THIDAGetPrm(info->da,&prm);
779: for (i=xs; i<xs+xm; i++) {
780: for (j=ys; j<ys+ym; j++) {
781: PrmNode pn[4];
782: QuadExtract(prm,i,j,pn);
783: for (k=0; k<zm-1; k++) {
784: PetscInt ls = 0;
785: Node n[8],*fn[8];
786: PetscReal zn[8],etabase = 0;
787: PrmHexGetZ(pn,k,zm,zn);
788: HexExtract(x,i,j,k,n);
789: HexExtractRef(f,i,j,k,fn);
790: if (thi->no_slip && k == 0) {
791: for (l=0; l<4; l++) n[l].u = n[l].v = 0;
792: /* The first 4 basis functions lie on the bottom layer, so their contribution is exactly 0, hence we can skip them */
793: ls = 4;
794: }
795: for (q=0; q<8; q++) {
796: PetscReal dz[3],phi[8],dphi[8][3],jw,eta,deta;
797: PetscScalar du[3],dv[3],u,v;
798: HexGrad(HexQDeriv[q],zn,dz);
799: HexComputeGeometry(q,hx,hy,dz,phi,dphi,&jw);
800: PointwiseNonlinearity(thi,n,phi,dphi,&u,&v,du,dv,&eta,&deta);
801: jw /= thi->rhog; /* scales residuals to be O(1) */
802: if (q == 0) etabase = eta;
803: RangeUpdate(&etamin,&etamax,eta);
804: for (l=ls; l<8; l++) { /* test functions */
805: const PetscReal ds[2] = {-PetscSinReal(thi->alpha),0};
806: const PetscReal pp = phi[l],*dp = dphi[l];
807: 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];
808: 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];
809: }
810: }
811: if (k == 0) { /* we are on a bottom face */
812: if (thi->no_slip) {
813: /* Note: Non-Galerkin coarse grid operators are very sensitive to the scaling of Dirichlet boundary
814: * conditions. After shenanigans above, etabase contains the effective viscosity at the closest quadrature
815: * point to the bed. We want the diagonal entry in the Dirichlet condition to have similar magnitude to the
816: * diagonal entry corresponding to the adjacent node. The fundamental scaling of the viscous part is in
817: * diagu, diagv below. This scaling is easy to recognize by considering the finite difference operator after
818: * scaling by element size. The no-slip Dirichlet condition is scaled by this factor, and also in the
819: * assembled matrix (see the similar block in THIJacobianLocal).
820: *
821: * Note that the residual at this Dirichlet node is linear in the state at this node, but also depends
822: * (nonlinearly in general) on the neighboring interior nodes through the local viscosity. This will make
823: * a matrix-free Jacobian have extra entries in the corresponding row. We assemble only the diagonal part,
824: * so the solution will exactly satisfy the boundary condition after the first linear iteration.
825: */
826: const PetscReal hz = PetscRealPart(pn[0].h)/(zm-1.);
827: 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);
828: fn[0]->u = thi->dirichlet_scale*diagu*x[i][j][k].u;
829: fn[0]->v = thi->dirichlet_scale*diagv*x[i][j][k].v;
830: } else { /* Integrate over bottom face to apply boundary condition */
831: for (q=0; q<4; q++) {
832: const PetscReal jw = 0.25*hx*hy/thi->rhog,*phi = QuadQInterp[q];
833: PetscScalar u =0,v=0,rbeta2=0;
834: PetscReal beta2,dbeta2;
835: for (l=0; l<4; l++) {
836: u += phi[l]*n[l].u;
837: v += phi[l]*n[l].v;
838: rbeta2 += phi[l]*pn[l].beta2;
839: }
840: THIFriction(thi,PetscRealPart(rbeta2),PetscRealPart(u*u+v*v)/2,&beta2,&dbeta2);
841: RangeUpdate(&beta2min,&beta2max,beta2);
842: for (l=0; l<4; l++) {
843: const PetscReal pp = phi[l];
844: fn[ls+l]->u += pp*jw*beta2*u;
845: fn[ls+l]->v += pp*jw*beta2*v;
846: }
847: }
848: }
849: }
850: }
851: }
852: }
854: THIDARestorePrm(info->da,&prm);
856: PRangeMinMax(&thi->eta,etamin,etamax);
857: PRangeMinMax(&thi->beta2,beta2min,beta2max);
858: return(0);
859: }
861: static PetscErrorCode THIMatrixStatistics(THI thi,Mat B,PetscViewer viewer)
862: {
864: PetscReal nrm;
865: PetscInt m;
866: PetscMPIInt rank;
869: MatNorm(B,NORM_FROBENIUS,&nrm);
870: MatGetSize(B,&m,0);
871: MPI_Comm_rank(PetscObjectComm((PetscObject)B),&rank);
872: if (rank == 0) {
873: PetscScalar val0,val2;
874: MatGetValue(B,0,0,&val0);
875: MatGetValue(B,2,2,&val2);
876: PetscViewerASCIIPrintf(viewer,"Matrix dim %D norm %8.2e (0,0) %8.2e (2,2) %8.2e %8.2e <= eta <= %8.2e %8.2e <= beta2 <= %8.2e\n",m,(double)nrm,(double)PetscRealPart(val0),(double)PetscRealPart(val2),(double)thi->eta.cmin,(double)thi->eta.cmax,(double)thi->beta2.cmin,(double)thi->beta2.cmax);
877: }
878: return(0);
879: }
881: static PetscErrorCode THISurfaceStatistics(DM da,Vec X,PetscReal *min,PetscReal *max,PetscReal *mean)
882: {
884: Node ***x;
885: PetscInt i,j,xs,ys,zs,xm,ym,zm,mx,my,mz;
886: PetscReal umin = 1e100,umax=-1e100;
887: PetscScalar usum = 0.0,gusum;
890: *min = *max = *mean = 0;
891: DMDAGetInfo(da,0, &mz,&my,&mx, 0,0,0, 0,0,0,0,0,0);
892: DMDAGetCorners(da,&zs,&ys,&xs,&zm,&ym,&xm);
893: if (zs != 0 || zm != mz) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Unexpected decomposition");
894: DMDAVecGetArray(da,X,&x);
895: for (i=xs; i<xs+xm; i++) {
896: for (j=ys; j<ys+ym; j++) {
897: PetscReal u = PetscRealPart(x[i][j][zm-1].u);
898: RangeUpdate(&umin,&umax,u);
899: usum += u;
900: }
901: }
902: DMDAVecRestoreArray(da,X,&x);
903: MPI_Allreduce(&umin,min,1,MPIU_REAL,MPIU_MIN,PetscObjectComm((PetscObject)da));
904: MPI_Allreduce(&umax,max,1,MPIU_REAL,MPIU_MAX,PetscObjectComm((PetscObject)da));
905: MPI_Allreduce(&usum,&gusum,1,MPIU_SCALAR,MPIU_SUM,PetscObjectComm((PetscObject)da));
906: *mean = PetscRealPart(gusum) / (mx*my);
907: return(0);
908: }
910: static PetscErrorCode THISolveStatistics(THI thi,SNES snes,PetscInt coarsened,const char name[])
911: {
912: MPI_Comm comm;
913: Vec X;
914: DM dm;
918: PetscObjectGetComm((PetscObject)thi,&comm);
919: SNESGetSolution(snes,&X);
920: SNESGetDM(snes,&dm);
921: PetscPrintf(comm,"Solution statistics after solve: %s\n",name);
922: {
923: PetscInt its,lits;
924: SNESConvergedReason reason;
925: SNESGetIterationNumber(snes,&its);
926: SNESGetConvergedReason(snes,&reason);
927: SNESGetLinearSolveIterations(snes,&lits);
928: PetscPrintf(comm,"%s: Number of SNES iterations = %D, total linear iterations = %D\n",SNESConvergedReasons[reason],its,lits);
929: }
930: {
931: PetscReal nrm2,tmin[3]={1e100,1e100,1e100},tmax[3]={-1e100,-1e100,-1e100},min[3],max[3];
932: PetscInt i,j,m;
933: const PetscScalar *x;
934: VecNorm(X,NORM_2,&nrm2);
935: VecGetLocalSize(X,&m);
936: VecGetArrayRead(X,&x);
937: for (i=0; i<m; i+=2) {
938: PetscReal u = PetscRealPart(x[i]),v = PetscRealPart(x[i+1]),c = PetscSqrtReal(u*u+v*v);
939: tmin[0] = PetscMin(u,tmin[0]);
940: tmin[1] = PetscMin(v,tmin[1]);
941: tmin[2] = PetscMin(c,tmin[2]);
942: tmax[0] = PetscMax(u,tmax[0]);
943: tmax[1] = PetscMax(v,tmax[1]);
944: tmax[2] = PetscMax(c,tmax[2]);
945: }
946: VecRestoreArrayRead(X,&x);
947: MPI_Allreduce(tmin,min,3,MPIU_REAL,MPIU_MIN,PetscObjectComm((PetscObject)thi));
948: MPI_Allreduce(tmax,max,3,MPIU_REAL,MPIU_MAX,PetscObjectComm((PetscObject)thi));
949: /* Dimensionalize to meters/year */
950: nrm2 *= thi->units->year / thi->units->meter;
951: for (j=0; j<3; j++) {
952: min[j] *= thi->units->year / thi->units->meter;
953: max[j] *= thi->units->year / thi->units->meter;
954: }
955: if (min[0] == 0.0) min[0] = 0.0;
956: PetscPrintf(comm,"|X|_2 %g %g <= u <= %g %g <= v <= %g %g <= c <= %g \n",(double)nrm2,(double)min[0],(double)max[0],(double)min[1],(double)max[1],(double)min[2],(double)max[2]);
957: {
958: PetscReal umin,umax,umean;
959: THISurfaceStatistics(dm,X,&umin,&umax,&umean);
960: umin *= thi->units->year / thi->units->meter;
961: umax *= thi->units->year / thi->units->meter;
962: umean *= thi->units->year / thi->units->meter;
963: PetscPrintf(comm,"Surface statistics: u in [%12.6e, %12.6e] mean %12.6e\n",(double)umin,(double)umax,(double)umean);
964: }
965: /* These values stay nondimensional */
966: PetscPrintf(comm,"Global eta range %g to %g converged range %g to %g\n",(double)thi->eta.min,(double)thi->eta.max,(double)thi->eta.cmin,(double)thi->eta.cmax);
967: PetscPrintf(comm,"Global beta2 range %g to %g converged range %g to %g\n",(double)thi->beta2.min,(double)thi->beta2.max,(double)thi->beta2.cmin,(double)thi->beta2.cmax);
968: }
969: return(0);
970: }
972: static PetscErrorCode THIJacobianLocal_2D(DMDALocalInfo *info,Node **x,Mat J,Mat B,THI thi)
973: {
974: PetscInt xs,ys,xm,ym,i,j,q,l,ll;
975: PetscReal hx,hy;
976: PrmNode **prm;
980: xs = info->ys;
981: ys = info->xs;
982: xm = info->ym;
983: ym = info->xm;
984: hx = thi->Lx / info->my;
985: hy = thi->Ly / info->mx;
987: MatZeroEntries(B);
988: THIDAGetPrm(info->da,&prm);
990: for (i=xs; i<xs+xm; i++) {
991: for (j=ys; j<ys+ym; j++) {
992: Node n[4];
993: PrmNode pn[4];
994: PetscScalar Ke[4*2][4*2];
995: QuadExtract(prm,i,j,pn);
996: QuadExtract(x,i,j,n);
997: PetscMemzero(Ke,sizeof(Ke));
998: for (q=0; q<4; q++) {
999: PetscReal phi[4],dphi[4][2],jw,eta,deta,beta2,dbeta2;
1000: PetscScalar u,v,du[2],dv[2],h = 0,rbeta2 = 0;
1001: for (l=0; l<4; l++) {
1002: phi[l] = QuadQInterp[q][l];
1003: dphi[l][0] = QuadQDeriv[q][l][0]*2./hx;
1004: dphi[l][1] = QuadQDeriv[q][l][1]*2./hy;
1005: h += phi[l] * pn[l].h;
1006: rbeta2 += phi[l] * pn[l].beta2;
1007: }
1008: jw = 0.25*hx*hy / thi->rhog; /* rhog is only scaling */
1009: PointwiseNonlinearity2D(thi,n,phi,dphi,&u,&v,du,dv,&eta,&deta);
1010: THIFriction(thi,PetscRealPart(rbeta2),PetscRealPart(u*u+v*v)/2,&beta2,&dbeta2);
1011: for (l=0; l<4; l++) {
1012: const PetscReal pp = phi[l],*dp = dphi[l];
1013: for (ll=0; ll<4; ll++) {
1014: const PetscReal ppl = phi[ll],*dpl = dphi[ll];
1015: PetscScalar dgdu,dgdv;
1016: dgdu = 2.*du[0]*dpl[0] + dv[1]*dpl[0] + 0.5*(du[1]+dv[0])*dpl[1];
1017: dgdv = 2.*dv[1]*dpl[1] + du[0]*dpl[1] + 0.5*(du[1]+dv[0])*dpl[0];
1018: /* Picard part */
1019: Ke[l*2+0][ll*2+0] += dp[0]*jw*eta*4.*dpl[0] + dp[1]*jw*eta*dpl[1] + pp*jw*(beta2/h)*ppl*thi->ssa_friction_scale;
1020: Ke[l*2+0][ll*2+1] += dp[0]*jw*eta*2.*dpl[1] + dp[1]*jw*eta*dpl[0];
1021: Ke[l*2+1][ll*2+0] += dp[1]*jw*eta*2.*dpl[0] + dp[0]*jw*eta*dpl[1];
1022: Ke[l*2+1][ll*2+1] += dp[1]*jw*eta*4.*dpl[1] + dp[0]*jw*eta*dpl[0] + pp*jw*(beta2/h)*ppl*thi->ssa_friction_scale;
1023: /* extra Newton terms */
1024: 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]) + pp*jw*(dbeta2/h)*u*u*ppl*thi->ssa_friction_scale;
1025: 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]) + pp*jw*(dbeta2/h)*u*v*ppl*thi->ssa_friction_scale;
1026: 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]) + pp*jw*(dbeta2/h)*v*u*ppl*thi->ssa_friction_scale;
1027: 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]) + pp*jw*(dbeta2/h)*v*v*ppl*thi->ssa_friction_scale;
1028: }
1029: }
1030: }
1031: {
1032: const MatStencil rc[4] = {{0,i,j,0},{0,i+1,j,0},{0,i+1,j+1,0},{0,i,j+1,0}};
1033: MatSetValuesBlockedStencil(B,4,rc,4,rc,&Ke[0][0],ADD_VALUES);
1034: }
1035: }
1036: }
1037: THIDARestorePrm(info->da,&prm);
1039: MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
1040: MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
1041: MatSetOption(B,MAT_SYMMETRIC,PETSC_TRUE);
1042: if (thi->verbose) {THIMatrixStatistics(thi,B,PETSC_VIEWER_STDOUT_WORLD);}
1043: return(0);
1044: }
1046: static PetscErrorCode THIJacobianLocal_3D(DMDALocalInfo *info,Node ***x,Mat B,THI thi,THIAssemblyMode amode)
1047: {
1048: PetscInt xs,ys,xm,ym,zm,i,j,k,q,l,ll;
1049: PetscReal hx,hy;
1050: PrmNode **prm;
1054: xs = info->zs;
1055: ys = info->ys;
1056: xm = info->zm;
1057: ym = info->ym;
1058: zm = info->xm;
1059: hx = thi->Lx / info->mz;
1060: hy = thi->Ly / info->my;
1062: MatZeroEntries(B);
1063: MatSetOption(B,MAT_SUBSET_OFF_PROC_ENTRIES,PETSC_TRUE);
1064: THIDAGetPrm(info->da,&prm);
1066: for (i=xs; i<xs+xm; i++) {
1067: for (j=ys; j<ys+ym; j++) {
1068: PrmNode pn[4];
1069: QuadExtract(prm,i,j,pn);
1070: for (k=0; k<zm-1; k++) {
1071: Node n[8];
1072: PetscReal zn[8],etabase = 0;
1073: PetscScalar Ke[8*2][8*2];
1074: PetscInt ls = 0;
1076: PrmHexGetZ(pn,k,zm,zn);
1077: HexExtract(x,i,j,k,n);
1078: PetscMemzero(Ke,sizeof(Ke));
1079: if (thi->no_slip && k == 0) {
1080: for (l=0; l<4; l++) n[l].u = n[l].v = 0;
1081: ls = 4;
1082: }
1083: for (q=0; q<8; q++) {
1084: PetscReal dz[3],phi[8],dphi[8][3],jw,eta,deta;
1085: PetscScalar du[3],dv[3],u,v;
1086: HexGrad(HexQDeriv[q],zn,dz);
1087: HexComputeGeometry(q,hx,hy,dz,phi,dphi,&jw);
1088: PointwiseNonlinearity(thi,n,phi,dphi,&u,&v,du,dv,&eta,&deta);
1089: jw /= thi->rhog; /* residuals are scaled by this factor */
1090: if (q == 0) etabase = eta;
1091: for (l=ls; l<8; l++) { /* test functions */
1092: const PetscReal *PETSC_RESTRICT dp = dphi[l];
1093: #if USE_SSE2_KERNELS
1094: /* gcc (up to my 4.5 snapshot) is really bad at hoisting intrinsics so we do it manually */
1095: __m128d
1096: p4 = _mm_set1_pd(4),p2 = _mm_set1_pd(2),p05 = _mm_set1_pd(0.5),
1097: p42 = _mm_setr_pd(4,2),p24 = _mm_shuffle_pd(p42,p42,_MM_SHUFFLE2(0,1)),
1098: du0 = _mm_set1_pd(du[0]),du1 = _mm_set1_pd(du[1]),du2 = _mm_set1_pd(du[2]),
1099: dv0 = _mm_set1_pd(dv[0]),dv1 = _mm_set1_pd(dv[1]),dv2 = _mm_set1_pd(dv[2]),
1100: jweta = _mm_set1_pd(jw*eta),jwdeta = _mm_set1_pd(jw*deta),
1101: dp0 = _mm_set1_pd(dp[0]),dp1 = _mm_set1_pd(dp[1]),dp2 = _mm_set1_pd(dp[2]),
1102: dp0jweta = _mm_mul_pd(dp0,jweta),dp1jweta = _mm_mul_pd(dp1,jweta),dp2jweta = _mm_mul_pd(dp2,jweta),
1103: p4du0p2dv1 = _mm_add_pd(_mm_mul_pd(p4,du0),_mm_mul_pd(p2,dv1)), /* 4 du0 + 2 dv1 */
1104: p4dv1p2du0 = _mm_add_pd(_mm_mul_pd(p4,dv1),_mm_mul_pd(p2,du0)), /* 4 dv1 + 2 du0 */
1105: pdu2dv2 = _mm_unpacklo_pd(du2,dv2), /* [du2, dv2] */
1106: du1pdv0 = _mm_add_pd(du1,dv0), /* du1 + dv0 */
1107: t1 = _mm_mul_pd(dp0,p4du0p2dv1), /* dp0 (4 du0 + 2 dv1) */
1108: t2 = _mm_mul_pd(dp1,p4dv1p2du0); /* dp1 (4 dv1 + 2 du0) */
1110: #endif
1111: #if defined COMPUTE_LOWER_TRIANGULAR /* The element matrices are always symmetric so computing the lower-triangular part is not necessary */
1112: for (ll=ls; ll<8; ll++) { /* trial functions */
1113: #else
1114: for (ll=l; ll<8; ll++) {
1115: #endif
1116: const PetscReal *PETSC_RESTRICT dpl = dphi[ll];
1117: if (amode == THIASSEMBLY_TRIDIAGONAL && (l-ll)%4) continue; /* these entries would not be inserted */
1118: #if !USE_SSE2_KERNELS
1119: /* The analytic Jacobian in nice, easy-to-read form */
1120: {
1121: PetscScalar dgdu,dgdv;
1122: dgdu = 2.*du[0]*dpl[0] + dv[1]*dpl[0] + 0.5*(du[1]+dv[0])*dpl[1] + 0.5*du[2]*dpl[2];
1123: dgdv = 2.*dv[1]*dpl[1] + du[0]*dpl[1] + 0.5*(du[1]+dv[0])*dpl[0] + 0.5*dv[2]*dpl[2];
1124: /* Picard part */
1125: 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];
1126: Ke[l*2+0][ll*2+1] += dp[0]*jw*eta*2.*dpl[1] + dp[1]*jw*eta*dpl[0];
1127: Ke[l*2+1][ll*2+0] += dp[1]*jw*eta*2.*dpl[0] + dp[0]*jw*eta*dpl[1];
1128: 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];
1129: /* extra Newton terms */
1130: 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];
1131: 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];
1132: 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];
1133: 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];
1134: }
1135: #else
1136: /* This SSE2 code is an exact replica of above, but uses explicit packed instructions for some speed
1137: * benefit. On my hardware, these intrinsics are almost twice as fast as above, reducing total assembly cost
1138: * by 25 to 30 percent. */
1139: {
1140: __m128d
1141: keu = _mm_loadu_pd(&Ke[l*2+0][ll*2+0]),
1142: kev = _mm_loadu_pd(&Ke[l*2+1][ll*2+0]),
1143: dpl01 = _mm_loadu_pd(&dpl[0]),dpl10 = _mm_shuffle_pd(dpl01,dpl01,_MM_SHUFFLE2(0,1)),dpl2 = _mm_set_sd(dpl[2]),
1144: t0,t3,pdgduv;
1145: keu = _mm_add_pd(keu,_mm_add_pd(_mm_mul_pd(_mm_mul_pd(dp0jweta,p42),dpl01),
1146: _mm_add_pd(_mm_mul_pd(dp1jweta,dpl10),
1147: _mm_mul_pd(dp2jweta,dpl2))));
1148: kev = _mm_add_pd(kev,_mm_add_pd(_mm_mul_pd(_mm_mul_pd(dp1jweta,p24),dpl01),
1149: _mm_add_pd(_mm_mul_pd(dp0jweta,dpl10),
1150: _mm_mul_pd(dp2jweta,_mm_shuffle_pd(dpl2,dpl2,_MM_SHUFFLE2(0,1))))));
1151: pdgduv = _mm_mul_pd(p05,_mm_add_pd(_mm_add_pd(_mm_mul_pd(p42,_mm_mul_pd(du0,dpl01)),
1152: _mm_mul_pd(p24,_mm_mul_pd(dv1,dpl01))),
1153: _mm_add_pd(_mm_mul_pd(du1pdv0,dpl10),
1154: _mm_mul_pd(pdu2dv2,_mm_set1_pd(dpl[2]))))); /* [dgdu, dgdv] */
1155: t0 = _mm_mul_pd(jwdeta,pdgduv); /* jw deta [dgdu, dgdv] */
1156: t3 = _mm_mul_pd(t0,du1pdv0); /* t0 (du1 + dv0) */
1157: _mm_storeu_pd(&Ke[l*2+0][ll*2+0],_mm_add_pd(keu,_mm_add_pd(_mm_mul_pd(t1,t0),
1158: _mm_add_pd(_mm_mul_pd(dp1,t3),
1159: _mm_mul_pd(t0,_mm_mul_pd(dp2,du2))))));
1160: _mm_storeu_pd(&Ke[l*2+1][ll*2+0],_mm_add_pd(kev,_mm_add_pd(_mm_mul_pd(t2,t0),
1161: _mm_add_pd(_mm_mul_pd(dp0,t3),
1162: _mm_mul_pd(t0,_mm_mul_pd(dp2,dv2))))));
1163: }
1164: #endif
1165: }
1166: }
1167: }
1168: if (k == 0) { /* on a bottom face */
1169: if (thi->no_slip) {
1170: const PetscReal hz = PetscRealPart(pn[0].h)/(zm-1);
1171: 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);
1172: Ke[0][0] = thi->dirichlet_scale*diagu;
1173: Ke[1][1] = thi->dirichlet_scale*diagv;
1174: } else {
1175: for (q=0; q<4; q++) {
1176: const PetscReal jw = 0.25*hx*hy/thi->rhog,*phi = QuadQInterp[q];
1177: PetscScalar u =0,v=0,rbeta2=0;
1178: PetscReal beta2,dbeta2;
1179: for (l=0; l<4; l++) {
1180: u += phi[l]*n[l].u;
1181: v += phi[l]*n[l].v;
1182: rbeta2 += phi[l]*pn[l].beta2;
1183: }
1184: THIFriction(thi,PetscRealPart(rbeta2),PetscRealPart(u*u+v*v)/2,&beta2,&dbeta2);
1185: for (l=0; l<4; l++) {
1186: const PetscReal pp = phi[l];
1187: for (ll=0; ll<4; ll++) {
1188: const PetscReal ppl = phi[ll];
1189: Ke[l*2+0][ll*2+0] += pp*jw*beta2*ppl + pp*jw*dbeta2*u*u*ppl;
1190: Ke[l*2+0][ll*2+1] += pp*jw*dbeta2*u*v*ppl;
1191: Ke[l*2+1][ll*2+0] += pp*jw*dbeta2*v*u*ppl;
1192: Ke[l*2+1][ll*2+1] += pp*jw*beta2*ppl + pp*jw*dbeta2*v*v*ppl;
1193: }
1194: }
1195: }
1196: }
1197: }
1198: {
1199: const MatStencil rc[8] = {{i,j,k,0},{i+1,j,k,0},{i+1,j+1,k,0},{i,j+1,k,0},{i,j,k+1,0},{i+1,j,k+1,0},{i+1,j+1,k+1,0},{i,j+1,k+1,0}};
1200: if (amode == THIASSEMBLY_TRIDIAGONAL) {
1201: for (l=0; l<4; l++) { /* Copy out each of the blocks, discarding horizontal coupling */
1202: const PetscInt l4 = l+4;
1203: const MatStencil rcl[2] = {{rc[l].k,rc[l].j,rc[l].i,0},{rc[l4].k,rc[l4].j,rc[l4].i,0}};
1204: #if defined COMPUTE_LOWER_TRIANGULAR
1205: const PetscScalar Kel[4][4] = {{Ke[2*l+0][2*l+0] ,Ke[2*l+0][2*l+1] ,Ke[2*l+0][2*l4+0] ,Ke[2*l+0][2*l4+1]},
1206: {Ke[2*l+1][2*l+0] ,Ke[2*l+1][2*l+1] ,Ke[2*l+1][2*l4+0] ,Ke[2*l+1][2*l4+1]},
1207: {Ke[2*l4+0][2*l+0],Ke[2*l4+0][2*l+1],Ke[2*l4+0][2*l4+0],Ke[2*l4+0][2*l4+1]},
1208: {Ke[2*l4+1][2*l+0],Ke[2*l4+1][2*l+1],Ke[2*l4+1][2*l4+0],Ke[2*l4+1][2*l4+1]}};
1209: #else
1210: /* Same as above except for the lower-left block */
1211: const PetscScalar Kel[4][4] = {{Ke[2*l+0][2*l+0] ,Ke[2*l+0][2*l+1] ,Ke[2*l+0][2*l4+0] ,Ke[2*l+0][2*l4+1]},
1212: {Ke[2*l+1][2*l+0] ,Ke[2*l+1][2*l+1] ,Ke[2*l+1][2*l4+0] ,Ke[2*l+1][2*l4+1]},
1213: {Ke[2*l+0][2*l4+0],Ke[2*l+1][2*l4+0],Ke[2*l4+0][2*l4+0],Ke[2*l4+0][2*l4+1]},
1214: {Ke[2*l+0][2*l4+1],Ke[2*l+1][2*l4+1],Ke[2*l4+1][2*l4+0],Ke[2*l4+1][2*l4+1]}};
1215: #endif
1216: MatSetValuesBlockedStencil(B,2,rcl,2,rcl,&Kel[0][0],ADD_VALUES);
1217: }
1218: } else {
1219: #if !defined COMPUTE_LOWER_TRIANGULAR /* fill in lower-triangular part, this is really cheap compared to computing the entries */
1220: for (l=0; l<8; l++) {
1221: for (ll=l+1; ll<8; ll++) {
1222: Ke[ll*2+0][l*2+0] = Ke[l*2+0][ll*2+0];
1223: Ke[ll*2+1][l*2+0] = Ke[l*2+0][ll*2+1];
1224: Ke[ll*2+0][l*2+1] = Ke[l*2+1][ll*2+0];
1225: Ke[ll*2+1][l*2+1] = Ke[l*2+1][ll*2+1];
1226: }
1227: }
1228: #endif
1229: MatSetValuesBlockedStencil(B,8,rc,8,rc,&Ke[0][0],ADD_VALUES);
1230: }
1231: }
1232: }
1233: }
1234: }
1235: THIDARestorePrm(info->da,&prm);
1237: MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
1238: MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
1239: MatSetOption(B,MAT_SYMMETRIC,PETSC_TRUE);
1240: if (thi->verbose) {THIMatrixStatistics(thi,B,PETSC_VIEWER_STDOUT_WORLD);}
1241: return(0);
1242: }
1244: static PetscErrorCode THIJacobianLocal_3D_Full(DMDALocalInfo *info,Node ***x,Mat A,Mat B,THI thi)
1245: {
1249: THIJacobianLocal_3D(info,x,B,thi,THIASSEMBLY_FULL);
1250: return(0);
1251: }
1253: static PetscErrorCode THIJacobianLocal_3D_Tridiagonal(DMDALocalInfo *info,Node ***x,Mat A,Mat B,THI thi)
1254: {
1258: THIJacobianLocal_3D(info,x,B,thi,THIASSEMBLY_TRIDIAGONAL);
1259: return(0);
1260: }
1262: static PetscErrorCode DMRefineHierarchy_THI(DM dac0,PetscInt nlevels,DM hierarchy[])
1263: {
1264: PetscErrorCode ierr;
1265: THI thi;
1266: PetscInt dim,M,N,m,n,s,dof;
1267: DM dac,daf;
1268: DMDAStencilType st;
1269: DM_DA *ddf,*ddc;
1272: PetscObjectQuery((PetscObject)dac0,"THI",(PetscObject*)&thi);
1273: if (!thi) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Cannot refine this DMDA, missing composed THI instance");
1274: if (nlevels > 1) {
1275: DMRefineHierarchy(dac0,nlevels-1,hierarchy);
1276: dac = hierarchy[nlevels-2];
1277: } else {
1278: dac = dac0;
1279: }
1280: DMDAGetInfo(dac,&dim, &N,&M,0, &n,&m,0, &dof,&s,0,0,0,&st);
1281: if (dim != 2) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"This function can only refine 2D DMDAs");
1283: /* Creates a 3D DMDA with the same map-plane layout as the 2D one, with contiguous columns */
1284: DMDACreate3d(PetscObjectComm((PetscObject)dac),DM_BOUNDARY_NONE,DM_BOUNDARY_PERIODIC,DM_BOUNDARY_PERIODIC,st,thi->zlevels,N,M,1,n,m,dof,s,NULL,NULL,NULL,&daf);
1285: DMSetUp(daf);
1287: daf->ops->creatematrix = dac->ops->creatematrix;
1288: daf->ops->createinterpolation = dac->ops->createinterpolation;
1289: daf->ops->getcoloring = dac->ops->getcoloring;
1290: ddf = (DM_DA*)daf->data;
1291: ddc = (DM_DA*)dac->data;
1292: ddf->interptype = ddc->interptype;
1294: DMDASetFieldName(daf,0,"x-velocity");
1295: DMDASetFieldName(daf,1,"y-velocity");
1297: hierarchy[nlevels-1] = daf;
1298: return(0);
1299: }
1301: static PetscErrorCode DMCreateInterpolation_DA_THI(DM dac,DM daf,Mat *A,Vec *scale)
1302: {
1304: PetscInt dim;
1311: DMDAGetInfo(daf,&dim,0,0,0,0,0,0,0,0,0,0,0,0);
1312: if (dim == 2) {
1313: /* We are in the 2D problem and use normal DMDA interpolation */
1314: DMCreateInterpolation(dac,daf,A,scale);
1315: } else {
1316: PetscInt i,j,k,xs,ys,zs,xm,ym,zm,mx,my,mz,rstart,cstart;
1317: Mat B;
1319: DMDAGetInfo(daf,0, &mz,&my,&mx, 0,0,0, 0,0,0,0,0,0);
1320: DMDAGetCorners(daf,&zs,&ys,&xs,&zm,&ym,&xm);
1321: if (zs) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"unexpected");
1322: MatCreate(PetscObjectComm((PetscObject)daf),&B);
1323: MatSetSizes(B,xm*ym*zm,xm*ym,mx*my*mz,mx*my);
1325: MatSetType(B,MATAIJ);
1326: MatSeqAIJSetPreallocation(B,1,NULL);
1327: MatMPIAIJSetPreallocation(B,1,NULL,0,NULL);
1328: MatGetOwnershipRange(B,&rstart,NULL);
1329: MatGetOwnershipRangeColumn(B,&cstart,NULL);
1330: for (i=xs; i<xs+xm; i++) {
1331: for (j=ys; j<ys+ym; j++) {
1332: for (k=zs; k<zs+zm; k++) {
1333: PetscInt i2 = i*ym+j,i3 = i2*zm+k;
1334: PetscScalar val = ((k == 0 || k == mz-1) ? 0.5 : 1.) / (mz-1.); /* Integration using trapezoid rule */
1335: MatSetValue(B,cstart+i3,rstart+i2,val,INSERT_VALUES);
1336: }
1337: }
1338: }
1339: MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
1340: MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
1341: MatCreateMAIJ(B,sizeof(Node)/sizeof(PetscScalar),A);
1342: MatDestroy(&B);
1343: }
1344: return(0);
1345: }
1347: static PetscErrorCode DMCreateMatrix_THI_Tridiagonal(DM da,Mat *J)
1348: {
1349: PetscErrorCode ierr;
1350: Mat A;
1351: PetscInt xm,ym,zm,dim,dof = 2,starts[3],dims[3];
1352: ISLocalToGlobalMapping ltog;
1355: DMDAGetInfo(da,&dim, 0,0,0, 0,0,0, 0,0,0,0,0,0);
1356: if (dim != 3) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Expected DMDA to be 3D");
1357: DMDAGetCorners(da,0,0,0,&zm,&ym,&xm);
1358: DMGetLocalToGlobalMapping(da,<og);
1359: MatCreate(PetscObjectComm((PetscObject)da),&A);
1360: MatSetSizes(A,dof*xm*ym*zm,dof*xm*ym*zm,PETSC_DETERMINE,PETSC_DETERMINE);
1361: MatSetType(A,da->mattype);
1362: MatSetFromOptions(A);
1363: MatSeqAIJSetPreallocation(A,3*2,NULL);
1364: MatMPIAIJSetPreallocation(A,3*2,NULL,0,NULL);
1365: MatSeqBAIJSetPreallocation(A,2,3,NULL);
1366: MatMPIBAIJSetPreallocation(A,2,3,NULL,0,NULL);
1367: MatSeqSBAIJSetPreallocation(A,2,2,NULL);
1368: MatMPISBAIJSetPreallocation(A,2,2,NULL,0,NULL);
1369: MatSetLocalToGlobalMapping(A,ltog,ltog);
1370: DMDAGetGhostCorners(da,&starts[0],&starts[1],&starts[2],&dims[0],&dims[1],&dims[2]);
1371: MatSetStencil(A,dim,dims,starts,dof);
1372: *J = A;
1373: return(0);
1374: }
1376: static PetscErrorCode THIDAVecView_VTK_XML(THI thi,DM da,Vec X,const char filename[])
1377: {
1378: const PetscInt dof = 2;
1379: Units units = thi->units;
1380: MPI_Comm comm;
1381: PetscErrorCode ierr;
1382: PetscViewer viewer;
1383: PetscMPIInt rank,size,tag,nn,nmax;
1384: PetscInt mx,my,mz,r,range[6];
1385: const PetscScalar *x;
1388: PetscObjectGetComm((PetscObject)thi,&comm);
1389: DMDAGetInfo(da,0, &mz,&my,&mx, 0,0,0, 0,0,0,0,0,0);
1390: MPI_Comm_size(comm,&size);
1391: MPI_Comm_rank(comm,&rank);
1392: PetscViewerASCIIOpen(comm,filename,&viewer);
1393: PetscViewerASCIIPrintf(viewer,"<VTKFile type=\"StructuredGrid\" version=\"0.1\" byte_order=\"LittleEndian\">\n");
1394: PetscViewerASCIIPrintf(viewer," <StructuredGrid WholeExtent=\"%d %D %d %D %d %D\">\n",0,mz-1,0,my-1,0,mx-1);
1396: DMDAGetCorners(da,range,range+1,range+2,range+3,range+4,range+5);
1397: PetscMPIIntCast(range[3]*range[4]*range[5]*dof,&nn);
1398: MPI_Reduce(&nn,&nmax,1,MPI_INT,MPI_MAX,0,comm);
1399: tag = ((PetscObject) viewer)->tag;
1400: VecGetArrayRead(X,&x);
1401: if (rank == 0) {
1402: PetscScalar *array;
1403: PetscMalloc1(nmax,&array);
1404: for (r=0; r<size; r++) {
1405: PetscInt i,j,k,xs,xm,ys,ym,zs,zm;
1406: const PetscScalar *ptr;
1407: MPI_Status status;
1408: if (r) {
1409: MPI_Recv(range,6,MPIU_INT,r,tag,comm,MPI_STATUS_IGNORE);
1410: }
1411: zs = range[0];ys = range[1];xs = range[2];zm = range[3];ym = range[4];xm = range[5];
1412: if (xm*ym*zm*dof > nmax) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"should not happen");
1413: if (r) {
1414: MPI_Recv(array,nmax,MPIU_SCALAR,r,tag,comm,&status);
1415: MPI_Get_count(&status,MPIU_SCALAR,&nn);
1416: if (nn != xm*ym*zm*dof) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"should not happen");
1417: ptr = array;
1418: } else ptr = x;
1419: PetscViewerASCIIPrintf(viewer," <Piece Extent=\"%D %D %D %D %D %D\">\n",zs,zs+zm-1,ys,ys+ym-1,xs,xs+xm-1);
1421: PetscViewerASCIIPrintf(viewer," <Points>\n");
1422: PetscViewerASCIIPrintf(viewer," <DataArray type=\"Float32\" NumberOfComponents=\"3\" format=\"ascii\">\n");
1423: for (i=xs; i<xs+xm; i++) {
1424: for (j=ys; j<ys+ym; j++) {
1425: for (k=zs; k<zs+zm; k++) {
1426: PrmNode p;
1427: PetscReal xx = thi->Lx*i/mx,yy = thi->Ly*j/my,zz;
1428: thi->initialize(thi,xx,yy,&p);
1429: zz = PetscRealPart(p.b) + PetscRealPart(p.h)*k/(mz-1);
1430: PetscViewerASCIIPrintf(viewer,"%f %f %f\n",(double)xx,(double)yy,(double)zz);
1431: }
1432: }
1433: }
1434: PetscViewerASCIIPrintf(viewer," </DataArray>\n");
1435: PetscViewerASCIIPrintf(viewer," </Points>\n");
1437: PetscViewerASCIIPrintf(viewer," <PointData>\n");
1438: PetscViewerASCIIPrintf(viewer," <DataArray type=\"Float32\" Name=\"velocity\" NumberOfComponents=\"3\" format=\"ascii\">\n");
1439: for (i=0; i<nn; i+=dof) {
1440: PetscViewerASCIIPrintf(viewer,"%f %f %f\n",(double)(PetscRealPart(ptr[i])*units->year/units->meter),(double)(PetscRealPart(ptr[i+1])*units->year/units->meter),0.0);
1441: }
1442: PetscViewerASCIIPrintf(viewer," </DataArray>\n");
1444: PetscViewerASCIIPrintf(viewer," <DataArray type=\"Int32\" Name=\"rank\" NumberOfComponents=\"1\" format=\"ascii\">\n");
1445: for (i=0; i<nn; i+=dof) {
1446: PetscViewerASCIIPrintf(viewer,"%D\n",r);
1447: }
1448: PetscViewerASCIIPrintf(viewer," </DataArray>\n");
1449: PetscViewerASCIIPrintf(viewer," </PointData>\n");
1451: PetscViewerASCIIPrintf(viewer," </Piece>\n");
1452: }
1453: PetscFree(array);
1454: } else {
1455: MPI_Send(range,6,MPIU_INT,0,tag,comm);
1456: MPI_Send((PetscScalar*)x,nn,MPIU_SCALAR,0,tag,comm);
1457: }
1458: VecRestoreArrayRead(X,&x);
1459: PetscViewerASCIIPrintf(viewer," </StructuredGrid>\n");
1460: PetscViewerASCIIPrintf(viewer,"</VTKFile>\n");
1461: PetscViewerDestroy(&viewer);
1462: return(0);
1463: }
1465: int main(int argc,char *argv[])
1466: {
1467: MPI_Comm comm;
1468: THI thi;
1470: DM da;
1471: SNES snes;
1473: PetscInitialize(&argc,&argv,0,help);if (ierr) return ierr;
1474: comm = PETSC_COMM_WORLD;
1476: THICreate(comm,&thi);
1477: {
1478: PetscInt M = 3,N = 3,P = 2;
1479: PetscOptionsBegin(comm,NULL,"Grid resolution options","");
1480: {
1481: PetscOptionsInt("-M","Number of elements in x-direction on coarse level","",M,&M,NULL);
1482: N = M;
1483: PetscOptionsInt("-N","Number of elements in y-direction on coarse level (if different from M)","",N,&N,NULL);
1484: if (thi->coarse2d) {
1485: PetscOptionsInt("-zlevels","Number of elements in z-direction on fine level","",thi->zlevels,&thi->zlevels,NULL);
1486: } else {
1487: PetscOptionsInt("-P","Number of elements in z-direction on coarse level","",P,&P,NULL);
1488: }
1489: }
1490: PetscOptionsEnd();
1491: if (thi->coarse2d) {
1492: DMDACreate2d(comm,DM_BOUNDARY_PERIODIC,DM_BOUNDARY_PERIODIC,DMDA_STENCIL_BOX,N,M,PETSC_DETERMINE,PETSC_DETERMINE,sizeof(Node)/sizeof(PetscScalar),1,0,0,&da);
1493: DMSetFromOptions(da);
1494: DMSetUp(da);
1495: da->ops->refinehierarchy = DMRefineHierarchy_THI;
1496: da->ops->createinterpolation = DMCreateInterpolation_DA_THI;
1498: PetscObjectCompose((PetscObject)da,"THI",(PetscObject)thi);
1499: } else {
1500: 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);
1501: DMSetFromOptions(da);
1502: DMSetUp(da);
1503: }
1504: DMDASetFieldName(da,0,"x-velocity");
1505: DMDASetFieldName(da,1,"y-velocity");
1506: }
1507: THISetUpDM(thi,da);
1508: if (thi->tridiagonal) da->ops->creatematrix = DMCreateMatrix_THI_Tridiagonal;
1510: { /* Set the fine level matrix type if -da_refine */
1511: PetscInt rlevel,clevel;
1512: DMGetRefineLevel(da,&rlevel);
1513: DMGetCoarsenLevel(da,&clevel);
1514: if (rlevel - clevel > 0) {DMSetMatType(da,thi->mattype);}
1515: }
1517: DMDASNESSetFunctionLocal(da,ADD_VALUES,(DMDASNESFunction)THIFunctionLocal,thi);
1518: if (thi->tridiagonal) {
1519: DMDASNESSetJacobianLocal(da,(DMDASNESJacobian)THIJacobianLocal_3D_Tridiagonal,thi);
1520: } else {
1521: DMDASNESSetJacobianLocal(da,(DMDASNESJacobian)THIJacobianLocal_3D_Full,thi);
1522: }
1523: DMCoarsenHookAdd(da,DMCoarsenHook_THI,NULL,thi);
1524: DMRefineHookAdd(da,DMRefineHook_THI,NULL,thi);
1526: DMSetApplicationContext(da,thi);
1528: SNESCreate(comm,&snes);
1529: SNESSetDM(snes,da);
1530: DMDestroy(&da);
1531: SNESSetComputeInitialGuess(snes,THIInitial,NULL);
1532: SNESSetFromOptions(snes);
1534: SNESSolve(snes,NULL,NULL);
1536: THISolveStatistics(thi,snes,0,"Full");
1538: {
1539: PetscBool flg;
1540: char filename[PETSC_MAX_PATH_LEN] = "";
1541: PetscOptionsGetString(NULL,NULL,"-o",filename,sizeof(filename),&flg);
1542: if (flg) {
1543: Vec X;
1544: DM dm;
1545: SNESGetSolution(snes,&X);
1546: SNESGetDM(snes,&dm);
1547: THIDAVecView_VTK_XML(thi,dm,X,filename);
1548: }
1549: }
1551: DMDestroy(&da);
1552: SNESDestroy(&snes);
1553: THIDestroy(&thi);
1554: PetscFinalize();
1555: return ierr;
1556: }
1558: /*TEST
1560: build:
1561: requires: !single
1563: test:
1564: args: -M 6 -P 4 -da_refine 1 -snes_monitor_short -snes_converged_reason -ksp_monitor_short -ksp_converged_reason -thi_mat_type sbaij -ksp_type fgmres -pc_type mg -pc_mg_type full -mg_levels_ksp_type gmres -mg_levels_ksp_max_it 1 -mg_levels_pc_type icc
1566: test:
1567: suffix: 2
1568: nsize: 2
1569: args: -M 6 -P 4 -thi_hom z -snes_monitor_short -snes_converged_reason -ksp_monitor_short -ksp_converged_reason -thi_mat_type sbaij -ksp_type fgmres -pc_type mg -pc_mg_type full -mg_levels_ksp_type gmres -mg_levels_ksp_max_it 1 -mg_levels_pc_type asm -mg_levels_pc_asm_blocks 6 -mg_levels_0_pc_type redundant -snes_grid_sequence 1 -mat_partitioning_type current -ksp_atol -1
1571: test:
1572: suffix: 3
1573: nsize: 3
1574: args: -M 7 -P 4 -thi_hom z -da_refine 1 -snes_monitor_short -snes_converged_reason -ksp_monitor_short -ksp_converged_reason -thi_mat_type baij -ksp_type fgmres -pc_type mg -pc_mg_type full -mg_levels_pc_asm_type restrict -mg_levels_pc_type asm -mg_levels_pc_asm_blocks 9 -mg_levels_ksp_type gmres -mg_levels_ksp_max_it 1 -mat_partitioning_type current
1576: test:
1577: suffix: 4
1578: nsize: 6
1579: args: -M 4 -P 2 -da_refine_hierarchy_x 1,1,3 -da_refine_hierarchy_y 2,2,1 -da_refine_hierarchy_z 2,2,1 -snes_grid_sequence 3 -ksp_converged_reason -ksp_type fgmres -ksp_rtol 1e-2 -pc_type mg -mg_levels_ksp_type gmres -mg_levels_ksp_max_it 1 -mg_levels_pc_type bjacobi -mg_levels_1_sub_pc_type cholesky -pc_mg_type multiplicative -snes_converged_reason -snes_stol 1e-12 -thi_L 80e3 -thi_alpha 0.05 -thi_friction_m 1 -thi_hom x -snes_view -mg_levels_0_pc_type redundant -mg_levels_0_ksp_type preonly -ksp_atol -1
1581: test:
1582: suffix: 5
1583: nsize: 6
1584: args: -M 12 -P 5 -snes_monitor_short -ksp_converged_reason -pc_type asm -pc_asm_type restrict -dm_mat_type {{aij baij sbaij}}
1586: TEST*/