Actual source code: ex48.c
petsc-dev 2014-02-02
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: #include <petscsnes.h>
59: #include <ctype.h> /* toupper() */
60: #include <petsc-private/dmdaimpl.h> /* There is not yet a public interface to manipulate dm->ops */
62: #if !defined __STDC_VERSION__ || __STDC_VERSION__ < 199901L
63: # if defined __cplusplus /* C++ restrict is nonstandard and compilers have inconsistent rules about where it can be used */
64: # define restrict
65: # else
66: # define restrict PETSC_RESTRICT
67: # endif
68: #endif
69: #if defined __SSE2__
70: # include <emmintrin.h>
71: #endif
73: /* The SSE2 kernels are only for PetscScalar=double on architectures that support it */
74: #define USE_SSE2_KERNELS (!defined NO_SSE2 \
75: && !defined PETSC_USE_COMPLEX \
76: && !defined PETSC_USE_REAL_SINGLE \
77: && !defined PETSC_USE_REAL___FLOAT128 \
78: && defined __SSE2__)
80: static PetscClassId THI_CLASSID;
82: typedef enum {QUAD_GAUSS,QUAD_LOBATTO} QuadratureType;
83: static const char *QuadratureTypes[] = {"gauss","lobatto","QuadratureType","QUAD_",0};
84: static const PetscReal HexQWeights[8] = {1,1,1,1,1,1,1,1};
85: static const PetscReal HexQNodes[] = {-0.57735026918962573, 0.57735026918962573};
86: #define G 0.57735026918962573
87: #define H (0.5*(1.+G))
88: #define L (0.5*(1.-G))
89: #define M (-0.5)
90: #define P (0.5)
91: /* Special quadrature: Lobatto in horizontal, Gauss in vertical */
92: static const PetscReal HexQInterp_Lobatto[8][8] = {{H,0,0,0,L,0,0,0},
93: {0,H,0,0,0,L,0,0},
94: {0,0,H,0,0,0,L,0},
95: {0,0,0,H,0,0,0,L},
96: {L,0,0,0,H,0,0,0},
97: {0,L,0,0,0,H,0,0},
98: {0,0,L,0,0,0,H,0},
99: {0,0,0,L,0,0,0,H}};
100: static const PetscReal HexQDeriv_Lobatto[8][8][3] = {
101: {{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} },
102: {{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} },
103: {{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} },
104: {{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}},
105: {{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} },
106: {{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} },
107: {{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} },
108: {{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}}};
109: /* Stanndard Gauss */
110: 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},
111: {L*H*H,H*H*H,H*L*H,L*L*H, L*H*L,H*H*L,H*L*L,L*L*L},
112: {L*L*H,H*L*H,H*H*H,L*H*H, L*L*L,H*L*L,H*H*L,L*H*L},
113: {H*L*H,L*L*H,L*H*H,H*H*H, H*L*L,L*L*L,L*H*L,H*H*L},
114: {H*H*L,L*H*L,L*L*L,H*L*L, H*H*H,L*H*H,L*L*H,H*L*H},
115: {L*H*L,H*H*L,H*L*L,L*L*L, L*H*H,H*H*H,H*L*H,L*L*H},
116: {L*L*L,H*L*L,H*H*L,L*H*L, L*L*H,H*L*H,H*H*H,L*H*H},
117: {H*L*L,L*L*L,L*H*L,H*H*L, H*L*H,L*L*H,L*H*H,H*H*H}};
118: static const PetscReal HexQDeriv_Gauss[8][8][3] = {
119: {{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}},
120: {{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}},
121: {{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}},
122: {{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}},
123: {{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}},
124: {{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}},
125: {{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}},
126: {{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}}};
127: static const PetscReal (*HexQInterp)[8],(*HexQDeriv)[8][3];
128: /* Standard 2x2 Gauss quadrature for the bottom layer. */
129: static const PetscReal QuadQInterp[4][4] = {{H*H,L*H,L*L,H*L},
130: {L*H,H*H,H*L,L*L},
131: {L*L,H*L,H*H,L*H},
132: {H*L,L*L,L*H,H*H}};
133: static const PetscReal QuadQDeriv[4][4][2] = {
134: {{M*H,M*H},{P*H,M*L},{P*L,P*L},{M*L,P*H}},
135: {{M*H,M*L},{P*H,M*H},{P*L,P*H},{M*L,P*L}},
136: {{M*L,M*L},{P*L,M*H},{P*H,P*H},{M*H,P*L}},
137: {{M*L,M*H},{P*L,M*L},{P*H,P*L},{M*H,P*H}}};
138: #undef G
139: #undef H
140: #undef L
141: #undef M
142: #undef P
144: #define HexExtract(x,i,j,k,n) do { \
145: (n)[0] = (x)[i][j][k]; \
146: (n)[1] = (x)[i+1][j][k]; \
147: (n)[2] = (x)[i+1][j+1][k]; \
148: (n)[3] = (x)[i][j+1][k]; \
149: (n)[4] = (x)[i][j][k+1]; \
150: (n)[5] = (x)[i+1][j][k+1]; \
151: (n)[6] = (x)[i+1][j+1][k+1]; \
152: (n)[7] = (x)[i][j+1][k+1]; \
153: } while (0)
155: #define HexExtractRef(x,i,j,k,n) do { \
156: (n)[0] = &(x)[i][j][k]; \
157: (n)[1] = &(x)[i+1][j][k]; \
158: (n)[2] = &(x)[i+1][j+1][k]; \
159: (n)[3] = &(x)[i][j+1][k]; \
160: (n)[4] = &(x)[i][j][k+1]; \
161: (n)[5] = &(x)[i+1][j][k+1]; \
162: (n)[6] = &(x)[i+1][j+1][k+1]; \
163: (n)[7] = &(x)[i][j+1][k+1]; \
164: } while (0)
166: #define QuadExtract(x,i,j,n) do { \
167: (n)[0] = (x)[i][j]; \
168: (n)[1] = (x)[i+1][j]; \
169: (n)[2] = (x)[i+1][j+1]; \
170: (n)[3] = (x)[i][j+1]; \
171: } while (0)
173: static PetscScalar Sqr(PetscScalar a) {return a*a;}
175: static void HexGrad(const PetscReal dphi[][3],const PetscReal zn[],PetscReal dz[])
176: {
177: PetscInt i;
178: dz[0] = dz[1] = dz[2] = 0;
179: for (i=0; i<8; i++) {
180: dz[0] += dphi[i][0] * zn[i];
181: dz[1] += dphi[i][1] * zn[i];
182: dz[2] += dphi[i][2] * zn[i];
183: }
184: }
186: static void HexComputeGeometry(PetscInt q,PetscReal hx,PetscReal hy,const PetscReal dz[restrict],PetscReal phi[restrict],PetscReal dphi[restrict][3],PetscReal *restrict jw)
187: {
188: const PetscReal jac[3][3] = {{hx/2,0,0}, {0,hy/2,0}, {dz[0],dz[1],dz[2]}};
189: 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]}};
190: const PetscReal jdet = jac[0][0]*jac[1][1]*jac[2][2];
191: PetscInt i;
193: for (i=0; i<8; i++) {
194: const PetscReal *dphir = HexQDeriv[q][i];
195: phi[i] = HexQInterp[q][i];
196: dphi[i][0] = dphir[0]*ijac[0][0] + dphir[1]*ijac[1][0] + dphir[2]*ijac[2][0];
197: dphi[i][1] = dphir[0]*ijac[0][1] + dphir[1]*ijac[1][1] + dphir[2]*ijac[2][1];
198: dphi[i][2] = dphir[0]*ijac[0][2] + dphir[1]*ijac[1][2] + dphir[2]*ijac[2][2];
199: }
200: *jw = 1.0 * jdet;
201: }
203: typedef struct _p_THI *THI;
204: typedef struct _n_Units *Units;
206: typedef struct {
207: PetscScalar u,v;
208: } Node;
210: typedef struct {
211: PetscScalar b; /* bed */
212: PetscScalar h; /* thickness */
213: PetscScalar beta2; /* friction */
214: } PrmNode;
216: typedef struct {
217: PetscReal min,max,cmin,cmax;
218: } PRange;
220: typedef enum {THIASSEMBLY_TRIDIAGONAL,THIASSEMBLY_FULL} THIAssemblyMode;
222: struct _p_THI {
223: PETSCHEADER(int);
224: void (*initialize)(THI,PetscReal x,PetscReal y,PrmNode *p);
225: PetscInt zlevels;
226: PetscReal Lx,Ly,Lz; /* Model domain */
227: PetscReal alpha; /* Bed angle */
228: Units units;
229: PetscReal dirichlet_scale;
230: PetscReal ssa_friction_scale;
231: PRange eta;
232: PRange beta2;
233: struct {
234: PetscReal Bd2,eps,exponent;
235: } viscosity;
236: struct {
237: PetscReal irefgam,eps2,exponent,refvel,epsvel;
238: } friction;
239: PetscReal rhog;
240: PetscBool no_slip;
241: PetscBool tridiagonal;
242: PetscBool coarse2d;
243: PetscBool verbose;
244: MatType mattype;
245: };
247: struct _n_Units {
248: /* fundamental */
249: PetscReal meter;
250: PetscReal kilogram;
251: PetscReal second;
252: /* derived */
253: PetscReal Pascal;
254: PetscReal year;
255: };
257: static PetscErrorCode THIJacobianLocal_3D_Full(DMDALocalInfo*,Node***,Mat,Mat,MatStructure*,THI);
258: static PetscErrorCode THIJacobianLocal_3D_Tridiagonal(DMDALocalInfo*,Node***,Mat,THI);
259: static PetscErrorCode THIJacobianLocal_2D(DMDALocalInfo*,Node**,Mat,THI);
261: static void PrmHexGetZ(const PrmNode pn[],PetscInt k,PetscInt zm,PetscReal zn[])
262: {
263: const PetscScalar zm1 = zm-1,
264: znl[8] = {pn[0].b + pn[0].h*(PetscScalar)k/zm1,
265: pn[1].b + pn[1].h*(PetscScalar)k/zm1,
266: pn[2].b + pn[2].h*(PetscScalar)k/zm1,
267: pn[3].b + pn[3].h*(PetscScalar)k/zm1,
268: pn[0].b + pn[0].h*(PetscScalar)(k+1)/zm1,
269: pn[1].b + pn[1].h*(PetscScalar)(k+1)/zm1,
270: pn[2].b + pn[2].h*(PetscScalar)(k+1)/zm1,
271: pn[3].b + pn[3].h*(PetscScalar)(k+1)/zm1};
272: PetscInt i;
273: for (i=0; i<8; i++) zn[i] = PetscRealPart(znl[i]);
274: }
276: /* Tests A and C are from the ISMIP-HOM paper (Pattyn et al. 2008) */
277: static void THIInitialize_HOM_A(THI thi,PetscReal x,PetscReal y,PrmNode *p)
278: {
279: Units units = thi->units;
280: PetscReal s = -x*PetscSinReal(thi->alpha);
282: p->b = s - 1000*units->meter + 500*units->meter * PetscSinReal(x*2*PETSC_PI/thi->Lx) * PetscSinReal(y*2*PETSC_PI/thi->Ly);
283: p->h = s - p->b;
284: p->beta2 = 1e30;
285: }
287: static void THIInitialize_HOM_C(THI thi,PetscReal x,PetscReal y,PrmNode *p)
288: {
289: Units units = thi->units;
290: PetscReal s = -x*PetscSinReal(thi->alpha);
292: p->b = s - 1000*units->meter;
293: p->h = s - p->b;
294: /* tau_b = beta2 v is a stress (Pa) */
295: p->beta2 = 1000 * (1 + PetscSinReal(x*2*PETSC_PI/thi->Lx)*PetscSinReal(y*2*PETSC_PI/thi->Ly)) * units->Pascal * units->year / units->meter;
296: }
298: /* These are just toys */
300: /* Same bed as test A, free slip everywhere except for a discontinuous jump to a circular sticky region in the middle. */
301: static void THIInitialize_HOM_X(THI thi,PetscReal xx,PetscReal yy,PrmNode *p)
302: {
303: Units units = thi->units;
304: PetscReal x = xx*2*PETSC_PI/thi->Lx - PETSC_PI,y = yy*2*PETSC_PI/thi->Ly - PETSC_PI; /* [-pi,pi] */
305: PetscReal r = PetscSqrtReal(x*x + y*y),s = -x*PetscSinReal(thi->alpha);
306: p->b = s - 1000*units->meter + 500*units->meter*PetscSinReal(x + PETSC_PI) * PetscSinReal(y + PETSC_PI);
307: p->h = s - p->b;
308: p->beta2 = 1000 * (r < 1 ? 2 : 0) * units->Pascal * units->year / units->meter;
309: }
311: /* Like Z, but with 200 meter cliffs */
312: static void THIInitialize_HOM_Y(THI thi,PetscReal xx,PetscReal yy,PrmNode *p)
313: {
314: Units units = thi->units;
315: PetscReal x = xx*2*PETSC_PI/thi->Lx - PETSC_PI,y = yy*2*PETSC_PI/thi->Ly - PETSC_PI; /* [-pi,pi] */
316: PetscReal r = PetscSqrtReal(x*x + y*y),s = -x*PetscSinReal(thi->alpha);
318: p->b = s - 1000*units->meter + 500*units->meter * PetscSinReal(x + PETSC_PI) * PetscSinReal(y + PETSC_PI);
319: if (PetscRealPart(p->b) > -700*units->meter) p->b += 200*units->meter;
320: p->h = s - p->b;
321: 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;
322: }
324: /* Same bed as A, smoothly varying slipperiness, similar to MATLAB's "sombrero" (uncorrelated with bathymetry) */
325: static void THIInitialize_HOM_Z(THI thi,PetscReal xx,PetscReal yy,PrmNode *p)
326: {
327: Units units = thi->units;
328: PetscReal x = xx*2*PETSC_PI/thi->Lx - PETSC_PI,y = yy*2*PETSC_PI/thi->Ly - PETSC_PI; /* [-pi,pi] */
329: PetscReal r = PetscSqrtReal(x*x + y*y),s = -x*PetscSinReal(thi->alpha);
331: p->b = s - 1000*units->meter + 500*units->meter * PetscSinReal(x + PETSC_PI) * PetscSinReal(y + PETSC_PI);
332: p->h = s - p->b;
333: 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;
334: }
336: static void THIFriction(THI thi,PetscReal rbeta2,PetscReal gam,PetscReal *beta2,PetscReal *dbeta2)
337: {
338: if (thi->friction.irefgam == 0) {
339: Units units = thi->units;
340: thi->friction.irefgam = 1./(0.5*PetscSqr(thi->friction.refvel * units->meter / units->year));
341: thi->friction.eps2 = 0.5*PetscSqr(thi->friction.epsvel * units->meter / units->year) * thi->friction.irefgam;
342: }
343: if (thi->friction.exponent == 0) {
344: *beta2 = rbeta2;
345: *dbeta2 = 0;
346: } else {
347: *beta2 = rbeta2 * PetscPowReal(thi->friction.eps2 + gam*thi->friction.irefgam,thi->friction.exponent);
348: *dbeta2 = thi->friction.exponent * *beta2 / (thi->friction.eps2 + gam*thi->friction.irefgam) * thi->friction.irefgam;
349: }
350: }
352: static void THIViscosity(THI thi,PetscReal gam,PetscReal *eta,PetscReal *deta)
353: {
354: PetscReal Bd2,eps,exponent;
355: if (thi->viscosity.Bd2 == 0) {
356: Units units = thi->units;
357: const PetscReal
358: n = 3., /* Glen exponent */
359: p = 1. + 1./n, /* for Stokes */
360: A = 1.e-16 * PetscPowReal(units->Pascal,-n) / units->year, /* softness parameter (Pa^{-n}/s) */
361: B = PetscPowReal(A,-1./n); /* hardness parameter */
362: thi->viscosity.Bd2 = B/2;
363: thi->viscosity.exponent = (p-2)/2;
364: thi->viscosity.eps = 0.5*PetscSqr(1e-5 / units->year);
365: }
366: Bd2 = thi->viscosity.Bd2;
367: exponent = thi->viscosity.exponent;
368: eps = thi->viscosity.eps;
369: *eta = Bd2 * PetscPowReal(eps + gam,exponent);
370: *deta = exponent * (*eta) / (eps + gam);
371: }
373: static void RangeUpdate(PetscReal *min,PetscReal *max,PetscReal x)
374: {
375: if (x < *min) *min = x;
376: if (x > *max) *max = x;
377: }
379: static void PRangeClear(PRange *p)
380: {
381: p->cmin = p->min = 1e100;
382: p->cmax = p->max = -1e100;
383: }
387: static PetscErrorCode PRangeMinMax(PRange *p,PetscReal min,PetscReal max)
388: {
391: p->cmin = min;
392: p->cmax = max;
393: if (min < p->min) p->min = min;
394: if (max > p->max) p->max = max;
395: return(0);
396: }
400: static PetscErrorCode THIDestroy(THI *thi)
401: {
405: if (!*thi) return(0);
406: if (--((PetscObject)(*thi))->refct > 0) {*thi = 0; return(0);}
407: PetscFree((*thi)->units);
408: PetscFree((*thi)->mattype);
409: PetscHeaderDestroy(thi);
410: return(0);
411: }
415: static PetscErrorCode THICreate(MPI_Comm comm,THI *inthi)
416: {
417: static PetscBool registered = PETSC_FALSE;
418: THI thi;
419: Units units;
420: PetscErrorCode ierr;
423: *inthi = 0;
424: if (!registered) {
425: PetscClassIdRegister("Toy Hydrostatic Ice",&THI_CLASSID);
426: registered = PETSC_TRUE;
427: }
428: PetscHeaderCreate(thi,_p_THI,0,THI_CLASSID,"THI","Toy Hydrostatic Ice","",comm,THIDestroy,0);
430: PetscNew(&thi->units);
431: units = thi->units;
432: units->meter = 1e-2;
433: units->second = 1e-7;
434: units->kilogram = 1e-12;
436: PetscOptionsBegin(comm,NULL,"Scaled units options","");
437: {
438: PetscOptionsReal("-units_meter","1 meter in scaled length units","",units->meter,&units->meter,NULL);
439: PetscOptionsReal("-units_second","1 second in scaled time units","",units->second,&units->second,NULL);
440: PetscOptionsReal("-units_kilogram","1 kilogram in scaled mass units","",units->kilogram,&units->kilogram,NULL);
441: }
442: PetscOptionsEnd();
443: units->Pascal = units->kilogram / (units->meter * PetscSqr(units->second));
444: units->year = 31556926. * units->second, /* seconds per year */
446: thi->Lx = 10.e3;
447: thi->Ly = 10.e3;
448: thi->Lz = 1000;
449: thi->dirichlet_scale = 1;
450: thi->verbose = PETSC_FALSE;
452: PetscOptionsBegin(comm,NULL,"Toy Hydrostatic Ice options","");
453: {
454: QuadratureType quad = QUAD_GAUSS;
455: char homexp[] = "A";
456: char mtype[256] = MATSBAIJ;
457: PetscReal L,m = 1.0;
458: PetscBool flg;
459: L = thi->Lx;
460: PetscOptionsReal("-thi_L","Domain size (m)","",L,&L,&flg);
461: if (flg) thi->Lx = thi->Ly = L;
462: PetscOptionsReal("-thi_Lx","X Domain size (m)","",thi->Lx,&thi->Lx,NULL);
463: PetscOptionsReal("-thi_Ly","Y Domain size (m)","",thi->Ly,&thi->Ly,NULL);
464: PetscOptionsReal("-thi_Lz","Z Domain size (m)","",thi->Lz,&thi->Lz,NULL);
465: PetscOptionsString("-thi_hom","ISMIP-HOM experiment (A or C)","",homexp,homexp,sizeof(homexp),NULL);
466: switch (homexp[0] = toupper(homexp[0])) {
467: case 'A':
468: thi->initialize = THIInitialize_HOM_A;
469: thi->no_slip = PETSC_TRUE;
470: thi->alpha = 0.5;
471: break;
472: case 'C':
473: thi->initialize = THIInitialize_HOM_C;
474: thi->no_slip = PETSC_FALSE;
475: thi->alpha = 0.1;
476: break;
477: case 'X':
478: thi->initialize = THIInitialize_HOM_X;
479: thi->no_slip = PETSC_FALSE;
480: thi->alpha = 0.3;
481: break;
482: case 'Y':
483: thi->initialize = THIInitialize_HOM_Y;
484: thi->no_slip = PETSC_FALSE;
485: thi->alpha = 0.5;
486: break;
487: case 'Z':
488: thi->initialize = THIInitialize_HOM_Z;
489: thi->no_slip = PETSC_FALSE;
490: thi->alpha = 0.5;
491: break;
492: default:
493: SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"HOM experiment '%c' not implemented",homexp[0]);
494: }
495: PetscOptionsEnum("-thi_quadrature","Quadrature to use for 3D elements","",QuadratureTypes,(PetscEnum)quad,(PetscEnum*)&quad,NULL);
496: switch (quad) {
497: case QUAD_GAUSS:
498: HexQInterp = HexQInterp_Gauss;
499: HexQDeriv = HexQDeriv_Gauss;
500: break;
501: case QUAD_LOBATTO:
502: HexQInterp = HexQInterp_Lobatto;
503: HexQDeriv = HexQDeriv_Lobatto;
504: break;
505: }
506: PetscOptionsReal("-thi_alpha","Bed angle (degrees)","",thi->alpha,&thi->alpha,NULL);
508: thi->friction.refvel = 100.;
509: thi->friction.epsvel = 1.;
511: PetscOptionsReal("-thi_friction_refvel","Reference velocity for sliding","",thi->friction.refvel,&thi->friction.refvel,NULL);
512: PetscOptionsReal("-thi_friction_epsvel","Regularization velocity for sliding","",thi->friction.epsvel,&thi->friction.epsvel,NULL);
513: PetscOptionsReal("-thi_friction_m","Friction exponent, 0=Coulomb, 1=Navier","",m,&m,NULL);
515: thi->friction.exponent = (m-1)/2;
517: PetscOptionsReal("-thi_dirichlet_scale","Scale Dirichlet boundary conditions by this factor","",thi->dirichlet_scale,&thi->dirichlet_scale,NULL);
518: 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);
519: PetscOptionsBool("-thi_coarse2d","Use a 2D coarse space corresponding to SSA","",thi->coarse2d,&thi->coarse2d,NULL);
520: PetscOptionsBool("-thi_tridiagonal","Assemble a tridiagonal system (column coupling only) on the finest level","",thi->tridiagonal,&thi->tridiagonal,NULL);
521: PetscOptionsFList("-thi_mat_type","Matrix type","MatSetType",MatList,mtype,(char*)mtype,sizeof(mtype),NULL);
522: PetscStrallocpy(mtype,(char**)&thi->mattype);
523: PetscOptionsBool("-thi_verbose","Enable verbose output (like matrix sizes and statistics)","",thi->verbose,&thi->verbose,NULL);
524: }
525: PetscOptionsEnd();
527: /* dimensionalize */
528: thi->Lx *= units->meter;
529: thi->Ly *= units->meter;
530: thi->Lz *= units->meter;
531: thi->alpha *= PETSC_PI / 180;
533: PRangeClear(&thi->eta);
534: PRangeClear(&thi->beta2);
536: {
537: PetscReal u = 1000*units->meter/(3e7*units->second),
538: gradu = u / (100*units->meter),eta,deta,
539: rho = 910 * units->kilogram/PetscPowReal(units->meter,3),
540: grav = 9.81 * units->meter/PetscSqr(units->second),
541: driving = rho * grav * PetscSinReal(thi->alpha) * 1000*units->meter;
542: THIViscosity(thi,0.5*gradu*gradu,&eta,&deta);
543: thi->rhog = rho * grav;
544: if (thi->verbose) {
545: 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);
546: 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);
547: 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));
548: THIViscosity(thi,0.5*PetscSqr(1e-3*gradu),&eta,&deta);
549: 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));
550: }
551: }
553: *inthi = thi;
554: return(0);
555: }
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: }
581: static PetscErrorCode THISetUpDM(THI thi,DM dm)
582: {
583: PetscErrorCode ierr;
584: PetscInt refinelevel,coarsenlevel,level,dim,Mx,My,Mz,mx,my,s;
585: DMDAStencilType st;
586: DM da2prm;
587: Vec X;
590: DMDAGetInfo(dm,&dim, &Mz,&My,&Mx, 0,&my,&mx, 0,&s,0,0,0,&st);
591: if (dim == 2) {
592: DMDAGetInfo(dm,&dim, &My,&Mx,0, &my,&mx,0, 0,&s,0,0,0,&st);
593: }
594: DMGetRefineLevel(dm,&refinelevel);
595: DMGetCoarsenLevel(dm,&coarsenlevel);
596: level = refinelevel - coarsenlevel;
597: DMDACreate2d(PetscObjectComm((PetscObject)thi),DMDA_BOUNDARY_PERIODIC,DMDA_BOUNDARY_PERIODIC,st,My,Mx,my,mx,sizeof(PrmNode)/sizeof(PetscScalar),s,0,0,&da2prm);
598: DMCreateLocalVector(da2prm,&X);
599: {
600: PetscReal Lx = thi->Lx / thi->units->meter,Ly = thi->Ly / thi->units->meter,Lz = thi->Lz / thi->units->meter;
601: if (dim == 2) {
602: 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));
603: } else {
604: 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)));
605: }
606: }
607: THIInitializePrm(thi,da2prm,X);
608: if (thi->tridiagonal) { /* Reset coarse Jacobian evaluation */
609: DMDASNESSetJacobianLocal(dm,(DMDASNESJacobian)THIJacobianLocal_3D_Full,thi);
610: }
611: if (thi->coarse2d) {
612: DMDASNESSetJacobianLocal(dm,(DMDASNESJacobian)THIJacobianLocal_2D,thi);
613: }
614: PetscObjectCompose((PetscObject)dm,"DMDA2Prm",(PetscObject)da2prm);
615: PetscObjectCompose((PetscObject)dm,"DMDA2Prm_Vec",(PetscObject)X);
616: DMDestroy(&da2prm);
617: VecDestroy(&X);
618: return(0);
619: }
623: static PetscErrorCode DMCoarsenHook_THI(DM dmf,DM dmc,void *ctx)
624: {
625: THI thi = (THI)ctx;
627: PetscInt rlevel,clevel;
630: THISetUpDM(thi,dmc);
631: DMGetRefineLevel(dmc,&rlevel);
632: DMGetCoarsenLevel(dmc,&clevel);
633: if (rlevel-clevel == 0) {DMSetMatType(dmc,MATAIJ);}
634: DMCoarsenHookAdd(dmc,DMCoarsenHook_THI,NULL,thi);
635: return(0);
636: }
640: static PetscErrorCode DMRefineHook_THI(DM dmc,DM dmf,void *ctx)
641: {
642: THI thi = (THI)ctx;
646: THISetUpDM(thi,dmf);
647: DMSetMatType(dmf,thi->mattype);
648: DMRefineHookAdd(dmf,DMRefineHook_THI,NULL,thi);
649: /* With grid sequencing, a formerly-refined DM will later be coarsened by PCSetUp_MG */
650: DMCoarsenHookAdd(dmf,DMCoarsenHook_THI,NULL,thi);
651: return(0);
652: }
656: static PetscErrorCode THIDAGetPrm(DM da,PrmNode ***prm)
657: {
659: DM da2prm;
660: Vec X;
663: PetscObjectQuery((PetscObject)da,"DMDA2Prm",(PetscObject*)&da2prm);
664: if (!da2prm) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"No DMDA2Prm composed with given DMDA");
665: PetscObjectQuery((PetscObject)da,"DMDA2Prm_Vec",(PetscObject*)&X);
666: if (!X) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"No DMDA2Prm_Vec composed with given DMDA");
667: DMDAVecGetArray(da2prm,X,prm);
668: return(0);
669: }
673: static PetscErrorCode THIDARestorePrm(DM da,PrmNode ***prm)
674: {
676: DM da2prm;
677: Vec X;
680: PetscObjectQuery((PetscObject)da,"DMDA2Prm",(PetscObject*)&da2prm);
681: if (!da2prm) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"No DMDA2Prm composed with given DMDA");
682: PetscObjectQuery((PetscObject)da,"DMDA2Prm_Vec",(PetscObject*)&X);
683: if (!X) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"No DMDA2Prm_Vec composed with given DMDA");
684: DMDAVecRestoreArray(da2prm,X,prm);
685: return(0);
686: }
690: static PetscErrorCode THIInitial(SNES snes,Vec X,void *ctx)
691: {
692: THI thi;
693: PetscInt i,j,k,xs,xm,ys,ym,zs,zm,mx,my;
694: PetscReal hx,hy;
695: PrmNode **prm;
696: Node ***x;
698: DM da;
701: SNESGetDM(snes,&da);
702: DMGetApplicationContext(da,&thi);
703: DMDAGetInfo(da,0, 0,&my,&mx, 0,0,0, 0,0,0,0,0,0);
704: DMDAGetCorners(da,&zs,&ys,&xs,&zm,&ym,&xm);
705: DMDAVecGetArray(da,X,&x);
706: THIDAGetPrm(da,&prm);
707: hx = thi->Lx / mx;
708: hy = thi->Ly / my;
709: for (i=xs; i<xs+xm; i++) {
710: for (j=ys; j<ys+ym; j++) {
711: for (k=zs; k<zs+zm; k++) {
712: const PetscScalar zm1 = zm-1,
713: 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),
714: 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);
715: x[i][j][k].u = 0. * drivingx * prm[i][j].h*(PetscScalar)k/zm1;
716: x[i][j][k].v = 0. * drivingy * prm[i][j].h*(PetscScalar)k/zm1;
717: }
718: }
719: }
720: DMDAVecRestoreArray(da,X,&x);
721: THIDARestorePrm(da,&prm);
722: return(0);
723: }
725: static void PointwiseNonlinearity(THI thi,const Node n[restrict],const PetscReal phi[restrict],PetscReal dphi[restrict][3],PetscScalar *restrict u,PetscScalar *restrict v,PetscScalar du[restrict],PetscScalar dv[restrict],PetscReal *eta,PetscReal *deta)
726: {
727: PetscInt l,ll;
728: PetscScalar gam;
730: du[0] = du[1] = du[2] = 0;
731: dv[0] = dv[1] = dv[2] = 0;
732: *u = 0;
733: *v = 0;
734: for (l=0; l<8; l++) {
735: *u += phi[l] * n[l].u;
736: *v += phi[l] * n[l].v;
737: for (ll=0; ll<3; ll++) {
738: du[ll] += dphi[l][ll] * n[l].u;
739: dv[ll] += dphi[l][ll] * n[l].v;
740: }
741: }
742: 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]);
743: THIViscosity(thi,PetscRealPart(gam),eta,deta);
744: }
746: 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)
747: {
748: PetscInt l,ll;
749: PetscScalar gam;
751: du[0] = du[1] = 0;
752: dv[0] = dv[1] = 0;
753: *u = 0;
754: *v = 0;
755: for (l=0; l<4; l++) {
756: *u += phi[l] * n[l].u;
757: *v += phi[l] * n[l].v;
758: for (ll=0; ll<2; ll++) {
759: du[ll] += dphi[l][ll] * n[l].u;
760: dv[ll] += dphi[l][ll] * n[l].v;
761: }
762: }
763: gam = Sqr(du[0]) + Sqr(dv[1]) + du[0]*dv[1] + 0.25*Sqr(du[1]+dv[0]);
764: THIViscosity(thi,PetscRealPart(gam),eta,deta);
765: }
769: static PetscErrorCode THIFunctionLocal(DMDALocalInfo *info,Node ***x,Node ***f,THI thi)
770: {
771: PetscInt xs,ys,xm,ym,zm,i,j,k,q,l;
772: PetscReal hx,hy,etamin,etamax,beta2min,beta2max;
773: PrmNode **prm;
777: xs = info->zs;
778: ys = info->ys;
779: xm = info->zm;
780: ym = info->ym;
781: zm = info->xm;
782: hx = thi->Lx / info->mz;
783: hy = thi->Ly / info->my;
785: etamin = 1e100;
786: etamax = 0;
787: beta2min = 1e100;
788: beta2max = 0;
790: THIDAGetPrm(info->da,&prm);
792: for (i=xs; i<xs+xm; i++) {
793: for (j=ys; j<ys+ym; j++) {
794: PrmNode pn[4];
795: QuadExtract(prm,i,j,pn);
796: for (k=0; k<zm-1; k++) {
797: PetscInt ls = 0;
798: Node n[8],*fn[8];
799: PetscReal zn[8],etabase = 0;
800: PrmHexGetZ(pn,k,zm,zn);
801: HexExtract(x,i,j,k,n);
802: HexExtractRef(f,i,j,k,fn);
803: if (thi->no_slip && k == 0) {
804: for (l=0; l<4; l++) n[l].u = n[l].v = 0;
805: /* The first 4 basis functions lie on the bottom layer, so their contribution is exactly 0, hence we can skip them */
806: ls = 4;
807: }
808: for (q=0; q<8; q++) {
809: PetscReal dz[3],phi[8],dphi[8][3],jw,eta,deta;
810: PetscScalar du[3],dv[3],u,v;
811: HexGrad(HexQDeriv[q],zn,dz);
812: HexComputeGeometry(q,hx,hy,dz,phi,dphi,&jw);
813: PointwiseNonlinearity(thi,n,phi,dphi,&u,&v,du,dv,&eta,&deta);
814: jw /= thi->rhog; /* scales residuals to be O(1) */
815: if (q == 0) etabase = eta;
816: RangeUpdate(&etamin,&etamax,eta);
817: for (l=ls; l<8; l++) { /* test functions */
818: const PetscReal ds[2] = {-PetscSinReal(thi->alpha),0};
819: const PetscReal pp = phi[l],*dp = dphi[l];
820: fn[l]->u += dp[0]*jw*eta*(4.*du[0]+2.*dv[1]) + dp[1]*jw*eta*(du[1]+dv[0]) + dp[2]*jw*eta*du[2] + pp*jw*thi->rhog*ds[0];
821: fn[l]->v += dp[1]*jw*eta*(2.*du[0]+4.*dv[1]) + dp[0]*jw*eta*(du[1]+dv[0]) + dp[2]*jw*eta*dv[2] + pp*jw*thi->rhog*ds[1];
822: }
823: }
824: if (k == 0) { /* we are on a bottom face */
825: if (thi->no_slip) {
826: /* Note: Non-Galerkin coarse grid operators are very sensitive to the scaling of Dirichlet boundary
827: * conditions. After shenanigans above, etabase contains the effective viscosity at the closest quadrature
828: * point to the bed. We want the diagonal entry in the Dirichlet condition to have similar magnitude to the
829: * diagonal entry corresponding to the adjacent node. The fundamental scaling of the viscous part is in
830: * diagu, diagv below. This scaling is easy to recognize by considering the finite difference operator after
831: * scaling by element size. The no-slip Dirichlet condition is scaled by this factor, and also in the
832: * assembled matrix (see the similar block in THIJacobianLocal).
833: *
834: * Note that the residual at this Dirichlet node is linear in the state at this node, but also depends
835: * (nonlinearly in general) on the neighboring interior nodes through the local viscosity. This will make
836: * a matrix-free Jacobian have extra entries in the corresponding row. We assemble only the diagonal part,
837: * so the solution will exactly satisfy the boundary condition after the first linear iteration.
838: */
839: const PetscReal hz = PetscRealPart(pn[0].h)/(zm-1.);
840: 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);
841: fn[0]->u = thi->dirichlet_scale*diagu*x[i][j][k].u;
842: fn[0]->v = thi->dirichlet_scale*diagv*x[i][j][k].v;
843: } else { /* Integrate over bottom face to apply boundary condition */
844: for (q=0; q<4; q++) {
845: const PetscReal jw = 0.25*hx*hy/thi->rhog,*phi = QuadQInterp[q];
846: PetscScalar u =0,v=0,rbeta2=0;
847: PetscReal beta2,dbeta2;
848: for (l=0; l<4; l++) {
849: u += phi[l]*n[l].u;
850: v += phi[l]*n[l].v;
851: rbeta2 += phi[l]*pn[l].beta2;
852: }
853: THIFriction(thi,PetscRealPart(rbeta2),PetscRealPart(u*u+v*v)/2,&beta2,&dbeta2);
854: RangeUpdate(&beta2min,&beta2max,beta2);
855: for (l=0; l<4; l++) {
856: const PetscReal pp = phi[l];
857: fn[ls+l]->u += pp*jw*beta2*u;
858: fn[ls+l]->v += pp*jw*beta2*v;
859: }
860: }
861: }
862: }
863: }
864: }
865: }
867: THIDARestorePrm(info->da,&prm);
869: PRangeMinMax(&thi->eta,etamin,etamax);
870: PRangeMinMax(&thi->beta2,beta2min,beta2max);
871: return(0);
872: }
876: static PetscErrorCode THIMatrixStatistics(THI thi,Mat B,PetscViewer viewer)
877: {
879: PetscReal nrm;
880: PetscInt m;
881: PetscMPIInt rank;
884: MatNorm(B,NORM_FROBENIUS,&nrm);
885: MatGetSize(B,&m,0);
886: MPI_Comm_rank(PetscObjectComm((PetscObject)B),&rank);
887: if (!rank) {
888: PetscScalar val0,val2;
889: MatGetValue(B,0,0,&val0);
890: MatGetValue(B,2,2,&val2);
891: 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);
892: }
893: return(0);
894: }
898: static PetscErrorCode THISurfaceStatistics(DM da,Vec X,PetscReal *min,PetscReal *max,PetscReal *mean)
899: {
901: Node ***x;
902: PetscInt i,j,xs,ys,zs,xm,ym,zm,mx,my,mz;
903: PetscReal umin = 1e100,umax=-1e100;
904: PetscScalar usum = 0.0,gusum;
907: *min = *max = *mean = 0;
908: DMDAGetInfo(da,0, &mz,&my,&mx, 0,0,0, 0,0,0,0,0,0);
909: DMDAGetCorners(da,&zs,&ys,&xs,&zm,&ym,&xm);
910: if (zs != 0 || zm != mz) SETERRQ(PETSC_COMM_SELF,1,"Unexpected decomposition");
911: DMDAVecGetArray(da,X,&x);
912: for (i=xs; i<xs+xm; i++) {
913: for (j=ys; j<ys+ym; j++) {
914: PetscReal u = PetscRealPart(x[i][j][zm-1].u);
915: RangeUpdate(&umin,&umax,u);
916: usum += u;
917: }
918: }
919: DMDAVecRestoreArray(da,X,&x);
920: MPI_Allreduce(&umin,min,1,MPIU_REAL,MPIU_MIN,PetscObjectComm((PetscObject)da));
921: MPI_Allreduce(&umax,max,1,MPIU_REAL,MPIU_MAX,PetscObjectComm((PetscObject)da));
922: MPI_Allreduce(&usum,&gusum,1,MPIU_SCALAR,MPIU_SUM,PetscObjectComm((PetscObject)da));
923: *mean = PetscRealPart(gusum) / (mx*my);
924: return(0);
925: }
929: static PetscErrorCode THISolveStatistics(THI thi,SNES snes,PetscInt coarsened,const char name[])
930: {
931: MPI_Comm comm;
932: Vec X;
933: DM dm;
937: PetscObjectGetComm((PetscObject)thi,&comm);
938: SNESGetSolution(snes,&X);
939: SNESGetDM(snes,&dm);
940: PetscPrintf(comm,"Solution statistics after solve: %s\n",name);
941: {
942: PetscInt its,lits;
943: SNESConvergedReason reason;
944: SNESGetIterationNumber(snes,&its);
945: SNESGetConvergedReason(snes,&reason);
946: SNESGetLinearSolveIterations(snes,&lits);
947: PetscPrintf(comm,"%s: Number of SNES iterations = %D, total linear iterations = %D\n",SNESConvergedReasons[reason],its,lits);
948: }
949: {
950: PetscReal nrm2,tmin[3]={1e100,1e100,1e100},tmax[3]={-1e100,-1e100,-1e100},min[3],max[3];
951: PetscInt i,j,m;
952: PetscScalar *x;
953: VecNorm(X,NORM_2,&nrm2);
954: VecGetLocalSize(X,&m);
955: VecGetArray(X,&x);
956: for (i=0; i<m; i+=2) {
957: PetscReal u = PetscRealPart(x[i]),v = PetscRealPart(x[i+1]),c = PetscSqrtReal(u*u+v*v);
958: tmin[0] = PetscMin(u,tmin[0]);
959: tmin[1] = PetscMin(v,tmin[1]);
960: tmin[2] = PetscMin(c,tmin[2]);
961: tmax[0] = PetscMax(u,tmax[0]);
962: tmax[1] = PetscMax(v,tmax[1]);
963: tmax[2] = PetscMax(c,tmax[2]);
964: }
965: VecRestoreArray(X,&x);
966: MPI_Allreduce(tmin,min,3,MPIU_REAL,MPIU_MIN,PetscObjectComm((PetscObject)thi));
967: MPI_Allreduce(tmax,max,3,MPIU_REAL,MPIU_MAX,PetscObjectComm((PetscObject)thi));
968: /* Dimensionalize to meters/year */
969: nrm2 *= thi->units->year / thi->units->meter;
970: for (j=0; j<3; j++) {
971: min[j] *= thi->units->year / thi->units->meter;
972: max[j] *= thi->units->year / thi->units->meter;
973: }
974: 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]);
975: {
976: PetscReal umin,umax,umean;
977: THISurfaceStatistics(dm,X,&umin,&umax,&umean);
978: umin *= thi->units->year / thi->units->meter;
979: umax *= thi->units->year / thi->units->meter;
980: umean *= thi->units->year / thi->units->meter;
981: PetscPrintf(comm,"Surface statistics: u in [%12.6e, %12.6e] mean %12.6e\n",(double)umin,(double)umax,(double)umean);
982: }
983: /* These values stay nondimensional */
984: 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);
985: 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);
986: }
987: PetscPrintf(comm,"\n");
988: return(0);
989: }
993: static PetscErrorCode THIJacobianLocal_2D(DMDALocalInfo *info,Node **x,Mat B,THI thi)
994: {
995: PetscInt xs,ys,xm,ym,i,j,q,l,ll;
996: PetscReal hx,hy;
997: PrmNode **prm;
1001: xs = info->ys;
1002: ys = info->xs;
1003: xm = info->ym;
1004: ym = info->xm;
1005: hx = thi->Lx / info->my;
1006: hy = thi->Ly / info->mx;
1008: MatZeroEntries(B);
1009: THIDAGetPrm(info->da,&prm);
1011: for (i=xs; i<xs+xm; i++) {
1012: for (j=ys; j<ys+ym; j++) {
1013: Node n[4];
1014: PrmNode pn[4];
1015: PetscScalar Ke[4*2][4*2];
1016: QuadExtract(prm,i,j,pn);
1017: QuadExtract(x,i,j,n);
1018: PetscMemzero(Ke,sizeof(Ke));
1019: for (q=0; q<4; q++) {
1020: PetscReal phi[4],dphi[4][2],jw,eta,deta,beta2,dbeta2;
1021: PetscScalar u,v,du[2],dv[2],h = 0,rbeta2 = 0;
1022: for (l=0; l<4; l++) {
1023: phi[l] = QuadQInterp[q][l];
1024: dphi[l][0] = QuadQDeriv[q][l][0]*2./hx;
1025: dphi[l][1] = QuadQDeriv[q][l][1]*2./hy;
1026: h += phi[l] * pn[l].h;
1027: rbeta2 += phi[l] * pn[l].beta2;
1028: }
1029: jw = 0.25*hx*hy / thi->rhog; /* rhog is only scaling */
1030: PointwiseNonlinearity2D(thi,n,phi,dphi,&u,&v,du,dv,&eta,&deta);
1031: THIFriction(thi,PetscRealPart(rbeta2),PetscRealPart(u*u+v*v)/2,&beta2,&dbeta2);
1032: for (l=0; l<4; l++) {
1033: const PetscReal pp = phi[l],*dp = dphi[l];
1034: for (ll=0; ll<4; ll++) {
1035: const PetscReal ppl = phi[ll],*dpl = dphi[ll];
1036: PetscScalar dgdu,dgdv;
1037: dgdu = 2.*du[0]*dpl[0] + dv[1]*dpl[0] + 0.5*(du[1]+dv[0])*dpl[1];
1038: dgdv = 2.*dv[1]*dpl[1] + du[0]*dpl[1] + 0.5*(du[1]+dv[0])*dpl[0];
1039: /* Picard part */
1040: 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;
1041: Ke[l*2+0][ll*2+1] += dp[0]*jw*eta*2.*dpl[1] + dp[1]*jw*eta*dpl[0];
1042: Ke[l*2+1][ll*2+0] += dp[1]*jw*eta*2.*dpl[0] + dp[0]*jw*eta*dpl[1];
1043: 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;
1044: /* extra Newton terms */
1045: 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;
1046: 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;
1047: 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;
1048: 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;
1049: }
1050: }
1051: }
1052: {
1053: const MatStencil rc[4] = {{0,i,j,0},{0,i+1,j,0},{0,i+1,j+1,0},{0,i,j+1,0}};
1054: MatSetValuesBlockedStencil(B,4,rc,4,rc,&Ke[0][0],ADD_VALUES);
1055: }
1056: }
1057: }
1058: THIDARestorePrm(info->da,&prm);
1060: MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
1061: MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
1062: MatSetOption(B,MAT_SYMMETRIC,PETSC_TRUE);
1063: if (thi->verbose) {THIMatrixStatistics(thi,B,PETSC_VIEWER_STDOUT_WORLD);}
1064: return(0);
1065: }
1069: static PetscErrorCode THIJacobianLocal_3D(DMDALocalInfo *info,Node ***x,Mat B,THI thi,THIAssemblyMode amode)
1070: {
1071: PetscInt xs,ys,xm,ym,zm,i,j,k,q,l,ll;
1072: PetscReal hx,hy;
1073: PrmNode **prm;
1077: xs = info->zs;
1078: ys = info->ys;
1079: xm = info->zm;
1080: ym = info->ym;
1081: zm = info->xm;
1082: hx = thi->Lx / info->mz;
1083: hy = thi->Ly / info->my;
1085: MatZeroEntries(B);
1086: THIDAGetPrm(info->da,&prm);
1088: for (i=xs; i<xs+xm; i++) {
1089: for (j=ys; j<ys+ym; j++) {
1090: PrmNode pn[4];
1091: QuadExtract(prm,i,j,pn);
1092: for (k=0; k<zm-1; k++) {
1093: Node n[8];
1094: PetscReal zn[8],etabase = 0;
1095: PetscScalar Ke[8*2][8*2];
1096: PetscInt ls = 0;
1098: PrmHexGetZ(pn,k,zm,zn);
1099: HexExtract(x,i,j,k,n);
1100: PetscMemzero(Ke,sizeof(Ke));
1101: if (thi->no_slip && k == 0) {
1102: for (l=0; l<4; l++) n[l].u = n[l].v = 0;
1103: ls = 4;
1104: }
1105: for (q=0; q<8; q++) {
1106: PetscReal dz[3],phi[8],dphi[8][3],jw,eta,deta;
1107: PetscScalar du[3],dv[3],u,v;
1108: HexGrad(HexQDeriv[q],zn,dz);
1109: HexComputeGeometry(q,hx,hy,dz,phi,dphi,&jw);
1110: PointwiseNonlinearity(thi,n,phi,dphi,&u,&v,du,dv,&eta,&deta);
1111: jw /= thi->rhog; /* residuals are scaled by this factor */
1112: if (q == 0) etabase = eta;
1113: for (l=ls; l<8; l++) { /* test functions */
1114: const PetscReal *restrict dp = dphi[l];
1115: #if USE_SSE2_KERNELS
1116: /* gcc (up to my 4.5 snapshot) is really bad at hoisting intrinsics so we do it manually */
1117: __m128d
1118: p4 = _mm_set1_pd(4),p2 = _mm_set1_pd(2),p05 = _mm_set1_pd(0.5),
1119: p42 = _mm_setr_pd(4,2),p24 = _mm_shuffle_pd(p42,p42,_MM_SHUFFLE2(0,1)),
1120: du0 = _mm_set1_pd(du[0]),du1 = _mm_set1_pd(du[1]),du2 = _mm_set1_pd(du[2]),
1121: dv0 = _mm_set1_pd(dv[0]),dv1 = _mm_set1_pd(dv[1]),dv2 = _mm_set1_pd(dv[2]),
1122: jweta = _mm_set1_pd(jw*eta),jwdeta = _mm_set1_pd(jw*deta),
1123: dp0 = _mm_set1_pd(dp[0]),dp1 = _mm_set1_pd(dp[1]),dp2 = _mm_set1_pd(dp[2]),
1124: dp0jweta = _mm_mul_pd(dp0,jweta),dp1jweta = _mm_mul_pd(dp1,jweta),dp2jweta = _mm_mul_pd(dp2,jweta),
1125: p4du0p2dv1 = _mm_add_pd(_mm_mul_pd(p4,du0),_mm_mul_pd(p2,dv1)), /* 4 du0 + 2 dv1 */
1126: p4dv1p2du0 = _mm_add_pd(_mm_mul_pd(p4,dv1),_mm_mul_pd(p2,du0)), /* 4 dv1 + 2 du0 */
1127: pdu2dv2 = _mm_unpacklo_pd(du2,dv2), /* [du2, dv2] */
1128: du1pdv0 = _mm_add_pd(du1,dv0), /* du1 + dv0 */
1129: t1 = _mm_mul_pd(dp0,p4du0p2dv1), /* dp0 (4 du0 + 2 dv1) */
1130: t2 = _mm_mul_pd(dp1,p4dv1p2du0); /* dp1 (4 dv1 + 2 du0) */
1132: #endif
1133: #if defined COMPUTE_LOWER_TRIANGULAR /* The element matrices are always symmetric so computing the lower-triangular part is not necessary */
1134: for (ll=ls; ll<8; ll++) { /* trial functions */
1135: #else
1136: for (ll=l; ll<8; ll++) {
1137: #endif
1138: const PetscReal *restrict dpl = dphi[ll];
1139: if (amode == THIASSEMBLY_TRIDIAGONAL && (l-ll)%4) continue; /* these entries would not be inserted */
1140: #if !USE_SSE2_KERNELS
1141: /* The analytic Jacobian in nice, easy-to-read form */
1142: {
1143: PetscScalar dgdu,dgdv;
1144: dgdu = 2.*du[0]*dpl[0] + dv[1]*dpl[0] + 0.5*(du[1]+dv[0])*dpl[1] + 0.5*du[2]*dpl[2];
1145: dgdv = 2.*dv[1]*dpl[1] + du[0]*dpl[1] + 0.5*(du[1]+dv[0])*dpl[0] + 0.5*dv[2]*dpl[2];
1146: /* Picard part */
1147: 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];
1148: Ke[l*2+0][ll*2+1] += dp[0]*jw*eta*2.*dpl[1] + dp[1]*jw*eta*dpl[0];
1149: Ke[l*2+1][ll*2+0] += dp[1]*jw*eta*2.*dpl[0] + dp[0]*jw*eta*dpl[1];
1150: 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];
1151: /* extra Newton terms */
1152: 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];
1153: 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];
1154: 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];
1155: 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];
1156: }
1157: #else
1158: /* This SSE2 code is an exact replica of above, but uses explicit packed instructions for some speed
1159: * benefit. On my hardware, these intrinsics are almost twice as fast as above, reducing total assembly cost
1160: * by 25 to 30 percent. */
1161: {
1162: __m128d
1163: keu = _mm_loadu_pd(&Ke[l*2+0][ll*2+0]),
1164: kev = _mm_loadu_pd(&Ke[l*2+1][ll*2+0]),
1165: dpl01 = _mm_loadu_pd(&dpl[0]),dpl10 = _mm_shuffle_pd(dpl01,dpl01,_MM_SHUFFLE2(0,1)),dpl2 = _mm_set_sd(dpl[2]),
1166: t0,t3,pdgduv;
1167: keu = _mm_add_pd(keu,_mm_add_pd(_mm_mul_pd(_mm_mul_pd(dp0jweta,p42),dpl01),
1168: _mm_add_pd(_mm_mul_pd(dp1jweta,dpl10),
1169: _mm_mul_pd(dp2jweta,dpl2))));
1170: kev = _mm_add_pd(kev,_mm_add_pd(_mm_mul_pd(_mm_mul_pd(dp1jweta,p24),dpl01),
1171: _mm_add_pd(_mm_mul_pd(dp0jweta,dpl10),
1172: _mm_mul_pd(dp2jweta,_mm_shuffle_pd(dpl2,dpl2,_MM_SHUFFLE2(0,1))))));
1173: pdgduv = _mm_mul_pd(p05,_mm_add_pd(_mm_add_pd(_mm_mul_pd(p42,_mm_mul_pd(du0,dpl01)),
1174: _mm_mul_pd(p24,_mm_mul_pd(dv1,dpl01))),
1175: _mm_add_pd(_mm_mul_pd(du1pdv0,dpl10),
1176: _mm_mul_pd(pdu2dv2,_mm_set1_pd(dpl[2]))))); /* [dgdu, dgdv] */
1177: t0 = _mm_mul_pd(jwdeta,pdgduv); /* jw deta [dgdu, dgdv] */
1178: t3 = _mm_mul_pd(t0,du1pdv0); /* t0 (du1 + dv0) */
1179: _mm_storeu_pd(&Ke[l*2+0][ll*2+0],_mm_add_pd(keu,_mm_add_pd(_mm_mul_pd(t1,t0),
1180: _mm_add_pd(_mm_mul_pd(dp1,t3),
1181: _mm_mul_pd(t0,_mm_mul_pd(dp2,du2))))));
1182: _mm_storeu_pd(&Ke[l*2+1][ll*2+0],_mm_add_pd(kev,_mm_add_pd(_mm_mul_pd(t2,t0),
1183: _mm_add_pd(_mm_mul_pd(dp0,t3),
1184: _mm_mul_pd(t0,_mm_mul_pd(dp2,dv2))))));
1185: }
1186: #endif
1187: }
1188: }
1189: }
1190: if (k == 0) { /* on a bottom face */
1191: if (thi->no_slip) {
1192: const PetscReal hz = PetscRealPart(pn[0].h)/(zm-1);
1193: 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);
1194: Ke[0][0] = thi->dirichlet_scale*diagu;
1195: Ke[1][1] = thi->dirichlet_scale*diagv;
1196: } else {
1197: for (q=0; q<4; q++) {
1198: const PetscReal jw = 0.25*hx*hy/thi->rhog,*phi = QuadQInterp[q];
1199: PetscScalar u =0,v=0,rbeta2=0;
1200: PetscReal beta2,dbeta2;
1201: for (l=0; l<4; l++) {
1202: u += phi[l]*n[l].u;
1203: v += phi[l]*n[l].v;
1204: rbeta2 += phi[l]*pn[l].beta2;
1205: }
1206: THIFriction(thi,PetscRealPart(rbeta2),PetscRealPart(u*u+v*v)/2,&beta2,&dbeta2);
1207: for (l=0; l<4; l++) {
1208: const PetscReal pp = phi[l];
1209: for (ll=0; ll<4; ll++) {
1210: const PetscReal ppl = phi[ll];
1211: Ke[l*2+0][ll*2+0] += pp*jw*beta2*ppl + pp*jw*dbeta2*u*u*ppl;
1212: Ke[l*2+0][ll*2+1] += pp*jw*dbeta2*u*v*ppl;
1213: Ke[l*2+1][ll*2+0] += pp*jw*dbeta2*v*u*ppl;
1214: Ke[l*2+1][ll*2+1] += pp*jw*beta2*ppl + pp*jw*dbeta2*v*v*ppl;
1215: }
1216: }
1217: }
1218: }
1219: }
1220: {
1221: 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}};
1222: if (amode == THIASSEMBLY_TRIDIAGONAL) {
1223: for (l=0; l<4; l++) { /* Copy out each of the blocks, discarding horizontal coupling */
1224: const PetscInt l4 = l+4;
1225: const MatStencil rcl[2] = {{rc[l].k,rc[l].j,rc[l].i,0},{rc[l4].k,rc[l4].j,rc[l4].i,0}};
1226: #if defined COMPUTE_LOWER_TRIANGULAR
1227: 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]},
1228: {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]},
1229: {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]},
1230: {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]}};
1231: #else
1232: /* Same as above except for the lower-left block */
1233: 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]},
1234: {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]},
1235: {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]},
1236: {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]}};
1237: #endif
1238: MatSetValuesBlockedStencil(B,2,rcl,2,rcl,&Kel[0][0],ADD_VALUES);
1239: }
1240: } else {
1241: #if !defined COMPUTE_LOWER_TRIANGULAR /* fill in lower-triangular part, this is really cheap compared to computing the entries */
1242: for (l=0; l<8; l++) {
1243: for (ll=l+1; ll<8; ll++) {
1244: Ke[ll*2+0][l*2+0] = Ke[l*2+0][ll*2+0];
1245: Ke[ll*2+1][l*2+0] = Ke[l*2+0][ll*2+1];
1246: Ke[ll*2+0][l*2+1] = Ke[l*2+1][ll*2+0];
1247: Ke[ll*2+1][l*2+1] = Ke[l*2+1][ll*2+1];
1248: }
1249: }
1250: #endif
1251: MatSetValuesBlockedStencil(B,8,rc,8,rc,&Ke[0][0],ADD_VALUES);
1252: }
1253: }
1254: }
1255: }
1256: }
1257: THIDARestorePrm(info->da,&prm);
1259: MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
1260: MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
1261: MatSetOption(B,MAT_SYMMETRIC,PETSC_TRUE);
1262: if (thi->verbose) {THIMatrixStatistics(thi,B,PETSC_VIEWER_STDOUT_WORLD);}
1263: return(0);
1264: }
1268: static PetscErrorCode THIJacobianLocal_3D_Full(DMDALocalInfo *info,Node ***x,Mat A,Mat B,MatStructure *mstr,THI thi)
1269: {
1273: THIJacobianLocal_3D(info,x,B,thi,THIASSEMBLY_FULL);
1274: *mstr = SAME_NONZERO_PATTERN;
1275: return(0);
1276: }
1280: static PetscErrorCode THIJacobianLocal_3D_Tridiagonal(DMDALocalInfo *info,Node ***x,Mat B,THI thi)
1281: {
1285: THIJacobianLocal_3D(info,x,B,thi,THIASSEMBLY_TRIDIAGONAL);
1286: return(0);
1287: }
1291: static PetscErrorCode DMRefineHierarchy_THI(DM dac0,PetscInt nlevels,DM hierarchy[])
1292: {
1293: PetscErrorCode ierr;
1294: THI thi;
1295: PetscInt dim,M,N,m,n,s,dof;
1296: DM dac,daf;
1297: DMDAStencilType st;
1298: DM_DA *ddf,*ddc;
1301: PetscObjectQuery((PetscObject)dac0,"THI",(PetscObject*)&thi);
1302: if (!thi) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Cannot refine this DMDA, missing composed THI instance");
1303: if (nlevels > 1) {
1304: DMRefineHierarchy(dac0,nlevels-1,hierarchy);
1305: dac = hierarchy[nlevels-2];
1306: } else {
1307: dac = dac0;
1308: }
1309: DMDAGetInfo(dac,&dim, &N,&M,0, &n,&m,0, &dof,&s,0,0,0,&st);
1310: if (dim != 2) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"This function can only refine 2D DMDAs");
1312: /* Creates a 3D DMDA with the same map-plane layout as the 2D one, with contiguous columns */
1313: DMDACreate3d(PetscObjectComm((PetscObject)dac),DMDA_BOUNDARY_NONE,DMDA_BOUNDARY_PERIODIC,DMDA_BOUNDARY_PERIODIC,st,thi->zlevels,N,M,1,n,m,dof,s,NULL,NULL,NULL,&daf);
1315: daf->ops->creatematrix = dac->ops->creatematrix;
1316: daf->ops->createinterpolation = dac->ops->createinterpolation;
1317: daf->ops->getcoloring = dac->ops->getcoloring;
1318: ddf = (DM_DA*)daf->data;
1319: ddc = (DM_DA*)dac->data;
1320: ddf->interptype = ddc->interptype;
1322: DMDASetFieldName(daf,0,"x-velocity");
1323: DMDASetFieldName(daf,1,"y-velocity");
1325: hierarchy[nlevels-1] = daf;
1326: return(0);
1327: }
1331: static PetscErrorCode DMCreateInterpolation_DA_THI(DM dac,DM daf,Mat *A,Vec *scale)
1332: {
1334: PetscInt dim;
1341: DMDAGetInfo(daf,&dim,0,0,0,0,0,0,0,0,0,0,0,0);
1342: if (dim == 2) {
1343: /* We are in the 2D problem and use normal DMDA interpolation */
1344: DMCreateInterpolation(dac,daf,A,scale);
1345: } else {
1346: PetscInt i,j,k,xs,ys,zs,xm,ym,zm,mx,my,mz,rstart,cstart;
1347: Mat B;
1349: DMDAGetInfo(daf,0, &mz,&my,&mx, 0,0,0, 0,0,0,0,0,0);
1350: DMDAGetCorners(daf,&zs,&ys,&xs,&zm,&ym,&xm);
1351: if (zs != 0) SETERRQ(PETSC_COMM_SELF,1,"unexpected");
1352: MatCreate(PetscObjectComm((PetscObject)daf),&B);
1353: MatSetSizes(B,xm*ym*zm,xm*ym,mx*my*mz,mx*my);
1355: MatSetType(B,MATAIJ);
1356: MatSeqAIJSetPreallocation(B,1,NULL);
1357: MatMPIAIJSetPreallocation(B,1,NULL,0,NULL);
1358: MatGetOwnershipRange(B,&rstart,NULL);
1359: MatGetOwnershipRangeColumn(B,&cstart,NULL);
1360: for (i=xs; i<xs+xm; i++) {
1361: for (j=ys; j<ys+ym; j++) {
1362: for (k=zs; k<zs+zm; k++) {
1363: PetscInt i2 = i*ym+j,i3 = i2*zm+k;
1364: PetscScalar val = ((k == 0 || k == mz-1) ? 0.5 : 1.) / (mz-1.); /* Integration using trapezoid rule */
1365: MatSetValue(B,cstart+i3,rstart+i2,val,INSERT_VALUES);
1366: }
1367: }
1368: }
1369: MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
1370: MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
1371: MatCreateMAIJ(B,sizeof(Node)/sizeof(PetscScalar),A);
1372: MatDestroy(&B);
1373: }
1374: return(0);
1375: }
1379: static PetscErrorCode DMCreateMatrix_THI_Tridiagonal(DM da,Mat *J)
1380: {
1381: PetscErrorCode ierr;
1382: Mat A;
1383: PetscInt xm,ym,zm,dim,dof = 2,starts[3],dims[3];
1384: ISLocalToGlobalMapping ltog,ltogb;
1387: DMDAGetInfo(da,&dim, 0,0,0, 0,0,0, 0,0,0,0,0,0);
1388: if (dim != 3) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Expected DMDA to be 3D");
1389: DMDAGetCorners(da,0,0,0,&zm,&ym,&xm);
1390: DMGetLocalToGlobalMapping(da,<og);
1391: DMGetLocalToGlobalMappingBlock(da,<ogb);
1392: MatCreate(PetscObjectComm((PetscObject)da),&A);
1393: MatSetSizes(A,dof*xm*ym*zm,dof*xm*ym*zm,PETSC_DETERMINE,PETSC_DETERMINE);
1394: MatSetType(A,da->mattype);
1395: MatSetFromOptions(A);
1396: MatSeqAIJSetPreallocation(A,3*2,NULL);
1397: MatMPIAIJSetPreallocation(A,3*2,NULL,0,NULL);
1398: MatSeqBAIJSetPreallocation(A,2,3,NULL);
1399: MatMPIBAIJSetPreallocation(A,2,3,NULL,0,NULL);
1400: MatSeqSBAIJSetPreallocation(A,2,2,NULL);
1401: MatMPISBAIJSetPreallocation(A,2,2,NULL,0,NULL);
1402: MatSetLocalToGlobalMapping(A,ltog,ltog);
1403: MatSetLocalToGlobalMappingBlock(A,ltogb,ltogb);
1404: DMDAGetGhostCorners(da,&starts[0],&starts[1],&starts[2],&dims[0],&dims[1],&dims[2]);
1405: MatSetStencil(A,dim,dims,starts,dof);
1406: *J = A;
1407: return(0);
1408: }
1412: static PetscErrorCode THIDAVecView_VTK_XML(THI thi,DM da,Vec X,const char filename[])
1413: {
1414: const PetscInt dof = 2;
1415: Units units = thi->units;
1416: MPI_Comm comm;
1418: PetscViewer viewer;
1419: PetscMPIInt rank,size,tag,nn,nmax;
1420: PetscInt mx,my,mz,r,range[6];
1421: PetscScalar *x;
1424: PetscObjectGetComm((PetscObject)thi,&comm);
1425: DMDAGetInfo(da,0, &mz,&my,&mx, 0,0,0, 0,0,0,0,0,0);
1426: MPI_Comm_size(comm,&size);
1427: MPI_Comm_rank(comm,&rank);
1428: PetscViewerASCIIOpen(comm,filename,&viewer);
1429: PetscViewerASCIIPrintf(viewer,"<VTKFile type=\"StructuredGrid\" version=\"0.1\" byte_order=\"LittleEndian\">\n");
1430: PetscViewerASCIIPrintf(viewer," <StructuredGrid WholeExtent=\"%d %D %d %D %d %D\">\n",0,mz-1,0,my-1,0,mx-1);
1432: DMDAGetCorners(da,range,range+1,range+2,range+3,range+4,range+5);
1433: PetscMPIIntCast(range[3]*range[4]*range[5]*dof,&nn);
1434: MPI_Reduce(&nn,&nmax,1,MPI_INT,MPI_MAX,0,comm);
1435: tag = ((PetscObject) viewer)->tag;
1436: VecGetArray(X,&x);
1437: if (!rank) {
1438: PetscScalar *array;
1439: PetscMalloc1(nmax,&array);
1440: for (r=0; r<size; r++) {
1441: PetscInt i,j,k,xs,xm,ys,ym,zs,zm;
1442: PetscScalar *ptr;
1443: MPI_Status status;
1444: if (r) {
1445: MPI_Recv(range,6,MPIU_INT,r,tag,comm,MPI_STATUS_IGNORE);
1446: }
1447: zs = range[0];ys = range[1];xs = range[2];zm = range[3];ym = range[4];xm = range[5];
1448: if (xm*ym*zm*dof > nmax) SETERRQ(PETSC_COMM_SELF,1,"should not happen");
1449: if (r) {
1450: MPI_Recv(array,nmax,MPIU_SCALAR,r,tag,comm,&status);
1451: MPI_Get_count(&status,MPIU_SCALAR,&nn);
1452: if (nn != xm*ym*zm*dof) SETERRQ(PETSC_COMM_SELF,1,"should not happen");
1453: ptr = array;
1454: } else ptr = x;
1455: PetscViewerASCIIPrintf(viewer," <Piece Extent=\"%D %D %D %D %D %D\">\n",zs,zs+zm-1,ys,ys+ym-1,xs,xs+xm-1);
1457: PetscViewerASCIIPrintf(viewer," <Points>\n");
1458: PetscViewerASCIIPrintf(viewer," <DataArray type=\"Float32\" NumberOfComponents=\"3\" format=\"ascii\">\n");
1459: for (i=xs; i<xs+xm; i++) {
1460: for (j=ys; j<ys+ym; j++) {
1461: for (k=zs; k<zs+zm; k++) {
1462: PrmNode p;
1463: PetscReal xx = thi->Lx*i/mx,yy = thi->Ly*j/my,zz;
1464: thi->initialize(thi,xx,yy,&p);
1465: zz = PetscRealPart(p.b) + PetscRealPart(p.h)*k/(mz-1);
1466: PetscViewerASCIIPrintf(viewer,"%f %f %f\n",(double)xx,(double)yy,(double)zz);
1467: }
1468: }
1469: }
1470: PetscViewerASCIIPrintf(viewer," </DataArray>\n");
1471: PetscViewerASCIIPrintf(viewer," </Points>\n");
1473: PetscViewerASCIIPrintf(viewer," <PointData>\n");
1474: PetscViewerASCIIPrintf(viewer," <DataArray type=\"Float32\" Name=\"velocity\" NumberOfComponents=\"3\" format=\"ascii\">\n");
1475: for (i=0; i<nn; i+=dof) {
1476: 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);
1477: }
1478: PetscViewerASCIIPrintf(viewer," </DataArray>\n");
1480: PetscViewerASCIIPrintf(viewer," <DataArray type=\"Int32\" Name=\"rank\" NumberOfComponents=\"1\" format=\"ascii\">\n");
1481: for (i=0; i<nn; i+=dof) {
1482: PetscViewerASCIIPrintf(viewer,"%D\n",r);
1483: }
1484: PetscViewerASCIIPrintf(viewer," </DataArray>\n");
1485: PetscViewerASCIIPrintf(viewer," </PointData>\n");
1487: PetscViewerASCIIPrintf(viewer," </Piece>\n");
1488: }
1489: PetscFree(array);
1490: } else {
1491: MPI_Send(range,6,MPIU_INT,0,tag,comm);
1492: MPI_Send(x,nn,MPIU_SCALAR,0,tag,comm);
1493: }
1494: VecRestoreArray(X,&x);
1495: PetscViewerASCIIPrintf(viewer," </StructuredGrid>\n");
1496: PetscViewerASCIIPrintf(viewer,"</VTKFile>\n");
1497: PetscViewerDestroy(&viewer);
1498: return(0);
1499: }
1503: int main(int argc,char *argv[])
1504: {
1505: MPI_Comm comm;
1506: THI thi;
1508: DM da;
1509: SNES snes;
1511: PetscInitialize(&argc,&argv,0,help);
1512: comm = PETSC_COMM_WORLD;
1514: THICreate(comm,&thi);
1515: {
1516: PetscInt M = 3,N = 3,P = 2;
1517: PetscOptionsBegin(comm,NULL,"Grid resolution options","");
1518: {
1519: PetscOptionsInt("-M","Number of elements in x-direction on coarse level","",M,&M,NULL);
1520: N = M;
1521: PetscOptionsInt("-N","Number of elements in y-direction on coarse level (if different from M)","",N,&N,NULL);
1522: if (thi->coarse2d) {
1523: PetscOptionsInt("-zlevels","Number of elements in z-direction on fine level","",thi->zlevels,&thi->zlevels,NULL);
1524: } else {
1525: PetscOptionsInt("-P","Number of elements in z-direction on coarse level","",P,&P,NULL);
1526: }
1527: }
1528: PetscOptionsEnd();
1529: if (thi->coarse2d) {
1530: DMDACreate2d(comm,DMDA_BOUNDARY_PERIODIC,DMDA_BOUNDARY_PERIODIC,DMDA_STENCIL_BOX,-N,-M,PETSC_DETERMINE,PETSC_DETERMINE,sizeof(Node)/sizeof(PetscScalar),1,0,0,&da);
1532: da->ops->refinehierarchy = DMRefineHierarchy_THI;
1533: da->ops->createinterpolation = DMCreateInterpolation_DA_THI;
1535: PetscObjectCompose((PetscObject)da,"THI",(PetscObject)thi);
1536: } else {
1537: DMDACreate3d(comm,DMDA_BOUNDARY_NONE,DMDA_BOUNDARY_PERIODIC,DMDA_BOUNDARY_PERIODIC, DMDA_STENCIL_BOX,-P,-N,-M,1,PETSC_DETERMINE,PETSC_DETERMINE,sizeof(Node)/sizeof(PetscScalar),1,0,0,0,&da);
1538: }
1539: DMDASetFieldName(da,0,"x-velocity");
1540: DMDASetFieldName(da,1,"y-velocity");
1541: }
1542: THISetUpDM(thi,da);
1543: if (thi->tridiagonal) da->ops->creatematrix = DMCreateMatrix_THI_Tridiagonal;
1545: { /* Set the fine level matrix type if -da_refine */
1546: PetscInt rlevel,clevel;
1547: DMGetRefineLevel(da,&rlevel);
1548: DMGetCoarsenLevel(da,&clevel);
1549: if (rlevel - clevel > 0) {DMSetMatType(da,thi->mattype);}
1550: }
1552: DMDASNESSetFunctionLocal(da,ADD_VALUES,(DMDASNESFunction)THIFunctionLocal,thi);
1553: if (thi->tridiagonal) {
1554: DMDASNESSetJacobianLocal(da,(DMDASNESJacobian)THIJacobianLocal_3D_Tridiagonal,thi);
1555: } else {
1556: DMDASNESSetJacobianLocal(da,(DMDASNESJacobian)THIJacobianLocal_3D_Full,thi);
1557: }
1558: DMCoarsenHookAdd(da,DMCoarsenHook_THI,NULL,thi);
1559: DMRefineHookAdd(da,DMRefineHook_THI,NULL,thi);
1561: DMSetApplicationContext(da,thi);
1563: SNESCreate(comm,&snes);
1564: SNESSetDM(snes,da);
1565: DMDestroy(&da);
1566: SNESSetComputeInitialGuess(snes,THIInitial,NULL);
1567: SNESSetFromOptions(snes);
1569: SNESSolve(snes,NULL,NULL);
1571: THISolveStatistics(thi,snes,0,"Full");
1573: {
1574: PetscBool flg;
1575: char filename[PETSC_MAX_PATH_LEN] = "";
1576: PetscOptionsGetString(NULL,"-o",filename,sizeof(filename),&flg);
1577: if (flg) {
1578: Vec X;
1579: DM dm;
1580: SNESGetSolution(snes,&X);
1581: SNESGetDM(snes,&dm);
1582: THIDAVecView_VTK_XML(thi,dm,X,filename);
1583: }
1584: }
1586: DMDestroy(&da);
1587: SNESDestroy(&snes);
1588: THIDestroy(&thi);
1589: PetscFinalize();
1590: return 0;
1591: }