Actual source code: ex48.c
petsc-3.6.1 2015-08-06
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
62: #include <petscsnes.h>
63: #include <petsc/private/dmdaimpl.h> /* There is not yet a public interface to manipulate dm->ops */
64: #endif
65: #include <ctype.h> /* toupper() */
67: #if !defined __STDC_VERSION__ || __STDC_VERSION__ < 199901L
68: # if defined __cplusplus /* C++ restrict is nonstandard and compilers have inconsistent rules about where it can be used */
69: # define restrict
70: # else
71: # define restrict PETSC_RESTRICT
72: # endif
73: #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: #define USE_SSE2_KERNELS (!defined NO_SSE2 \
80: && !defined PETSC_USE_COMPLEX \
81: && !defined PETSC_USE_REAL_SINGLE \
82: && !defined PETSC_USE_REAL___FLOAT128 \
83: && defined __SSE2__)
85: static PetscClassId THI_CLASSID;
87: typedef enum {QUAD_GAUSS,QUAD_LOBATTO} QuadratureType;
88: static const char *QuadratureTypes[] = {"gauss","lobatto","QuadratureType","QUAD_",0};
89: PETSC_UNUSED static const PetscReal HexQWeights[8] = {1,1,1,1,1,1,1,1};
90: PETSC_UNUSED static const PetscReal HexQNodes[] = {-0.57735026918962573, 0.57735026918962573};
91: #define G 0.57735026918962573
92: #define H (0.5*(1.+G))
93: #define L (0.5*(1.-G))
94: #define M (-0.5)
95: #define P (0.5)
96: /* Special quadrature: Lobatto in horizontal, Gauss in vertical */
97: static const PetscReal HexQInterp_Lobatto[8][8] = {{H,0,0,0,L,0,0,0},
98: {0,H,0,0,0,L,0,0},
99: {0,0,H,0,0,0,L,0},
100: {0,0,0,H,0,0,0,L},
101: {L,0,0,0,H,0,0,0},
102: {0,L,0,0,0,H,0,0},
103: {0,0,L,0,0,0,H,0},
104: {0,0,0,L,0,0,0,H}};
105: static const PetscReal HexQDeriv_Lobatto[8][8][3] = {
106: {{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} },
107: {{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} },
108: {{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} },
109: {{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}},
110: {{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} },
111: {{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} },
112: {{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} },
113: {{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}}};
114: /* Stanndard Gauss */
115: 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},
116: {L*H*H,H*H*H,H*L*H,L*L*H, L*H*L,H*H*L,H*L*L,L*L*L},
117: {L*L*H,H*L*H,H*H*H,L*H*H, L*L*L,H*L*L,H*H*L,L*H*L},
118: {H*L*H,L*L*H,L*H*H,H*H*H, H*L*L,L*L*L,L*H*L,H*H*L},
119: {H*H*L,L*H*L,L*L*L,H*L*L, H*H*H,L*H*H,L*L*H,H*L*H},
120: {L*H*L,H*H*L,H*L*L,L*L*L, L*H*H,H*H*H,H*L*H,L*L*H},
121: {L*L*L,H*L*L,H*H*L,L*H*L, L*L*H,H*L*H,H*H*H,L*H*H},
122: {H*L*L,L*L*L,L*H*L,H*H*L, H*L*H,L*L*H,L*H*H,H*H*H}};
123: static const PetscReal HexQDeriv_Gauss[8][8][3] = {
124: {{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}},
125: {{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}},
126: {{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}},
127: {{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}},
128: {{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}},
129: {{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}},
130: {{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}},
131: {{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}}};
132: static const PetscReal (*HexQInterp)[8],(*HexQDeriv)[8][3];
133: /* Standard 2x2 Gauss quadrature for the bottom layer. */
134: static const PetscReal QuadQInterp[4][4] = {{H*H,L*H,L*L,H*L},
135: {L*H,H*H,H*L,L*L},
136: {L*L,H*L,H*H,L*H},
137: {H*L,L*L,L*H,H*H}};
138: static const PetscReal QuadQDeriv[4][4][2] = {
139: {{M*H,M*H},{P*H,M*L},{P*L,P*L},{M*L,P*H}},
140: {{M*H,M*L},{P*H,M*H},{P*L,P*H},{M*L,P*L}},
141: {{M*L,M*L},{P*L,M*H},{P*H,P*H},{M*H,P*L}},
142: {{M*L,M*H},{P*L,M*L},{P*H,P*L},{M*H,P*H}}};
143: #undef G
144: #undef H
145: #undef L
146: #undef M
147: #undef P
149: #define HexExtract(x,i,j,k,n) do { \
150: (n)[0] = (x)[i][j][k]; \
151: (n)[1] = (x)[i+1][j][k]; \
152: (n)[2] = (x)[i+1][j+1][k]; \
153: (n)[3] = (x)[i][j+1][k]; \
154: (n)[4] = (x)[i][j][k+1]; \
155: (n)[5] = (x)[i+1][j][k+1]; \
156: (n)[6] = (x)[i+1][j+1][k+1]; \
157: (n)[7] = (x)[i][j+1][k+1]; \
158: } while (0)
160: #define HexExtractRef(x,i,j,k,n) do { \
161: (n)[0] = &(x)[i][j][k]; \
162: (n)[1] = &(x)[i+1][j][k]; \
163: (n)[2] = &(x)[i+1][j+1][k]; \
164: (n)[3] = &(x)[i][j+1][k]; \
165: (n)[4] = &(x)[i][j][k+1]; \
166: (n)[5] = &(x)[i+1][j][k+1]; \
167: (n)[6] = &(x)[i+1][j+1][k+1]; \
168: (n)[7] = &(x)[i][j+1][k+1]; \
169: } while (0)
171: #define QuadExtract(x,i,j,n) do { \
172: (n)[0] = (x)[i][j]; \
173: (n)[1] = (x)[i+1][j]; \
174: (n)[2] = (x)[i+1][j+1]; \
175: (n)[3] = (x)[i][j+1]; \
176: } while (0)
178: static PetscScalar Sqr(PetscScalar a) {return a*a;}
180: static void HexGrad(const PetscReal dphi[][3],const PetscReal zn[],PetscReal dz[])
181: {
182: PetscInt i;
183: dz[0] = dz[1] = dz[2] = 0;
184: for (i=0; i<8; i++) {
185: dz[0] += dphi[i][0] * zn[i];
186: dz[1] += dphi[i][1] * zn[i];
187: dz[2] += dphi[i][2] * zn[i];
188: }
189: }
191: static void HexComputeGeometry(PetscInt q,PetscReal hx,PetscReal hy,const PetscReal dz[restrict],PetscReal phi[restrict],PetscReal dphi[restrict][3],PetscReal *restrict jw)
192: {
193: const PetscReal jac[3][3] = {{hx/2,0,0}, {0,hy/2,0}, {dz[0],dz[1],dz[2]}};
194: 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]}};
195: const PetscReal jdet = jac[0][0]*jac[1][1]*jac[2][2];
196: PetscInt i;
198: for (i=0; i<8; i++) {
199: const PetscReal *dphir = HexQDeriv[q][i];
200: phi[i] = HexQInterp[q][i];
201: dphi[i][0] = dphir[0]*ijac[0][0] + dphir[1]*ijac[1][0] + dphir[2]*ijac[2][0];
202: dphi[i][1] = dphir[0]*ijac[0][1] + dphir[1]*ijac[1][1] + dphir[2]*ijac[2][1];
203: dphi[i][2] = dphir[0]*ijac[0][2] + dphir[1]*ijac[1][2] + dphir[2]*ijac[2][2];
204: }
205: *jw = 1.0 * jdet;
206: }
208: typedef struct _p_THI *THI;
209: typedef struct _n_Units *Units;
211: typedef struct {
212: PetscScalar u,v;
213: } Node;
215: typedef struct {
216: PetscScalar b; /* bed */
217: PetscScalar h; /* thickness */
218: PetscScalar beta2; /* friction */
219: } PrmNode;
221: typedef struct {
222: PetscReal min,max,cmin,cmax;
223: } PRange;
225: typedef enum {THIASSEMBLY_TRIDIAGONAL,THIASSEMBLY_FULL} THIAssemblyMode;
227: struct _p_THI {
228: PETSCHEADER(int);
229: void (*initialize)(THI,PetscReal x,PetscReal y,PrmNode *p);
230: PetscInt zlevels;
231: PetscReal Lx,Ly,Lz; /* Model domain */
232: PetscReal alpha; /* Bed angle */
233: Units units;
234: PetscReal dirichlet_scale;
235: PetscReal ssa_friction_scale;
236: PRange eta;
237: PRange beta2;
238: struct {
239: PetscReal Bd2,eps,exponent;
240: } viscosity;
241: struct {
242: PetscReal irefgam,eps2,exponent,refvel,epsvel;
243: } friction;
244: PetscReal rhog;
245: PetscBool no_slip;
246: PetscBool tridiagonal;
247: PetscBool coarse2d;
248: PetscBool verbose;
249: MatType mattype;
250: };
252: struct _n_Units {
253: /* fundamental */
254: PetscReal meter;
255: PetscReal kilogram;
256: PetscReal second;
257: /* derived */
258: PetscReal Pascal;
259: PetscReal year;
260: };
262: static PetscErrorCode THIJacobianLocal_3D_Full(DMDALocalInfo*,Node***,Mat,Mat,THI);
263: static PetscErrorCode THIJacobianLocal_3D_Tridiagonal(DMDALocalInfo*,Node***,Mat,Mat,THI);
264: static PetscErrorCode THIJacobianLocal_2D(DMDALocalInfo*,Node**,Mat,Mat,THI);
266: static void PrmHexGetZ(const PrmNode pn[],PetscInt k,PetscInt zm,PetscReal zn[])
267: {
268: const PetscScalar zm1 = zm-1,
269: znl[8] = {pn[0].b + pn[0].h*(PetscScalar)k/zm1,
270: pn[1].b + pn[1].h*(PetscScalar)k/zm1,
271: pn[2].b + pn[2].h*(PetscScalar)k/zm1,
272: pn[3].b + pn[3].h*(PetscScalar)k/zm1,
273: pn[0].b + pn[0].h*(PetscScalar)(k+1)/zm1,
274: pn[1].b + pn[1].h*(PetscScalar)(k+1)/zm1,
275: pn[2].b + pn[2].h*(PetscScalar)(k+1)/zm1,
276: pn[3].b + pn[3].h*(PetscScalar)(k+1)/zm1};
277: PetscInt i;
278: for (i=0; i<8; i++) zn[i] = PetscRealPart(znl[i]);
279: }
281: /* Tests A and C are from the ISMIP-HOM paper (Pattyn et al. 2008) */
282: static void THIInitialize_HOM_A(THI thi,PetscReal x,PetscReal y,PrmNode *p)
283: {
284: Units units = thi->units;
285: PetscReal s = -x*PetscSinReal(thi->alpha);
287: p->b = s - 1000*units->meter + 500*units->meter * PetscSinReal(x*2*PETSC_PI/thi->Lx) * PetscSinReal(y*2*PETSC_PI/thi->Ly);
288: p->h = s - p->b;
289: p->beta2 = 1e30;
290: }
292: static void THIInitialize_HOM_C(THI thi,PetscReal x,PetscReal y,PrmNode *p)
293: {
294: Units units = thi->units;
295: PetscReal s = -x*PetscSinReal(thi->alpha);
297: p->b = s - 1000*units->meter;
298: p->h = s - p->b;
299: /* tau_b = beta2 v is a stress (Pa) */
300: p->beta2 = 1000 * (1 + PetscSinReal(x*2*PETSC_PI/thi->Lx)*PetscSinReal(y*2*PETSC_PI/thi->Ly)) * units->Pascal * units->year / units->meter;
301: }
303: /* These are just toys */
305: /* Same bed as test A, free slip everywhere except for a discontinuous jump to a circular sticky region in the middle. */
306: static void THIInitialize_HOM_X(THI thi,PetscReal xx,PetscReal yy,PrmNode *p)
307: {
308: Units units = thi->units;
309: PetscReal x = xx*2*PETSC_PI/thi->Lx - PETSC_PI,y = yy*2*PETSC_PI/thi->Ly - PETSC_PI; /* [-pi,pi] */
310: PetscReal r = PetscSqrtReal(x*x + y*y),s = -x*PetscSinReal(thi->alpha);
311: p->b = s - 1000*units->meter + 500*units->meter*PetscSinReal(x + PETSC_PI) * PetscSinReal(y + PETSC_PI);
312: p->h = s - p->b;
313: p->beta2 = 1000 * (r < 1 ? 2 : 0) * units->Pascal * units->year / units->meter;
314: }
316: /* Like Z, but with 200 meter cliffs */
317: static void THIInitialize_HOM_Y(THI thi,PetscReal xx,PetscReal yy,PrmNode *p)
318: {
319: Units units = thi->units;
320: PetscReal x = xx*2*PETSC_PI/thi->Lx - PETSC_PI,y = yy*2*PETSC_PI/thi->Ly - PETSC_PI; /* [-pi,pi] */
321: PetscReal r = PetscSqrtReal(x*x + y*y),s = -x*PetscSinReal(thi->alpha);
323: p->b = s - 1000*units->meter + 500*units->meter * PetscSinReal(x + PETSC_PI) * PetscSinReal(y + PETSC_PI);
324: if (PetscRealPart(p->b) > -700*units->meter) p->b += 200*units->meter;
325: p->h = s - p->b;
326: 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;
327: }
329: /* Same bed as A, smoothly varying slipperiness, similar to MATLAB's "sombrero" (uncorrelated with bathymetry) */
330: static void THIInitialize_HOM_Z(THI thi,PetscReal xx,PetscReal yy,PrmNode *p)
331: {
332: Units units = thi->units;
333: PetscReal x = xx*2*PETSC_PI/thi->Lx - PETSC_PI,y = yy*2*PETSC_PI/thi->Ly - PETSC_PI; /* [-pi,pi] */
334: PetscReal r = PetscSqrtReal(x*x + y*y),s = -x*PetscSinReal(thi->alpha);
336: p->b = s - 1000*units->meter + 500*units->meter * PetscSinReal(x + PETSC_PI) * PetscSinReal(y + PETSC_PI);
337: p->h = s - p->b;
338: 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;
339: }
341: static void THIFriction(THI thi,PetscReal rbeta2,PetscReal gam,PetscReal *beta2,PetscReal *dbeta2)
342: {
343: if (thi->friction.irefgam == 0) {
344: Units units = thi->units;
345: thi->friction.irefgam = 1./(0.5*PetscSqr(thi->friction.refvel * units->meter / units->year));
346: thi->friction.eps2 = 0.5*PetscSqr(thi->friction.epsvel * units->meter / units->year) * thi->friction.irefgam;
347: }
348: if (thi->friction.exponent == 0) {
349: *beta2 = rbeta2;
350: *dbeta2 = 0;
351: } else {
352: *beta2 = rbeta2 * PetscPowReal(thi->friction.eps2 + gam*thi->friction.irefgam,thi->friction.exponent);
353: *dbeta2 = thi->friction.exponent * *beta2 / (thi->friction.eps2 + gam*thi->friction.irefgam) * thi->friction.irefgam;
354: }
355: }
357: static void THIViscosity(THI thi,PetscReal gam,PetscReal *eta,PetscReal *deta)
358: {
359: PetscReal Bd2,eps,exponent;
360: if (thi->viscosity.Bd2 == 0) {
361: Units units = thi->units;
362: const PetscReal
363: n = 3., /* Glen exponent */
364: p = 1. + 1./n, /* for Stokes */
365: A = 1.e-16 * PetscPowReal(units->Pascal,-n) / units->year, /* softness parameter (Pa^{-n}/s) */
366: B = PetscPowReal(A,-1./n); /* hardness parameter */
367: thi->viscosity.Bd2 = B/2;
368: thi->viscosity.exponent = (p-2)/2;
369: thi->viscosity.eps = 0.5*PetscSqr(1e-5 / units->year);
370: }
371: Bd2 = thi->viscosity.Bd2;
372: exponent = thi->viscosity.exponent;
373: eps = thi->viscosity.eps;
374: *eta = Bd2 * PetscPowReal(eps + gam,exponent);
375: *deta = exponent * (*eta) / (eps + gam);
376: }
378: static void RangeUpdate(PetscReal *min,PetscReal *max,PetscReal x)
379: {
380: if (x < *min) *min = x;
381: if (x > *max) *max = x;
382: }
384: static void PRangeClear(PRange *p)
385: {
386: p->cmin = p->min = 1e100;
387: p->cmax = p->max = -1e100;
388: }
392: static PetscErrorCode PRangeMinMax(PRange *p,PetscReal min,PetscReal max)
393: {
396: p->cmin = min;
397: p->cmax = max;
398: if (min < p->min) p->min = min;
399: if (max > p->max) p->max = max;
400: return(0);
401: }
405: static PetscErrorCode THIDestroy(THI *thi)
406: {
410: if (!*thi) return(0);
411: if (--((PetscObject)(*thi))->refct > 0) {*thi = 0; return(0);}
412: PetscFree((*thi)->units);
413: PetscFree((*thi)->mattype);
414: PetscHeaderDestroy(thi);
415: return(0);
416: }
420: static PetscErrorCode THICreate(MPI_Comm comm,THI *inthi)
421: {
422: static PetscBool registered = PETSC_FALSE;
423: THI thi;
424: Units units;
425: PetscErrorCode ierr;
428: *inthi = 0;
429: if (!registered) {
430: PetscClassIdRegister("Toy Hydrostatic Ice",&THI_CLASSID);
431: registered = PETSC_TRUE;
432: }
433: PetscHeaderCreate(thi,THI_CLASSID,"THI","Toy Hydrostatic Ice","",comm,THIDestroy,0);
435: PetscNew(&thi->units);
436: units = thi->units;
437: units->meter = 1e-2;
438: units->second = 1e-7;
439: units->kilogram = 1e-12;
441: PetscOptionsBegin(comm,NULL,"Scaled units options","");
442: {
443: PetscOptionsReal("-units_meter","1 meter in scaled length units","",units->meter,&units->meter,NULL);
444: PetscOptionsReal("-units_second","1 second in scaled time units","",units->second,&units->second,NULL);
445: PetscOptionsReal("-units_kilogram","1 kilogram in scaled mass units","",units->kilogram,&units->kilogram,NULL);
446: }
447: PetscOptionsEnd();
448: units->Pascal = units->kilogram / (units->meter * PetscSqr(units->second));
449: units->year = 31556926. * units->second, /* seconds per year */
451: thi->Lx = 10.e3;
452: thi->Ly = 10.e3;
453: thi->Lz = 1000;
454: thi->dirichlet_scale = 1;
455: thi->verbose = PETSC_FALSE;
457: PetscOptionsBegin(comm,NULL,"Toy Hydrostatic Ice options","");
458: {
459: QuadratureType quad = QUAD_GAUSS;
460: char homexp[] = "A";
461: char mtype[256] = MATSBAIJ;
462: PetscReal L,m = 1.0;
463: PetscBool flg;
464: L = thi->Lx;
465: PetscOptionsReal("-thi_L","Domain size (m)","",L,&L,&flg);
466: if (flg) thi->Lx = thi->Ly = L;
467: PetscOptionsReal("-thi_Lx","X Domain size (m)","",thi->Lx,&thi->Lx,NULL);
468: PetscOptionsReal("-thi_Ly","Y Domain size (m)","",thi->Ly,&thi->Ly,NULL);
469: PetscOptionsReal("-thi_Lz","Z Domain size (m)","",thi->Lz,&thi->Lz,NULL);
470: PetscOptionsString("-thi_hom","ISMIP-HOM experiment (A or C)","",homexp,homexp,sizeof(homexp),NULL);
471: switch (homexp[0] = toupper(homexp[0])) {
472: case 'A':
473: thi->initialize = THIInitialize_HOM_A;
474: thi->no_slip = PETSC_TRUE;
475: thi->alpha = 0.5;
476: break;
477: case 'C':
478: thi->initialize = THIInitialize_HOM_C;
479: thi->no_slip = PETSC_FALSE;
480: thi->alpha = 0.1;
481: break;
482: case 'X':
483: thi->initialize = THIInitialize_HOM_X;
484: thi->no_slip = PETSC_FALSE;
485: thi->alpha = 0.3;
486: break;
487: case 'Y':
488: thi->initialize = THIInitialize_HOM_Y;
489: thi->no_slip = PETSC_FALSE;
490: thi->alpha = 0.5;
491: break;
492: case 'Z':
493: thi->initialize = THIInitialize_HOM_Z;
494: thi->no_slip = PETSC_FALSE;
495: thi->alpha = 0.5;
496: break;
497: default:
498: SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"HOM experiment '%c' not implemented",homexp[0]);
499: }
500: PetscOptionsEnum("-thi_quadrature","Quadrature to use for 3D elements","",QuadratureTypes,(PetscEnum)quad,(PetscEnum*)&quad,NULL);
501: switch (quad) {
502: case QUAD_GAUSS:
503: HexQInterp = HexQInterp_Gauss;
504: HexQDeriv = HexQDeriv_Gauss;
505: break;
506: case QUAD_LOBATTO:
507: HexQInterp = HexQInterp_Lobatto;
508: HexQDeriv = HexQDeriv_Lobatto;
509: break;
510: }
511: PetscOptionsReal("-thi_alpha","Bed angle (degrees)","",thi->alpha,&thi->alpha,NULL);
513: thi->friction.refvel = 100.;
514: thi->friction.epsvel = 1.;
516: PetscOptionsReal("-thi_friction_refvel","Reference velocity for sliding","",thi->friction.refvel,&thi->friction.refvel,NULL);
517: PetscOptionsReal("-thi_friction_epsvel","Regularization velocity for sliding","",thi->friction.epsvel,&thi->friction.epsvel,NULL);
518: PetscOptionsReal("-thi_friction_m","Friction exponent, 0=Coulomb, 1=Navier","",m,&m,NULL);
520: thi->friction.exponent = (m-1)/2;
522: PetscOptionsReal("-thi_dirichlet_scale","Scale Dirichlet boundary conditions by this factor","",thi->dirichlet_scale,&thi->dirichlet_scale,NULL);
523: 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);
524: PetscOptionsBool("-thi_coarse2d","Use a 2D coarse space corresponding to SSA","",thi->coarse2d,&thi->coarse2d,NULL);
525: PetscOptionsBool("-thi_tridiagonal","Assemble a tridiagonal system (column coupling only) on the finest level","",thi->tridiagonal,&thi->tridiagonal,NULL);
526: PetscOptionsFList("-thi_mat_type","Matrix type","MatSetType",MatList,mtype,(char*)mtype,sizeof(mtype),NULL);
527: PetscStrallocpy(mtype,(char**)&thi->mattype);
528: PetscOptionsBool("-thi_verbose","Enable verbose output (like matrix sizes and statistics)","",thi->verbose,&thi->verbose,NULL);
529: }
530: PetscOptionsEnd();
532: /* dimensionalize */
533: thi->Lx *= units->meter;
534: thi->Ly *= units->meter;
535: thi->Lz *= units->meter;
536: thi->alpha *= PETSC_PI / 180;
538: PRangeClear(&thi->eta);
539: PRangeClear(&thi->beta2);
541: {
542: PetscReal u = 1000*units->meter/(3e7*units->second),
543: gradu = u / (100*units->meter),eta,deta,
544: rho = 910 * units->kilogram/PetscPowReal(units->meter,3),
545: grav = 9.81 * units->meter/PetscSqr(units->second),
546: driving = rho * grav * PetscSinReal(thi->alpha) * 1000*units->meter;
547: THIViscosity(thi,0.5*gradu*gradu,&eta,&deta);
548: thi->rhog = rho * grav;
549: if (thi->verbose) {
550: 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);
551: 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);
552: 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));
553: THIViscosity(thi,0.5*PetscSqr(1e-3*gradu),&eta,&deta);
554: 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));
555: }
556: }
558: *inthi = thi;
559: return(0);
560: }
564: static PetscErrorCode THIInitializePrm(THI thi,DM da2prm,Vec prm)
565: {
566: PrmNode **p;
567: PetscInt i,j,xs,xm,ys,ym,mx,my;
571: DMDAGetGhostCorners(da2prm,&ys,&xs,0,&ym,&xm,0);
572: DMDAGetInfo(da2prm,0, &my,&mx,0, 0,0,0, 0,0,0,0,0,0);
573: DMDAVecGetArray(da2prm,prm,&p);
574: for (i=xs; i<xs+xm; i++) {
575: for (j=ys; j<ys+ym; j++) {
576: PetscReal xx = thi->Lx*i/mx,yy = thi->Ly*j/my;
577: thi->initialize(thi,xx,yy,&p[i][j]);
578: }
579: }
580: DMDAVecRestoreArray(da2prm,prm,&p);
581: return(0);
582: }
586: static PetscErrorCode THISetUpDM(THI thi,DM dm)
587: {
588: PetscErrorCode ierr;
589: PetscInt refinelevel,coarsenlevel,level,dim,Mx,My,Mz,mx,my,s;
590: DMDAStencilType st;
591: DM da2prm;
592: Vec X;
595: DMDAGetInfo(dm,&dim, &Mz,&My,&Mx, 0,&my,&mx, 0,&s,0,0,0,&st);
596: if (dim == 2) {
597: DMDAGetInfo(dm,&dim, &My,&Mx,0, &my,&mx,0, 0,&s,0,0,0,&st);
598: }
599: DMGetRefineLevel(dm,&refinelevel);
600: DMGetCoarsenLevel(dm,&coarsenlevel);
601: level = refinelevel - coarsenlevel;
602: DMDACreate2d(PetscObjectComm((PetscObject)thi),DM_BOUNDARY_PERIODIC,DM_BOUNDARY_PERIODIC,st,My,Mx,my,mx,sizeof(PrmNode)/sizeof(PetscScalar),s,0,0,&da2prm);
603: DMCreateLocalVector(da2prm,&X);
604: {
605: PetscReal Lx = thi->Lx / thi->units->meter,Ly = thi->Ly / thi->units->meter,Lz = thi->Lz / thi->units->meter;
606: if (dim == 2) {
607: 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));
608: } else {
609: 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)));
610: }
611: }
612: THIInitializePrm(thi,da2prm,X);
613: if (thi->tridiagonal) { /* Reset coarse Jacobian evaluation */
614: DMDASNESSetJacobianLocal(dm,(DMDASNESJacobian)THIJacobianLocal_3D_Full,thi);
615: }
616: if (thi->coarse2d) {
617: DMDASNESSetJacobianLocal(dm,(DMDASNESJacobian)THIJacobianLocal_2D,thi);
618: }
619: PetscObjectCompose((PetscObject)dm,"DMDA2Prm",(PetscObject)da2prm);
620: PetscObjectCompose((PetscObject)dm,"DMDA2Prm_Vec",(PetscObject)X);
621: DMDestroy(&da2prm);
622: VecDestroy(&X);
623: return(0);
624: }
628: static PetscErrorCode DMCoarsenHook_THI(DM dmf,DM dmc,void *ctx)
629: {
630: THI thi = (THI)ctx;
632: PetscInt rlevel,clevel;
635: THISetUpDM(thi,dmc);
636: DMGetRefineLevel(dmc,&rlevel);
637: DMGetCoarsenLevel(dmc,&clevel);
638: if (rlevel-clevel == 0) {DMSetMatType(dmc,MATAIJ);}
639: DMCoarsenHookAdd(dmc,DMCoarsenHook_THI,NULL,thi);
640: return(0);
641: }
645: static PetscErrorCode DMRefineHook_THI(DM dmc,DM dmf,void *ctx)
646: {
647: THI thi = (THI)ctx;
651: THISetUpDM(thi,dmf);
652: DMSetMatType(dmf,thi->mattype);
653: DMRefineHookAdd(dmf,DMRefineHook_THI,NULL,thi);
654: /* With grid sequencing, a formerly-refined DM will later be coarsened by PCSetUp_MG */
655: DMCoarsenHookAdd(dmf,DMCoarsenHook_THI,NULL,thi);
656: return(0);
657: }
661: static PetscErrorCode THIDAGetPrm(DM da,PrmNode ***prm)
662: {
664: DM da2prm;
665: Vec X;
668: PetscObjectQuery((PetscObject)da,"DMDA2Prm",(PetscObject*)&da2prm);
669: if (!da2prm) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"No DMDA2Prm composed with given DMDA");
670: PetscObjectQuery((PetscObject)da,"DMDA2Prm_Vec",(PetscObject*)&X);
671: if (!X) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"No DMDA2Prm_Vec composed with given DMDA");
672: DMDAVecGetArray(da2prm,X,prm);
673: return(0);
674: }
678: static PetscErrorCode THIDARestorePrm(DM da,PrmNode ***prm)
679: {
681: DM da2prm;
682: Vec X;
685: PetscObjectQuery((PetscObject)da,"DMDA2Prm",(PetscObject*)&da2prm);
686: if (!da2prm) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"No DMDA2Prm composed with given DMDA");
687: PetscObjectQuery((PetscObject)da,"DMDA2Prm_Vec",(PetscObject*)&X);
688: if (!X) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"No DMDA2Prm_Vec composed with given DMDA");
689: DMDAVecRestoreArray(da2prm,X,prm);
690: return(0);
691: }
695: static PetscErrorCode THIInitial(SNES snes,Vec X,void *ctx)
696: {
697: THI thi;
698: PetscInt i,j,k,xs,xm,ys,ym,zs,zm,mx,my;
699: PetscReal hx,hy;
700: PrmNode **prm;
701: Node ***x;
703: DM da;
706: SNESGetDM(snes,&da);
707: DMGetApplicationContext(da,&thi);
708: DMDAGetInfo(da,0, 0,&my,&mx, 0,0,0, 0,0,0,0,0,0);
709: DMDAGetCorners(da,&zs,&ys,&xs,&zm,&ym,&xm);
710: DMDAVecGetArray(da,X,&x);
711: THIDAGetPrm(da,&prm);
712: hx = thi->Lx / mx;
713: hy = thi->Ly / my;
714: for (i=xs; i<xs+xm; i++) {
715: for (j=ys; j<ys+ym; j++) {
716: for (k=zs; k<zs+zm; k++) {
717: const PetscScalar zm1 = zm-1,
718: 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),
719: 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);
720: x[i][j][k].u = 0. * drivingx * prm[i][j].h*(PetscScalar)k/zm1;
721: x[i][j][k].v = 0. * drivingy * prm[i][j].h*(PetscScalar)k/zm1;
722: }
723: }
724: }
725: DMDAVecRestoreArray(da,X,&x);
726: THIDARestorePrm(da,&prm);
727: return(0);
728: }
730: 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)
731: {
732: PetscInt l,ll;
733: PetscScalar gam;
735: du[0] = du[1] = du[2] = 0;
736: dv[0] = dv[1] = dv[2] = 0;
737: *u = 0;
738: *v = 0;
739: for (l=0; l<8; l++) {
740: *u += phi[l] * n[l].u;
741: *v += phi[l] * n[l].v;
742: for (ll=0; ll<3; ll++) {
743: du[ll] += dphi[l][ll] * n[l].u;
744: dv[ll] += dphi[l][ll] * n[l].v;
745: }
746: }
747: 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]);
748: THIViscosity(thi,PetscRealPart(gam),eta,deta);
749: }
751: 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)
752: {
753: PetscInt l,ll;
754: PetscScalar gam;
756: du[0] = du[1] = 0;
757: dv[0] = dv[1] = 0;
758: *u = 0;
759: *v = 0;
760: for (l=0; l<4; l++) {
761: *u += phi[l] * n[l].u;
762: *v += phi[l] * n[l].v;
763: for (ll=0; ll<2; ll++) {
764: du[ll] += dphi[l][ll] * n[l].u;
765: dv[ll] += dphi[l][ll] * n[l].v;
766: }
767: }
768: gam = Sqr(du[0]) + Sqr(dv[1]) + du[0]*dv[1] + 0.25*Sqr(du[1]+dv[0]);
769: THIViscosity(thi,PetscRealPart(gam),eta,deta);
770: }
774: static PetscErrorCode THIFunctionLocal(DMDALocalInfo *info,Node ***x,Node ***f,THI thi)
775: {
776: PetscInt xs,ys,xm,ym,zm,i,j,k,q,l;
777: PetscReal hx,hy,etamin,etamax,beta2min,beta2max;
778: PrmNode **prm;
782: xs = info->zs;
783: ys = info->ys;
784: xm = info->zm;
785: ym = info->ym;
786: zm = info->xm;
787: hx = thi->Lx / info->mz;
788: hy = thi->Ly / info->my;
790: etamin = 1e100;
791: etamax = 0;
792: beta2min = 1e100;
793: beta2max = 0;
795: THIDAGetPrm(info->da,&prm);
797: for (i=xs; i<xs+xm; i++) {
798: for (j=ys; j<ys+ym; j++) {
799: PrmNode pn[4];
800: QuadExtract(prm,i,j,pn);
801: for (k=0; k<zm-1; k++) {
802: PetscInt ls = 0;
803: Node n[8],*fn[8];
804: PetscReal zn[8],etabase = 0;
805: PrmHexGetZ(pn,k,zm,zn);
806: HexExtract(x,i,j,k,n);
807: HexExtractRef(f,i,j,k,fn);
808: if (thi->no_slip && k == 0) {
809: for (l=0; l<4; l++) n[l].u = n[l].v = 0;
810: /* The first 4 basis functions lie on the bottom layer, so their contribution is exactly 0, hence we can skip them */
811: ls = 4;
812: }
813: for (q=0; q<8; q++) {
814: PetscReal dz[3],phi[8],dphi[8][3],jw,eta,deta;
815: PetscScalar du[3],dv[3],u,v;
816: HexGrad(HexQDeriv[q],zn,dz);
817: HexComputeGeometry(q,hx,hy,dz,phi,dphi,&jw);
818: PointwiseNonlinearity(thi,n,phi,dphi,&u,&v,du,dv,&eta,&deta);
819: jw /= thi->rhog; /* scales residuals to be O(1) */
820: if (q == 0) etabase = eta;
821: RangeUpdate(&etamin,&etamax,eta);
822: for (l=ls; l<8; l++) { /* test functions */
823: const PetscReal ds[2] = {-PetscSinReal(thi->alpha),0};
824: const PetscReal pp = phi[l],*dp = dphi[l];
825: 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];
826: 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];
827: }
828: }
829: if (k == 0) { /* we are on a bottom face */
830: if (thi->no_slip) {
831: /* Note: Non-Galerkin coarse grid operators are very sensitive to the scaling of Dirichlet boundary
832: * conditions. After shenanigans above, etabase contains the effective viscosity at the closest quadrature
833: * point to the bed. We want the diagonal entry in the Dirichlet condition to have similar magnitude to the
834: * diagonal entry corresponding to the adjacent node. The fundamental scaling of the viscous part is in
835: * diagu, diagv below. This scaling is easy to recognize by considering the finite difference operator after
836: * scaling by element size. The no-slip Dirichlet condition is scaled by this factor, and also in the
837: * assembled matrix (see the similar block in THIJacobianLocal).
838: *
839: * Note that the residual at this Dirichlet node is linear in the state at this node, but also depends
840: * (nonlinearly in general) on the neighboring interior nodes through the local viscosity. This will make
841: * a matrix-free Jacobian have extra entries in the corresponding row. We assemble only the diagonal part,
842: * so the solution will exactly satisfy the boundary condition after the first linear iteration.
843: */
844: const PetscReal hz = PetscRealPart(pn[0].h)/(zm-1.);
845: 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);
846: fn[0]->u = thi->dirichlet_scale*diagu*x[i][j][k].u;
847: fn[0]->v = thi->dirichlet_scale*diagv*x[i][j][k].v;
848: } else { /* Integrate over bottom face to apply boundary condition */
849: for (q=0; q<4; q++) {
850: const PetscReal jw = 0.25*hx*hy/thi->rhog,*phi = QuadQInterp[q];
851: PetscScalar u =0,v=0,rbeta2=0;
852: PetscReal beta2,dbeta2;
853: for (l=0; l<4; l++) {
854: u += phi[l]*n[l].u;
855: v += phi[l]*n[l].v;
856: rbeta2 += phi[l]*pn[l].beta2;
857: }
858: THIFriction(thi,PetscRealPart(rbeta2),PetscRealPart(u*u+v*v)/2,&beta2,&dbeta2);
859: RangeUpdate(&beta2min,&beta2max,beta2);
860: for (l=0; l<4; l++) {
861: const PetscReal pp = phi[l];
862: fn[ls+l]->u += pp*jw*beta2*u;
863: fn[ls+l]->v += pp*jw*beta2*v;
864: }
865: }
866: }
867: }
868: }
869: }
870: }
872: THIDARestorePrm(info->da,&prm);
874: PRangeMinMax(&thi->eta,etamin,etamax);
875: PRangeMinMax(&thi->beta2,beta2min,beta2max);
876: return(0);
877: }
881: static PetscErrorCode THIMatrixStatistics(THI thi,Mat B,PetscViewer viewer)
882: {
884: PetscReal nrm;
885: PetscInt m;
886: PetscMPIInt rank;
889: MatNorm(B,NORM_FROBENIUS,&nrm);
890: MatGetSize(B,&m,0);
891: MPI_Comm_rank(PetscObjectComm((PetscObject)B),&rank);
892: if (!rank) {
893: PetscScalar val0,val2;
894: MatGetValue(B,0,0,&val0);
895: MatGetValue(B,2,2,&val2);
896: 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);
897: }
898: return(0);
899: }
903: static PetscErrorCode THISurfaceStatistics(DM da,Vec X,PetscReal *min,PetscReal *max,PetscReal *mean)
904: {
906: Node ***x;
907: PetscInt i,j,xs,ys,zs,xm,ym,zm,mx,my,mz;
908: PetscReal umin = 1e100,umax=-1e100;
909: PetscScalar usum = 0.0,gusum;
912: *min = *max = *mean = 0;
913: DMDAGetInfo(da,0, &mz,&my,&mx, 0,0,0, 0,0,0,0,0,0);
914: DMDAGetCorners(da,&zs,&ys,&xs,&zm,&ym,&xm);
915: if (zs != 0 || zm != mz) SETERRQ(PETSC_COMM_SELF,1,"Unexpected decomposition");
916: DMDAVecGetArray(da,X,&x);
917: for (i=xs; i<xs+xm; i++) {
918: for (j=ys; j<ys+ym; j++) {
919: PetscReal u = PetscRealPart(x[i][j][zm-1].u);
920: RangeUpdate(&umin,&umax,u);
921: usum += u;
922: }
923: }
924: DMDAVecRestoreArray(da,X,&x);
925: MPI_Allreduce(&umin,min,1,MPIU_REAL,MPIU_MIN,PetscObjectComm((PetscObject)da));
926: MPI_Allreduce(&umax,max,1,MPIU_REAL,MPIU_MAX,PetscObjectComm((PetscObject)da));
927: MPI_Allreduce(&usum,&gusum,1,MPIU_SCALAR,MPIU_SUM,PetscObjectComm((PetscObject)da));
928: *mean = PetscRealPart(gusum) / (mx*my);
929: return(0);
930: }
934: static PetscErrorCode THISolveStatistics(THI thi,SNES snes,PetscInt coarsened,const char name[])
935: {
936: MPI_Comm comm;
937: Vec X;
938: DM dm;
942: PetscObjectGetComm((PetscObject)thi,&comm);
943: SNESGetSolution(snes,&X);
944: SNESGetDM(snes,&dm);
945: PetscPrintf(comm,"Solution statistics after solve: %s\n",name);
946: {
947: PetscInt its,lits;
948: SNESConvergedReason reason;
949: SNESGetIterationNumber(snes,&its);
950: SNESGetConvergedReason(snes,&reason);
951: SNESGetLinearSolveIterations(snes,&lits);
952: PetscPrintf(comm,"%s: Number of SNES iterations = %D, total linear iterations = %D\n",SNESConvergedReasons[reason],its,lits);
953: }
954: {
955: PetscReal nrm2,tmin[3]={1e100,1e100,1e100},tmax[3]={-1e100,-1e100,-1e100},min[3],max[3];
956: PetscInt i,j,m;
957: const PetscScalar *x;
958: VecNorm(X,NORM_2,&nrm2);
959: VecGetLocalSize(X,&m);
960: VecGetArrayRead(X,&x);
961: for (i=0; i<m; i+=2) {
962: PetscReal u = PetscRealPart(x[i]),v = PetscRealPart(x[i+1]),c = PetscSqrtReal(u*u+v*v);
963: tmin[0] = PetscMin(u,tmin[0]);
964: tmin[1] = PetscMin(v,tmin[1]);
965: tmin[2] = PetscMin(c,tmin[2]);
966: tmax[0] = PetscMax(u,tmax[0]);
967: tmax[1] = PetscMax(v,tmax[1]);
968: tmax[2] = PetscMax(c,tmax[2]);
969: }
970: VecRestoreArrayRead(X,&x);
971: MPI_Allreduce(tmin,min,3,MPIU_REAL,MPIU_MIN,PetscObjectComm((PetscObject)thi));
972: MPI_Allreduce(tmax,max,3,MPIU_REAL,MPIU_MAX,PetscObjectComm((PetscObject)thi));
973: /* Dimensionalize to meters/year */
974: nrm2 *= thi->units->year / thi->units->meter;
975: for (j=0; j<3; j++) {
976: min[j] *= thi->units->year / thi->units->meter;
977: max[j] *= thi->units->year / thi->units->meter;
978: }
979: 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]);
980: {
981: PetscReal umin,umax,umean;
982: THISurfaceStatistics(dm,X,&umin,&umax,&umean);
983: umin *= thi->units->year / thi->units->meter;
984: umax *= thi->units->year / thi->units->meter;
985: umean *= thi->units->year / thi->units->meter;
986: PetscPrintf(comm,"Surface statistics: u in [%12.6e, %12.6e] mean %12.6e\n",(double)umin,(double)umax,(double)umean);
987: }
988: /* These values stay nondimensional */
989: 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);
990: 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);
991: }
992: return(0);
993: }
997: static PetscErrorCode THIJacobianLocal_2D(DMDALocalInfo *info,Node **x,Mat J,Mat B,THI thi)
998: {
999: PetscInt xs,ys,xm,ym,i,j,q,l,ll;
1000: PetscReal hx,hy;
1001: PrmNode **prm;
1005: xs = info->ys;
1006: ys = info->xs;
1007: xm = info->ym;
1008: ym = info->xm;
1009: hx = thi->Lx / info->my;
1010: hy = thi->Ly / info->mx;
1012: MatZeroEntries(B);
1013: THIDAGetPrm(info->da,&prm);
1015: for (i=xs; i<xs+xm; i++) {
1016: for (j=ys; j<ys+ym; j++) {
1017: Node n[4];
1018: PrmNode pn[4];
1019: PetscScalar Ke[4*2][4*2];
1020: QuadExtract(prm,i,j,pn);
1021: QuadExtract(x,i,j,n);
1022: PetscMemzero(Ke,sizeof(Ke));
1023: for (q=0; q<4; q++) {
1024: PetscReal phi[4],dphi[4][2],jw,eta,deta,beta2,dbeta2;
1025: PetscScalar u,v,du[2],dv[2],h = 0,rbeta2 = 0;
1026: for (l=0; l<4; l++) {
1027: phi[l] = QuadQInterp[q][l];
1028: dphi[l][0] = QuadQDeriv[q][l][0]*2./hx;
1029: dphi[l][1] = QuadQDeriv[q][l][1]*2./hy;
1030: h += phi[l] * pn[l].h;
1031: rbeta2 += phi[l] * pn[l].beta2;
1032: }
1033: jw = 0.25*hx*hy / thi->rhog; /* rhog is only scaling */
1034: PointwiseNonlinearity2D(thi,n,phi,dphi,&u,&v,du,dv,&eta,&deta);
1035: THIFriction(thi,PetscRealPart(rbeta2),PetscRealPart(u*u+v*v)/2,&beta2,&dbeta2);
1036: for (l=0; l<4; l++) {
1037: const PetscReal pp = phi[l],*dp = dphi[l];
1038: for (ll=0; ll<4; ll++) {
1039: const PetscReal ppl = phi[ll],*dpl = dphi[ll];
1040: PetscScalar dgdu,dgdv;
1041: dgdu = 2.*du[0]*dpl[0] + dv[1]*dpl[0] + 0.5*(du[1]+dv[0])*dpl[1];
1042: dgdv = 2.*dv[1]*dpl[1] + du[0]*dpl[1] + 0.5*(du[1]+dv[0])*dpl[0];
1043: /* Picard part */
1044: 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;
1045: Ke[l*2+0][ll*2+1] += dp[0]*jw*eta*2.*dpl[1] + dp[1]*jw*eta*dpl[0];
1046: Ke[l*2+1][ll*2+0] += dp[1]*jw*eta*2.*dpl[0] + dp[0]*jw*eta*dpl[1];
1047: 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;
1048: /* extra Newton terms */
1049: 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;
1050: 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;
1051: 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;
1052: 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;
1053: }
1054: }
1055: }
1056: {
1057: const MatStencil rc[4] = {{0,i,j,0},{0,i+1,j,0},{0,i+1,j+1,0},{0,i,j+1,0}};
1058: MatSetValuesBlockedStencil(B,4,rc,4,rc,&Ke[0][0],ADD_VALUES);
1059: }
1060: }
1061: }
1062: THIDARestorePrm(info->da,&prm);
1064: MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
1065: MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
1066: MatSetOption(B,MAT_SYMMETRIC,PETSC_TRUE);
1067: if (thi->verbose) {THIMatrixStatistics(thi,B,PETSC_VIEWER_STDOUT_WORLD);}
1068: return(0);
1069: }
1073: static PetscErrorCode THIJacobianLocal_3D(DMDALocalInfo *info,Node ***x,Mat B,THI thi,THIAssemblyMode amode)
1074: {
1075: PetscInt xs,ys,xm,ym,zm,i,j,k,q,l,ll;
1076: PetscReal hx,hy;
1077: PrmNode **prm;
1081: xs = info->zs;
1082: ys = info->ys;
1083: xm = info->zm;
1084: ym = info->ym;
1085: zm = info->xm;
1086: hx = thi->Lx / info->mz;
1087: hy = thi->Ly / info->my;
1089: MatZeroEntries(B);
1090: THIDAGetPrm(info->da,&prm);
1092: for (i=xs; i<xs+xm; i++) {
1093: for (j=ys; j<ys+ym; j++) {
1094: PrmNode pn[4];
1095: QuadExtract(prm,i,j,pn);
1096: for (k=0; k<zm-1; k++) {
1097: Node n[8];
1098: PetscReal zn[8],etabase = 0;
1099: PetscScalar Ke[8*2][8*2];
1100: PetscInt ls = 0;
1102: PrmHexGetZ(pn,k,zm,zn);
1103: HexExtract(x,i,j,k,n);
1104: PetscMemzero(Ke,sizeof(Ke));
1105: if (thi->no_slip && k == 0) {
1106: for (l=0; l<4; l++) n[l].u = n[l].v = 0;
1107: ls = 4;
1108: }
1109: for (q=0; q<8; q++) {
1110: PetscReal dz[3],phi[8],dphi[8][3],jw,eta,deta;
1111: PetscScalar du[3],dv[3],u,v;
1112: HexGrad(HexQDeriv[q],zn,dz);
1113: HexComputeGeometry(q,hx,hy,dz,phi,dphi,&jw);
1114: PointwiseNonlinearity(thi,n,phi,dphi,&u,&v,du,dv,&eta,&deta);
1115: jw /= thi->rhog; /* residuals are scaled by this factor */
1116: if (q == 0) etabase = eta;
1117: for (l=ls; l<8; l++) { /* test functions */
1118: const PetscReal *restrict dp = dphi[l];
1119: #if USE_SSE2_KERNELS
1120: /* gcc (up to my 4.5 snapshot) is really bad at hoisting intrinsics so we do it manually */
1121: __m128d
1122: p4 = _mm_set1_pd(4),p2 = _mm_set1_pd(2),p05 = _mm_set1_pd(0.5),
1123: p42 = _mm_setr_pd(4,2),p24 = _mm_shuffle_pd(p42,p42,_MM_SHUFFLE2(0,1)),
1124: du0 = _mm_set1_pd(du[0]),du1 = _mm_set1_pd(du[1]),du2 = _mm_set1_pd(du[2]),
1125: dv0 = _mm_set1_pd(dv[0]),dv1 = _mm_set1_pd(dv[1]),dv2 = _mm_set1_pd(dv[2]),
1126: jweta = _mm_set1_pd(jw*eta),jwdeta = _mm_set1_pd(jw*deta),
1127: dp0 = _mm_set1_pd(dp[0]),dp1 = _mm_set1_pd(dp[1]),dp2 = _mm_set1_pd(dp[2]),
1128: dp0jweta = _mm_mul_pd(dp0,jweta),dp1jweta = _mm_mul_pd(dp1,jweta),dp2jweta = _mm_mul_pd(dp2,jweta),
1129: p4du0p2dv1 = _mm_add_pd(_mm_mul_pd(p4,du0),_mm_mul_pd(p2,dv1)), /* 4 du0 + 2 dv1 */
1130: p4dv1p2du0 = _mm_add_pd(_mm_mul_pd(p4,dv1),_mm_mul_pd(p2,du0)), /* 4 dv1 + 2 du0 */
1131: pdu2dv2 = _mm_unpacklo_pd(du2,dv2), /* [du2, dv2] */
1132: du1pdv0 = _mm_add_pd(du1,dv0), /* du1 + dv0 */
1133: t1 = _mm_mul_pd(dp0,p4du0p2dv1), /* dp0 (4 du0 + 2 dv1) */
1134: t2 = _mm_mul_pd(dp1,p4dv1p2du0); /* dp1 (4 dv1 + 2 du0) */
1136: #endif
1137: #if defined COMPUTE_LOWER_TRIANGULAR /* The element matrices are always symmetric so computing the lower-triangular part is not necessary */
1138: for (ll=ls; ll<8; ll++) { /* trial functions */
1139: #else
1140: for (ll=l; ll<8; ll++) {
1141: #endif
1142: const PetscReal *restrict dpl = dphi[ll];
1143: if (amode == THIASSEMBLY_TRIDIAGONAL && (l-ll)%4) continue; /* these entries would not be inserted */
1144: #if !USE_SSE2_KERNELS
1145: /* The analytic Jacobian in nice, easy-to-read form */
1146: {
1147: PetscScalar dgdu,dgdv;
1148: dgdu = 2.*du[0]*dpl[0] + dv[1]*dpl[0] + 0.5*(du[1]+dv[0])*dpl[1] + 0.5*du[2]*dpl[2];
1149: dgdv = 2.*dv[1]*dpl[1] + du[0]*dpl[1] + 0.5*(du[1]+dv[0])*dpl[0] + 0.5*dv[2]*dpl[2];
1150: /* Picard part */
1151: 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];
1152: Ke[l*2+0][ll*2+1] += dp[0]*jw*eta*2.*dpl[1] + dp[1]*jw*eta*dpl[0];
1153: Ke[l*2+1][ll*2+0] += dp[1]*jw*eta*2.*dpl[0] + dp[0]*jw*eta*dpl[1];
1154: 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];
1155: /* extra Newton terms */
1156: 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];
1157: 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];
1158: 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];
1159: 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];
1160: }
1161: #else
1162: /* This SSE2 code is an exact replica of above, but uses explicit packed instructions for some speed
1163: * benefit. On my hardware, these intrinsics are almost twice as fast as above, reducing total assembly cost
1164: * by 25 to 30 percent. */
1165: {
1166: __m128d
1167: keu = _mm_loadu_pd(&Ke[l*2+0][ll*2+0]),
1168: kev = _mm_loadu_pd(&Ke[l*2+1][ll*2+0]),
1169: dpl01 = _mm_loadu_pd(&dpl[0]),dpl10 = _mm_shuffle_pd(dpl01,dpl01,_MM_SHUFFLE2(0,1)),dpl2 = _mm_set_sd(dpl[2]),
1170: t0,t3,pdgduv;
1171: keu = _mm_add_pd(keu,_mm_add_pd(_mm_mul_pd(_mm_mul_pd(dp0jweta,p42),dpl01),
1172: _mm_add_pd(_mm_mul_pd(dp1jweta,dpl10),
1173: _mm_mul_pd(dp2jweta,dpl2))));
1174: kev = _mm_add_pd(kev,_mm_add_pd(_mm_mul_pd(_mm_mul_pd(dp1jweta,p24),dpl01),
1175: _mm_add_pd(_mm_mul_pd(dp0jweta,dpl10),
1176: _mm_mul_pd(dp2jweta,_mm_shuffle_pd(dpl2,dpl2,_MM_SHUFFLE2(0,1))))));
1177: pdgduv = _mm_mul_pd(p05,_mm_add_pd(_mm_add_pd(_mm_mul_pd(p42,_mm_mul_pd(du0,dpl01)),
1178: _mm_mul_pd(p24,_mm_mul_pd(dv1,dpl01))),
1179: _mm_add_pd(_mm_mul_pd(du1pdv0,dpl10),
1180: _mm_mul_pd(pdu2dv2,_mm_set1_pd(dpl[2]))))); /* [dgdu, dgdv] */
1181: t0 = _mm_mul_pd(jwdeta,pdgduv); /* jw deta [dgdu, dgdv] */
1182: t3 = _mm_mul_pd(t0,du1pdv0); /* t0 (du1 + dv0) */
1183: _mm_storeu_pd(&Ke[l*2+0][ll*2+0],_mm_add_pd(keu,_mm_add_pd(_mm_mul_pd(t1,t0),
1184: _mm_add_pd(_mm_mul_pd(dp1,t3),
1185: _mm_mul_pd(t0,_mm_mul_pd(dp2,du2))))));
1186: _mm_storeu_pd(&Ke[l*2+1][ll*2+0],_mm_add_pd(kev,_mm_add_pd(_mm_mul_pd(t2,t0),
1187: _mm_add_pd(_mm_mul_pd(dp0,t3),
1188: _mm_mul_pd(t0,_mm_mul_pd(dp2,dv2))))));
1189: }
1190: #endif
1191: }
1192: }
1193: }
1194: if (k == 0) { /* on a bottom face */
1195: if (thi->no_slip) {
1196: const PetscReal hz = PetscRealPart(pn[0].h)/(zm-1);
1197: 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);
1198: Ke[0][0] = thi->dirichlet_scale*diagu;
1199: Ke[1][1] = thi->dirichlet_scale*diagv;
1200: } else {
1201: for (q=0; q<4; q++) {
1202: const PetscReal jw = 0.25*hx*hy/thi->rhog,*phi = QuadQInterp[q];
1203: PetscScalar u =0,v=0,rbeta2=0;
1204: PetscReal beta2,dbeta2;
1205: for (l=0; l<4; l++) {
1206: u += phi[l]*n[l].u;
1207: v += phi[l]*n[l].v;
1208: rbeta2 += phi[l]*pn[l].beta2;
1209: }
1210: THIFriction(thi,PetscRealPart(rbeta2),PetscRealPart(u*u+v*v)/2,&beta2,&dbeta2);
1211: for (l=0; l<4; l++) {
1212: const PetscReal pp = phi[l];
1213: for (ll=0; ll<4; ll++) {
1214: const PetscReal ppl = phi[ll];
1215: Ke[l*2+0][ll*2+0] += pp*jw*beta2*ppl + pp*jw*dbeta2*u*u*ppl;
1216: Ke[l*2+0][ll*2+1] += pp*jw*dbeta2*u*v*ppl;
1217: Ke[l*2+1][ll*2+0] += pp*jw*dbeta2*v*u*ppl;
1218: Ke[l*2+1][ll*2+1] += pp*jw*beta2*ppl + pp*jw*dbeta2*v*v*ppl;
1219: }
1220: }
1221: }
1222: }
1223: }
1224: {
1225: 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}};
1226: if (amode == THIASSEMBLY_TRIDIAGONAL) {
1227: for (l=0; l<4; l++) { /* Copy out each of the blocks, discarding horizontal coupling */
1228: const PetscInt l4 = l+4;
1229: const MatStencil rcl[2] = {{rc[l].k,rc[l].j,rc[l].i,0},{rc[l4].k,rc[l4].j,rc[l4].i,0}};
1230: #if defined COMPUTE_LOWER_TRIANGULAR
1231: 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]},
1232: {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]},
1233: {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]},
1234: {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]}};
1235: #else
1236: /* Same as above except for the lower-left block */
1237: 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]},
1238: {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]},
1239: {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]},
1240: {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]}};
1241: #endif
1242: MatSetValuesBlockedStencil(B,2,rcl,2,rcl,&Kel[0][0],ADD_VALUES);
1243: }
1244: } else {
1245: #if !defined COMPUTE_LOWER_TRIANGULAR /* fill in lower-triangular part, this is really cheap compared to computing the entries */
1246: for (l=0; l<8; l++) {
1247: for (ll=l+1; ll<8; ll++) {
1248: Ke[ll*2+0][l*2+0] = Ke[l*2+0][ll*2+0];
1249: Ke[ll*2+1][l*2+0] = Ke[l*2+0][ll*2+1];
1250: Ke[ll*2+0][l*2+1] = Ke[l*2+1][ll*2+0];
1251: Ke[ll*2+1][l*2+1] = Ke[l*2+1][ll*2+1];
1252: }
1253: }
1254: #endif
1255: MatSetValuesBlockedStencil(B,8,rc,8,rc,&Ke[0][0],ADD_VALUES);
1256: }
1257: }
1258: }
1259: }
1260: }
1261: THIDARestorePrm(info->da,&prm);
1263: MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
1264: MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
1265: MatSetOption(B,MAT_SYMMETRIC,PETSC_TRUE);
1266: if (thi->verbose) {THIMatrixStatistics(thi,B,PETSC_VIEWER_STDOUT_WORLD);}
1267: return(0);
1268: }
1272: static PetscErrorCode THIJacobianLocal_3D_Full(DMDALocalInfo *info,Node ***x,Mat A,Mat B,THI thi)
1273: {
1277: THIJacobianLocal_3D(info,x,B,thi,THIASSEMBLY_FULL);
1278: return(0);
1279: }
1283: static PetscErrorCode THIJacobianLocal_3D_Tridiagonal(DMDALocalInfo *info,Node ***x,Mat A,Mat B,THI thi)
1284: {
1288: THIJacobianLocal_3D(info,x,B,thi,THIASSEMBLY_TRIDIAGONAL);
1289: return(0);
1290: }
1294: static PetscErrorCode DMRefineHierarchy_THI(DM dac0,PetscInt nlevels,DM hierarchy[])
1295: {
1296: PetscErrorCode ierr;
1297: THI thi;
1298: PetscInt dim,M,N,m,n,s,dof;
1299: DM dac,daf;
1300: DMDAStencilType st;
1301: DM_DA *ddf,*ddc;
1304: PetscObjectQuery((PetscObject)dac0,"THI",(PetscObject*)&thi);
1305: if (!thi) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Cannot refine this DMDA, missing composed THI instance");
1306: if (nlevels > 1) {
1307: DMRefineHierarchy(dac0,nlevels-1,hierarchy);
1308: dac = hierarchy[nlevels-2];
1309: } else {
1310: dac = dac0;
1311: }
1312: DMDAGetInfo(dac,&dim, &N,&M,0, &n,&m,0, &dof,&s,0,0,0,&st);
1313: if (dim != 2) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"This function can only refine 2D DMDAs");
1315: /* Creates a 3D DMDA with the same map-plane layout as the 2D one, with contiguous columns */
1316: 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);
1318: daf->ops->creatematrix = dac->ops->creatematrix;
1319: daf->ops->createinterpolation = dac->ops->createinterpolation;
1320: daf->ops->getcoloring = dac->ops->getcoloring;
1321: ddf = (DM_DA*)daf->data;
1322: ddc = (DM_DA*)dac->data;
1323: ddf->interptype = ddc->interptype;
1325: DMDASetFieldName(daf,0,"x-velocity");
1326: DMDASetFieldName(daf,1,"y-velocity");
1328: hierarchy[nlevels-1] = daf;
1329: return(0);
1330: }
1334: static PetscErrorCode DMCreateInterpolation_DA_THI(DM dac,DM daf,Mat *A,Vec *scale)
1335: {
1337: PetscInt dim;
1344: DMDAGetInfo(daf,&dim,0,0,0,0,0,0,0,0,0,0,0,0);
1345: if (dim == 2) {
1346: /* We are in the 2D problem and use normal DMDA interpolation */
1347: DMCreateInterpolation(dac,daf,A,scale);
1348: } else {
1349: PetscInt i,j,k,xs,ys,zs,xm,ym,zm,mx,my,mz,rstart,cstart;
1350: Mat B;
1352: DMDAGetInfo(daf,0, &mz,&my,&mx, 0,0,0, 0,0,0,0,0,0);
1353: DMDAGetCorners(daf,&zs,&ys,&xs,&zm,&ym,&xm);
1354: if (zs != 0) SETERRQ(PETSC_COMM_SELF,1,"unexpected");
1355: MatCreate(PetscObjectComm((PetscObject)daf),&B);
1356: MatSetSizes(B,xm*ym*zm,xm*ym,mx*my*mz,mx*my);
1358: MatSetType(B,MATAIJ);
1359: MatSeqAIJSetPreallocation(B,1,NULL);
1360: MatMPIAIJSetPreallocation(B,1,NULL,0,NULL);
1361: MatGetOwnershipRange(B,&rstart,NULL);
1362: MatGetOwnershipRangeColumn(B,&cstart,NULL);
1363: for (i=xs; i<xs+xm; i++) {
1364: for (j=ys; j<ys+ym; j++) {
1365: for (k=zs; k<zs+zm; k++) {
1366: PetscInt i2 = i*ym+j,i3 = i2*zm+k;
1367: PetscScalar val = ((k == 0 || k == mz-1) ? 0.5 : 1.) / (mz-1.); /* Integration using trapezoid rule */
1368: MatSetValue(B,cstart+i3,rstart+i2,val,INSERT_VALUES);
1369: }
1370: }
1371: }
1372: MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
1373: MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
1374: MatCreateMAIJ(B,sizeof(Node)/sizeof(PetscScalar),A);
1375: MatDestroy(&B);
1376: }
1377: return(0);
1378: }
1382: static PetscErrorCode DMCreateMatrix_THI_Tridiagonal(DM da,Mat *J)
1383: {
1384: PetscErrorCode ierr;
1385: Mat A;
1386: PetscInt xm,ym,zm,dim,dof = 2,starts[3],dims[3];
1387: ISLocalToGlobalMapping ltog;
1390: DMDAGetInfo(da,&dim, 0,0,0, 0,0,0, 0,0,0,0,0,0);
1391: if (dim != 3) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Expected DMDA to be 3D");
1392: DMDAGetCorners(da,0,0,0,&zm,&ym,&xm);
1393: DMGetLocalToGlobalMapping(da,<og);
1394: MatCreate(PetscObjectComm((PetscObject)da),&A);
1395: MatSetSizes(A,dof*xm*ym*zm,dof*xm*ym*zm,PETSC_DETERMINE,PETSC_DETERMINE);
1396: MatSetType(A,da->mattype);
1397: MatSetFromOptions(A);
1398: MatSeqAIJSetPreallocation(A,3*2,NULL);
1399: MatMPIAIJSetPreallocation(A,3*2,NULL,0,NULL);
1400: MatSeqBAIJSetPreallocation(A,2,3,NULL);
1401: MatMPIBAIJSetPreallocation(A,2,3,NULL,0,NULL);
1402: MatSeqSBAIJSetPreallocation(A,2,2,NULL);
1403: MatMPISBAIJSetPreallocation(A,2,2,NULL,0,NULL);
1404: MatSetLocalToGlobalMapping(A,ltog,ltog);
1405: DMDAGetGhostCorners(da,&starts[0],&starts[1],&starts[2],&dims[0],&dims[1],&dims[2]);
1406: MatSetStencil(A,dim,dims,starts,dof);
1407: *J = A;
1408: return(0);
1409: }
1413: static PetscErrorCode THIDAVecView_VTK_XML(THI thi,DM da,Vec X,const char filename[])
1414: {
1415: const PetscInt dof = 2;
1416: Units units = thi->units;
1417: MPI_Comm comm;
1418: PetscErrorCode ierr;
1419: PetscViewer viewer;
1420: PetscMPIInt rank,size,tag,nn,nmax;
1421: PetscInt mx,my,mz,r,range[6];
1422: const PetscScalar *x;
1425: PetscObjectGetComm((PetscObject)thi,&comm);
1426: DMDAGetInfo(da,0, &mz,&my,&mx, 0,0,0, 0,0,0,0,0,0);
1427: MPI_Comm_size(comm,&size);
1428: MPI_Comm_rank(comm,&rank);
1429: PetscViewerASCIIOpen(comm,filename,&viewer);
1430: PetscViewerASCIIPrintf(viewer,"<VTKFile type=\"StructuredGrid\" version=\"0.1\" byte_order=\"LittleEndian\">\n");
1431: PetscViewerASCIIPrintf(viewer," <StructuredGrid WholeExtent=\"%d %D %d %D %d %D\">\n",0,mz-1,0,my-1,0,mx-1);
1433: DMDAGetCorners(da,range,range+1,range+2,range+3,range+4,range+5);
1434: PetscMPIIntCast(range[3]*range[4]*range[5]*dof,&nn);
1435: MPI_Reduce(&nn,&nmax,1,MPI_INT,MPI_MAX,0,comm);
1436: tag = ((PetscObject) viewer)->tag;
1437: VecGetArrayRead(X,&x);
1438: if (!rank) {
1439: PetscScalar *array;
1440: PetscMalloc1(nmax,&array);
1441: for (r=0; r<size; r++) {
1442: PetscInt i,j,k,xs,xm,ys,ym,zs,zm;
1443: const PetscScalar *ptr;
1444: MPI_Status status;
1445: if (r) {
1446: MPI_Recv(range,6,MPIU_INT,r,tag,comm,MPI_STATUS_IGNORE);
1447: }
1448: zs = range[0];ys = range[1];xs = range[2];zm = range[3];ym = range[4];xm = range[5];
1449: if (xm*ym*zm*dof > nmax) SETERRQ(PETSC_COMM_SELF,1,"should not happen");
1450: if (r) {
1451: MPI_Recv(array,nmax,MPIU_SCALAR,r,tag,comm,&status);
1452: MPI_Get_count(&status,MPIU_SCALAR,&nn);
1453: if (nn != xm*ym*zm*dof) SETERRQ(PETSC_COMM_SELF,1,"should not happen");
1454: ptr = array;
1455: } else ptr = x;
1456: PetscViewerASCIIPrintf(viewer," <Piece Extent=\"%D %D %D %D %D %D\">\n",zs,zs+zm-1,ys,ys+ym-1,xs,xs+xm-1);
1458: PetscViewerASCIIPrintf(viewer," <Points>\n");
1459: PetscViewerASCIIPrintf(viewer," <DataArray type=\"Float32\" NumberOfComponents=\"3\" format=\"ascii\">\n");
1460: for (i=xs; i<xs+xm; i++) {
1461: for (j=ys; j<ys+ym; j++) {
1462: for (k=zs; k<zs+zm; k++) {
1463: PrmNode p;
1464: PetscReal xx = thi->Lx*i/mx,yy = thi->Ly*j/my,zz;
1465: thi->initialize(thi,xx,yy,&p);
1466: zz = PetscRealPart(p.b) + PetscRealPart(p.h)*k/(mz-1);
1467: PetscViewerASCIIPrintf(viewer,"%f %f %f\n",(double)xx,(double)yy,(double)zz);
1468: }
1469: }
1470: }
1471: PetscViewerASCIIPrintf(viewer," </DataArray>\n");
1472: PetscViewerASCIIPrintf(viewer," </Points>\n");
1474: PetscViewerASCIIPrintf(viewer," <PointData>\n");
1475: PetscViewerASCIIPrintf(viewer," <DataArray type=\"Float32\" Name=\"velocity\" NumberOfComponents=\"3\" format=\"ascii\">\n");
1476: for (i=0; i<nn; i+=dof) {
1477: 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);
1478: }
1479: PetscViewerASCIIPrintf(viewer," </DataArray>\n");
1481: PetscViewerASCIIPrintf(viewer," <DataArray type=\"Int32\" Name=\"rank\" NumberOfComponents=\"1\" format=\"ascii\">\n");
1482: for (i=0; i<nn; i+=dof) {
1483: PetscViewerASCIIPrintf(viewer,"%D\n",r);
1484: }
1485: PetscViewerASCIIPrintf(viewer," </DataArray>\n");
1486: PetscViewerASCIIPrintf(viewer," </PointData>\n");
1488: PetscViewerASCIIPrintf(viewer," </Piece>\n");
1489: }
1490: PetscFree(array);
1491: } else {
1492: MPI_Send(range,6,MPIU_INT,0,tag,comm);
1493: MPI_Send((PetscScalar*)x,nn,MPIU_SCALAR,0,tag,comm);
1494: }
1495: VecRestoreArrayRead(X,&x);
1496: PetscViewerASCIIPrintf(viewer," </StructuredGrid>\n");
1497: PetscViewerASCIIPrintf(viewer,"</VTKFile>\n");
1498: PetscViewerDestroy(&viewer);
1499: return(0);
1500: }
1504: int main(int argc,char *argv[])
1505: {
1506: MPI_Comm comm;
1507: THI thi;
1509: DM da;
1510: SNES snes;
1512: PetscInitialize(&argc,&argv,0,help);
1513: comm = PETSC_COMM_WORLD;
1515: THICreate(comm,&thi);
1516: {
1517: PetscInt M = 3,N = 3,P = 2;
1518: PetscOptionsBegin(comm,NULL,"Grid resolution options","");
1519: {
1520: PetscOptionsInt("-M","Number of elements in x-direction on coarse level","",M,&M,NULL);
1521: N = M;
1522: PetscOptionsInt("-N","Number of elements in y-direction on coarse level (if different from M)","",N,&N,NULL);
1523: if (thi->coarse2d) {
1524: PetscOptionsInt("-zlevels","Number of elements in z-direction on fine level","",thi->zlevels,&thi->zlevels,NULL);
1525: } else {
1526: PetscOptionsInt("-P","Number of elements in z-direction on coarse level","",P,&P,NULL);
1527: }
1528: }
1529: PetscOptionsEnd();
1530: if (thi->coarse2d) {
1531: 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);
1533: da->ops->refinehierarchy = DMRefineHierarchy_THI;
1534: da->ops->createinterpolation = DMCreateInterpolation_DA_THI;
1536: PetscObjectCompose((PetscObject)da,"THI",(PetscObject)thi);
1537: } else {
1538: 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);
1539: }
1540: DMDASetFieldName(da,0,"x-velocity");
1541: DMDASetFieldName(da,1,"y-velocity");
1542: }
1543: THISetUpDM(thi,da);
1544: if (thi->tridiagonal) da->ops->creatematrix = DMCreateMatrix_THI_Tridiagonal;
1546: { /* Set the fine level matrix type if -da_refine */
1547: PetscInt rlevel,clevel;
1548: DMGetRefineLevel(da,&rlevel);
1549: DMGetCoarsenLevel(da,&clevel);
1550: if (rlevel - clevel > 0) {DMSetMatType(da,thi->mattype);}
1551: }
1553: DMDASNESSetFunctionLocal(da,ADD_VALUES,(DMDASNESFunction)THIFunctionLocal,thi);
1554: if (thi->tridiagonal) {
1555: DMDASNESSetJacobianLocal(da,(DMDASNESJacobian)THIJacobianLocal_3D_Tridiagonal,thi);
1556: } else {
1557: DMDASNESSetJacobianLocal(da,(DMDASNESJacobian)THIJacobianLocal_3D_Full,thi);
1558: }
1559: DMCoarsenHookAdd(da,DMCoarsenHook_THI,NULL,thi);
1560: DMRefineHookAdd(da,DMRefineHook_THI,NULL,thi);
1562: DMSetApplicationContext(da,thi);
1564: SNESCreate(comm,&snes);
1565: SNESSetDM(snes,da);
1566: DMDestroy(&da);
1567: SNESSetComputeInitialGuess(snes,THIInitial,NULL);
1568: SNESSetFromOptions(snes);
1570: SNESSolve(snes,NULL,NULL);
1572: THISolveStatistics(thi,snes,0,"Full");
1574: {
1575: PetscBool flg;
1576: char filename[PETSC_MAX_PATH_LEN] = "";
1577: PetscOptionsGetString(NULL,"-o",filename,sizeof(filename),&flg);
1578: if (flg) {
1579: Vec X;
1580: DM dm;
1581: SNESGetSolution(snes,&X);
1582: SNESGetDM(snes,&dm);
1583: THIDAVecView_VTK_XML(thi,dm,X,filename);
1584: }
1585: }
1587: DMDestroy(&da);
1588: SNESDestroy(&snes);
1589: THIDestroy(&thi);
1590: PetscFinalize();
1591: return 0;
1592: }