Actual source code: ex42.c
petsc-3.7.5 2017-01-01
1: static char help[] = "Solves the incompressible, variable viscosity stokes equation in 3d using Q1Q1 elements, \n\
2: stabilized with Bochev's polynomial projection method. Note that implementation here assumes \n\
3: all boundaries are free-slip, i.e. zero normal flow and zero tangential stress \n\
4: -mx : number elements in x-direction \n\
5: -my : number elements in y-direction \n\
6: -mz : number elements in z-direction \n\
7: -stokes_ksp_monitor_blocks : active monitor for each component u,v,w,p \n\
8: -model : defines viscosity and forcing function. Choose either: 0 (isoviscous), 1 (manufactured-broken), 2 (solcx-2d), 3 (sinker) \n";
10: /* Contributed by Dave May */
12: #include <petscksp.h>
13: #include <petscdmda.h>
15: #define PROFILE_TIMING
16: #define ASSEMBLE_LOWER_TRIANGULAR
18: #define NSD 3 /* number of spatial dimensions */
19: #define NODES_PER_EL 8 /* nodes per element */
20: #define U_DOFS 3 /* degrees of freedom per velocity node */
21: #define P_DOFS 1 /* degrees of freedom per pressure node */
22: #define GAUSS_POINTS 8
24: /* Gauss point based evaluation */
25: typedef struct {
26: PetscScalar gp_coords[NSD*GAUSS_POINTS];
27: PetscScalar eta[GAUSS_POINTS];
28: PetscScalar fx[GAUSS_POINTS];
29: PetscScalar fy[GAUSS_POINTS];
30: PetscScalar fz[GAUSS_POINTS];
31: PetscScalar hc[GAUSS_POINTS];
32: } GaussPointCoefficients;
34: typedef struct {
35: PetscScalar u_dof;
36: PetscScalar v_dof;
37: PetscScalar w_dof;
38: PetscScalar p_dof;
39: } StokesDOF;
41: typedef struct _p_CellProperties *CellProperties;
42: struct _p_CellProperties {
43: PetscInt ncells;
44: PetscInt mx,my,mz;
45: PetscInt sex,sey,sez;
46: GaussPointCoefficients *gpc;
47: };
49: static PetscErrorCode DMDAGetElementCorners(DM da,PetscInt *sx,PetscInt *sy,PetscInt *sz,PetscInt *mx,PetscInt *my,PetscInt *mz);
51: /* elements */
54: PetscErrorCode CellPropertiesCreate(DM da_stokes,CellProperties *C)
55: {
57: CellProperties cells;
58: PetscInt mx,my,mz,sex,sey,sez;
61: PetscMalloc(sizeof(struct _p_CellProperties),&cells);
63: DMDAGetElementCorners(da_stokes,&sex,&sey,&sez,&mx,&my,&mz);
65: cells->mx = mx;
66: cells->my = my;
67: cells->mz = mz;
68: cells->ncells = mx * my * mz;
69: cells->sex = sex;
70: cells->sey = sey;
71: cells->sez = sez;
73: PetscMalloc1(mx*my*mz,&cells->gpc);
75: *C = cells;
76: return(0);
77: }
81: PetscErrorCode CellPropertiesDestroy(CellProperties *C)
82: {
84: CellProperties cells;
87: if (!C) return(0);
88: cells = *C;
89: PetscFree(cells->gpc);
90: PetscFree(cells);
91: *C = NULL;
92: return(0);
93: }
97: PetscErrorCode CellPropertiesGetCell(CellProperties C,PetscInt II,PetscInt J,PetscInt K,GaussPointCoefficients **G)
98: {
100: *G = &C->gpc[(II-C->sex) + (J-C->sey)*C->mx + (K-C->sez)*C->mx*C->my];
101: return(0);
102: }
104: /* FEM routines */
105: /*
106: Element: Local basis function ordering
107: 1-----2
108: | |
109: | |
110: 0-----3
111: */
112: static void ShapeFunctionQ13D_Evaluate(PetscScalar _xi[],PetscScalar Ni[])
113: {
114: PetscReal xi = PetscRealPart(_xi[0]);
115: PetscReal eta = PetscRealPart(_xi[1]);
116: PetscReal zeta = PetscRealPart(_xi[2]);
118: Ni[0] = 0.125 * (1.0 - xi) * (1.0 - eta) * (1.0 - zeta);
119: Ni[1] = 0.125 * (1.0 - xi) * (1.0 + eta) * (1.0 - zeta);
120: Ni[2] = 0.125 * (1.0 + xi) * (1.0 + eta) * (1.0 - zeta);
121: Ni[3] = 0.125 * (1.0 + xi) * (1.0 - eta) * (1.0 - zeta);
123: Ni[4] = 0.125 * (1.0 - xi) * (1.0 - eta) * (1.0 + zeta);
124: Ni[5] = 0.125 * (1.0 - xi) * (1.0 + eta) * (1.0 + zeta);
125: Ni[6] = 0.125 * (1.0 + xi) * (1.0 + eta) * (1.0 + zeta);
126: Ni[7] = 0.125 * (1.0 + xi) * (1.0 - eta) * (1.0 + zeta);
127: }
129: static void ShapeFunctionQ13D_Evaluate_dxi(PetscScalar _xi[],PetscScalar GNi[][NODES_PER_EL])
130: {
131: PetscReal xi = PetscRealPart(_xi[0]);
132: PetscReal eta = PetscRealPart(_xi[1]);
133: PetscReal zeta = PetscRealPart(_xi[2]);
134: /* xi deriv */
135: GNi[0][0] = -0.125 * (1.0 - eta) * (1.0 - zeta);
136: GNi[0][1] = -0.125 * (1.0 + eta) * (1.0 - zeta);
137: GNi[0][2] = 0.125 * (1.0 + eta) * (1.0 - zeta);
138: GNi[0][3] = 0.125 * (1.0 - eta) * (1.0 - zeta);
140: GNi[0][4] = -0.125 * (1.0 - eta) * (1.0 + zeta);
141: GNi[0][5] = -0.125 * (1.0 + eta) * (1.0 + zeta);
142: GNi[0][6] = 0.125 * (1.0 + eta) * (1.0 + zeta);
143: GNi[0][7] = 0.125 * (1.0 - eta) * (1.0 + zeta);
144: /* eta deriv */
145: GNi[1][0] = -0.125 * (1.0 - xi) * (1.0 - zeta);
146: GNi[1][1] = 0.125 * (1.0 - xi) * (1.0 - zeta);
147: GNi[1][2] = 0.125 * (1.0 + xi) * (1.0 - zeta);
148: GNi[1][3] = -0.125 * (1.0 + xi) * (1.0 - zeta);
150: GNi[1][4] = -0.125 * (1.0 - xi) * (1.0 + zeta);
151: GNi[1][5] = 0.125 * (1.0 - xi) * (1.0 + zeta);
152: GNi[1][6] = 0.125 * (1.0 + xi) * (1.0 + zeta);
153: GNi[1][7] = -0.125 * (1.0 + xi) * (1.0 + zeta);
154: /* zeta deriv */
155: GNi[2][0] = -0.125 * (1.0 - xi) * (1.0 - eta);
156: GNi[2][1] = -0.125 * (1.0 - xi) * (1.0 + eta);
157: GNi[2][2] = -0.125 * (1.0 + xi) * (1.0 + eta);
158: GNi[2][3] = -0.125 * (1.0 + xi) * (1.0 - eta);
160: GNi[2][4] = 0.125 * (1.0 - xi) * (1.0 - eta);
161: GNi[2][5] = 0.125 * (1.0 - xi) * (1.0 + eta);
162: GNi[2][6] = 0.125 * (1.0 + xi) * (1.0 + eta);
163: GNi[2][7] = 0.125 * (1.0 + xi) * (1.0 - eta);
164: }
166: static void matrix_inverse_3x3(PetscScalar A[3][3],PetscScalar B[3][3])
167: {
168: PetscScalar t4, t6, t8, t10, t12, t14, t17;
170: t4 = A[2][0] * A[0][1];
171: t6 = A[2][0] * A[0][2];
172: t8 = A[1][0] * A[0][1];
173: t10 = A[1][0] * A[0][2];
174: t12 = A[0][0] * A[1][1];
175: t14 = A[0][0] * A[1][2];
176: t17 = 0.1e1 / (t4 * A[1][2] - t6 * A[1][1] - t8 * A[2][2] + t10 * A[2][1] + t12 * A[2][2] - t14 * A[2][1]);
178: B[0][0] = (A[1][1] * A[2][2] - A[1][2] * A[2][1]) * t17;
179: B[0][1] = -(A[0][1] * A[2][2] - A[0][2] * A[2][1]) * t17;
180: B[0][2] = (A[0][1] * A[1][2] - A[0][2] * A[1][1]) * t17;
181: B[1][0] = -(-A[2][0] * A[1][2] + A[1][0] * A[2][2]) * t17;
182: B[1][1] = (-t6 + A[0][0] * A[2][2]) * t17;
183: B[1][2] = -(-t10 + t14) * t17;
184: B[2][0] = (-A[2][0] * A[1][1] + A[1][0] * A[2][1]) * t17;
185: B[2][1] = -(-t4 + A[0][0] * A[2][1]) * t17;
186: B[2][2] = (-t8 + t12) * t17;
187: }
189: static void ShapeFunctionQ13D_Evaluate_dx(PetscScalar GNi[][NODES_PER_EL],PetscScalar GNx[][NODES_PER_EL],PetscScalar coords[],PetscScalar *det_J)
190: {
191: PetscScalar J00,J01,J02,J10,J11,J12,J20,J21,J22;
192: PetscInt n;
193: PetscScalar iJ[3][3],JJ[3][3];
195: J00 = J01 = J02 = 0.0;
196: J10 = J11 = J12 = 0.0;
197: J20 = J21 = J22 = 0.0;
198: for (n=0; n<NODES_PER_EL; n++) {
199: PetscScalar cx = coords[NSD*n + 0];
200: PetscScalar cy = coords[NSD*n + 1];
201: PetscScalar cz = coords[NSD*n + 2];
203: /* J_ij = d(x_j) / d(xi_i) */ /* J_ij = \sum _I GNi[j][I} * x_i */
204: J00 = J00 + GNi[0][n] * cx; /* J_xx */
205: J01 = J01 + GNi[0][n] * cy; /* J_xy = dx/deta */
206: J02 = J02 + GNi[0][n] * cz; /* J_xz = dx/dzeta */
208: J10 = J10 + GNi[1][n] * cx; /* J_yx = dy/dxi */
209: J11 = J11 + GNi[1][n] * cy; /* J_yy */
210: J12 = J12 + GNi[1][n] * cz; /* J_yz */
212: J20 = J20 + GNi[2][n] * cx; /* J_zx */
213: J21 = J21 + GNi[2][n] * cy; /* J_zy */
214: J22 = J22 + GNi[2][n] * cz; /* J_zz */
215: }
217: JJ[0][0] = J00; JJ[0][1] = J01; JJ[0][2] = J02;
218: JJ[1][0] = J10; JJ[1][1] = J11; JJ[1][2] = J12;
219: JJ[2][0] = J20; JJ[2][1] = J21; JJ[2][2] = J22;
221: matrix_inverse_3x3(JJ,iJ);
223: *det_J = J00*J11*J22 - J00*J12*J21 - J10*J01*J22 + J10*J02*J21 + J20*J01*J12 - J20*J02*J11;
225: for (n=0; n<NODES_PER_EL; n++) {
226: GNx[0][n] = GNi[0][n]*iJ[0][0] + GNi[1][n]*iJ[0][1] + GNi[2][n]*iJ[0][2];
227: GNx[1][n] = GNi[0][n]*iJ[1][0] + GNi[1][n]*iJ[1][1] + GNi[2][n]*iJ[1][2];
228: GNx[2][n] = GNi[0][n]*iJ[2][0] + GNi[1][n]*iJ[2][1] + GNi[2][n]*iJ[2][2];
229: }
230: }
232: static void ConstructGaussQuadrature3D(PetscInt *ngp,PetscScalar gp_xi[][NSD],PetscScalar gp_weight[])
233: {
234: *ngp = 8;
235: gp_xi[0][0] = -0.57735026919; gp_xi[0][1] = -0.57735026919; gp_xi[0][2] = -0.57735026919;
236: gp_xi[1][0] = -0.57735026919; gp_xi[1][1] = 0.57735026919; gp_xi[1][2] = -0.57735026919;
237: gp_xi[2][0] = 0.57735026919; gp_xi[2][1] = 0.57735026919; gp_xi[2][2] = -0.57735026919;
238: gp_xi[3][0] = 0.57735026919; gp_xi[3][1] = -0.57735026919; gp_xi[3][2] = -0.57735026919;
240: gp_xi[4][0] = -0.57735026919; gp_xi[4][1] = -0.57735026919; gp_xi[4][2] = 0.57735026919;
241: gp_xi[5][0] = -0.57735026919; gp_xi[5][1] = 0.57735026919; gp_xi[5][2] = 0.57735026919;
242: gp_xi[6][0] = 0.57735026919; gp_xi[6][1] = 0.57735026919; gp_xi[6][2] = 0.57735026919;
243: gp_xi[7][0] = 0.57735026919; gp_xi[7][1] = -0.57735026919; gp_xi[7][2] = 0.57735026919;
245: gp_weight[0] = 1.0;
246: gp_weight[1] = 1.0;
247: gp_weight[2] = 1.0;
248: gp_weight[3] = 1.0;
250: gp_weight[4] = 1.0;
251: gp_weight[5] = 1.0;
252: gp_weight[6] = 1.0;
253: gp_weight[7] = 1.0;
254: }
256: /* procs to the left claim the ghost node as their element */
259: static PetscErrorCode DMDAGetLocalElementSize(DM da,PetscInt *mxl,PetscInt *myl,PetscInt *mzl)
260: {
261: PetscInt m,n,p,M,N,P;
262: PetscInt sx,sy,sz;
266: DMDAGetInfo(da,0,&M,&N,&P,0,0,0,0,0,0,0,0,0);
267: DMDAGetCorners(da,&sx,&sy,&sz,&m,&n,&p);
269: if (mxl) {
270: *mxl = m;
271: if ((sx+m) == M) *mxl = m-1; /* last proc */
272: }
273: if (myl) {
274: *myl = n;
275: if ((sy+n) == N) *myl = n-1; /* last proc */
276: }
277: if (mzl) {
278: *mzl = p;
279: if ((sz+p) == P) *mzl = p-1; /* last proc */
280: }
281: return(0);
282: }
286: static PetscErrorCode DMDAGetElementCorners(DM da,PetscInt *sx,PetscInt *sy,PetscInt *sz,PetscInt *mx,PetscInt *my,PetscInt *mz)
287: {
288: PetscInt si,sj,sk;
292: DMDAGetGhostCorners(da,&si,&sj,&sk,0,0,0);
294: if (sx) {
295: *sx = si;
296: if (si != 0) *sx = si+1;
297: }
298: if (sy) {
299: *sy = sj;
300: if (sj != 0) *sy = sj+1;
301: }
302: if (sz) {
303: *sz = sk;
304: if (sk != 0) *sz = sk+1;
305: }
306: DMDAGetLocalElementSize(da,mx,my,mz);
307: return(0);
308: }
310: /*
311: i,j are the element indices
312: The unknown is a vector quantity.
313: The s[].c is used to indicate the degree of freedom.
314: */
317: static PetscErrorCode DMDAGetElementEqnums3D_up(MatStencil s_u[],MatStencil s_p[],PetscInt i,PetscInt j,PetscInt k)
318: {
319: PetscInt n;
322: /* velocity */
323: n = 0;
324: /* node 0 */
325: s_u[n].i = i; s_u[n].j = j; s_u[n].k = k; s_u[n].c = 0; n++; /* Vx0 */
326: s_u[n].i = i; s_u[n].j = j; s_u[n].k = k; s_u[n].c = 1; n++; /* Vy0 */
327: s_u[n].i = i; s_u[n].j = j; s_u[n].k = k; s_u[n].c = 2; n++; /* Vz0 */
329: s_u[n].i = i; s_u[n].j = j+1; s_u[n].k = k; s_u[n].c = 0; n++;
330: s_u[n].i = i; s_u[n].j = j+1; s_u[n].k = k; s_u[n].c = 1; n++;
331: s_u[n].i = i; s_u[n].j = j+1; s_u[n].k = k; s_u[n].c = 2; n++;
333: s_u[n].i = i+1; s_u[n].j = j+1; s_u[n].k = k; s_u[n].c = 0; n++;
334: s_u[n].i = i+1; s_u[n].j = j+1; s_u[n].k = k; s_u[n].c = 1; n++;
335: s_u[n].i = i+1; s_u[n].j = j+1; s_u[n].k = k; s_u[n].c = 2; n++;
337: s_u[n].i = i+1; s_u[n].j = j; s_u[n].k = k; s_u[n].c = 0; n++;
338: s_u[n].i = i+1; s_u[n].j = j; s_u[n].k = k; s_u[n].c = 1; n++;
339: s_u[n].i = i+1; s_u[n].j = j; s_u[n].k = k; s_u[n].c = 2; n++;
341: /* */
342: s_u[n].i = i; s_u[n].j = j; s_u[n].k = k+1; s_u[n].c = 0; n++; /* Vx4 */
343: s_u[n].i = i; s_u[n].j = j; s_u[n].k = k+1; s_u[n].c = 1; n++; /* Vy4 */
344: s_u[n].i = i; s_u[n].j = j; s_u[n].k = k+1; s_u[n].c = 2; n++; /* Vz4 */
346: s_u[n].i = i; s_u[n].j = j+1; s_u[n].k = k+1; s_u[n].c = 0; n++;
347: s_u[n].i = i; s_u[n].j = j+1; s_u[n].k = k+1; s_u[n].c = 1; n++;
348: s_u[n].i = i; s_u[n].j = j+1; s_u[n].k = k+1; s_u[n].c = 2; n++;
350: s_u[n].i = i+1; s_u[n].j = j+1; s_u[n].k = k+1; s_u[n].c = 0; n++;
351: s_u[n].i = i+1; s_u[n].j = j+1; s_u[n].k = k+1; s_u[n].c = 1; n++;
352: s_u[n].i = i+1; s_u[n].j = j+1; s_u[n].k = k+1; s_u[n].c = 2; n++;
354: s_u[n].i = i+1; s_u[n].j = j; s_u[n].k = k+1; s_u[n].c = 0; n++;
355: s_u[n].i = i+1; s_u[n].j = j; s_u[n].k = k+1; s_u[n].c = 1; n++;
356: s_u[n].i = i+1; s_u[n].j = j; s_u[n].k = k+1; s_u[n].c = 2; n++;
358: /* pressure */
359: n = 0;
361: s_p[n].i = i; s_p[n].j = j; s_p[n].k = k; s_p[n].c = 3; n++; /* P0 */
362: s_p[n].i = i; s_p[n].j = j+1; s_p[n].k = k; s_p[n].c = 3; n++;
363: s_p[n].i = i+1; s_p[n].j = j+1; s_p[n].k = k; s_p[n].c = 3; n++;
364: s_p[n].i = i+1; s_p[n].j = j; s_p[n].k = k; s_p[n].c = 3; n++;
366: s_p[n].i = i; s_p[n].j = j; s_p[n].k = k+1; s_p[n].c = 3; n++; /* P0 */
367: s_p[n].i = i; s_p[n].j = j+1; s_p[n].k = k+1; s_p[n].c = 3; n++;
368: s_p[n].i = i+1; s_p[n].j = j+1; s_p[n].k = k+1; s_p[n].c = 3; n++;
369: s_p[n].i = i+1; s_p[n].j = j; s_p[n].k = k+1; s_p[n].c = 3; n++;
370: return(0);
371: }
375: static PetscErrorCode GetElementCoords3D(DMDACoor3d ***coords,PetscInt i,PetscInt j,PetscInt k,PetscScalar el_coord[])
376: {
378: /* get coords for the element */
379: el_coord[0] = coords[k][j][i].x;
380: el_coord[1] = coords[k][j][i].y;
381: el_coord[2] = coords[k][j][i].z;
383: el_coord[3] = coords[k][j+1][i].x;
384: el_coord[4] = coords[k][j+1][i].y;
385: el_coord[5] = coords[k][j+1][i].z;
387: el_coord[6] = coords[k][j+1][i+1].x;
388: el_coord[7] = coords[k][j+1][i+1].y;
389: el_coord[8] = coords[k][j+1][i+1].z;
391: el_coord[9] = coords[k][j][i+1].x;
392: el_coord[10] = coords[k][j][i+1].y;
393: el_coord[11] = coords[k][j][i+1].z;
395: el_coord[12] = coords[k+1][j][i].x;
396: el_coord[13] = coords[k+1][j][i].y;
397: el_coord[14] = coords[k+1][j][i].z;
399: el_coord[15] = coords[k+1][j+1][i].x;
400: el_coord[16] = coords[k+1][j+1][i].y;
401: el_coord[17] = coords[k+1][j+1][i].z;
403: el_coord[18] = coords[k+1][j+1][i+1].x;
404: el_coord[19] = coords[k+1][j+1][i+1].y;
405: el_coord[20] = coords[k+1][j+1][i+1].z;
407: el_coord[21] = coords[k+1][j][i+1].x;
408: el_coord[22] = coords[k+1][j][i+1].y;
409: el_coord[23] = coords[k+1][j][i+1].z;
410: return(0);
411: }
415: static PetscErrorCode StokesDAGetNodalFields3D(StokesDOF ***field,PetscInt i,PetscInt j,PetscInt k,StokesDOF nodal_fields[])
416: {
418: /* get the nodal fields for u */
419: nodal_fields[0].u_dof = field[k][j][i].u_dof;
420: nodal_fields[0].v_dof = field[k][j][i].v_dof;
421: nodal_fields[0].w_dof = field[k][j][i].w_dof;
423: nodal_fields[1].u_dof = field[k][j+1][i].u_dof;
424: nodal_fields[1].v_dof = field[k][j+1][i].v_dof;
425: nodal_fields[1].w_dof = field[k][j+1][i].w_dof;
427: nodal_fields[2].u_dof = field[k][j+1][i+1].u_dof;
428: nodal_fields[2].v_dof = field[k][j+1][i+1].v_dof;
429: nodal_fields[2].w_dof = field[k][j+1][i+1].w_dof;
431: nodal_fields[3].u_dof = field[k][j][i+1].u_dof;
432: nodal_fields[3].v_dof = field[k][j][i+1].v_dof;
433: nodal_fields[3].w_dof = field[k][j][i+1].w_dof;
435: nodal_fields[4].u_dof = field[k+1][j][i].u_dof;
436: nodal_fields[4].v_dof = field[k+1][j][i].v_dof;
437: nodal_fields[4].w_dof = field[k+1][j][i].w_dof;
439: nodal_fields[5].u_dof = field[k+1][j+1][i].u_dof;
440: nodal_fields[5].v_dof = field[k+1][j+1][i].v_dof;
441: nodal_fields[5].w_dof = field[k+1][j+1][i].w_dof;
443: nodal_fields[6].u_dof = field[k+1][j+1][i+1].u_dof;
444: nodal_fields[6].v_dof = field[k+1][j+1][i+1].v_dof;
445: nodal_fields[6].w_dof = field[k+1][j+1][i+1].w_dof;
447: nodal_fields[7].u_dof = field[k+1][j][i+1].u_dof;
448: nodal_fields[7].v_dof = field[k+1][j][i+1].v_dof;
449: nodal_fields[7].w_dof = field[k+1][j][i+1].w_dof;
451: /* get the nodal fields for p */
452: nodal_fields[0].p_dof = field[k][j][i].p_dof;
453: nodal_fields[1].p_dof = field[k][j+1][i].p_dof;
454: nodal_fields[2].p_dof = field[k][j+1][i+1].p_dof;
455: nodal_fields[3].p_dof = field[k][j][i+1].p_dof;
457: nodal_fields[4].p_dof = field[k+1][j][i].p_dof;
458: nodal_fields[5].p_dof = field[k+1][j+1][i].p_dof;
459: nodal_fields[6].p_dof = field[k+1][j+1][i+1].p_dof;
460: nodal_fields[7].p_dof = field[k+1][j][i+1].p_dof;
461: return(0);
462: }
464: static PetscInt ASS_MAP_wIwDI_uJuDJ(PetscInt wi,PetscInt wd,PetscInt w_NPE,PetscInt w_dof,PetscInt ui,PetscInt ud,PetscInt u_NPE,PetscInt u_dof)
465: {
466: PetscInt ij;
467: PETSC_UNUSED PetscInt r,c,nr,nc;
469: nr = w_NPE*w_dof;
470: nc = u_NPE*u_dof;
472: r = w_dof*wi+wd;
473: c = u_dof*ui+ud;
475: ij = r*nc+c;
477: return ij;
478: }
482: static PetscErrorCode DMDASetValuesLocalStencil3D_ADD_VALUES(StokesDOF ***fields_F,MatStencil u_eqn[],MatStencil p_eqn[],PetscScalar Fe_u[],PetscScalar Fe_p[])
483: {
484: PetscInt n,II,J,K;
487: for (n = 0; n<NODES_PER_EL; n++) {
488: II = u_eqn[NSD*n].i;
489: J = u_eqn[NSD*n].j;
490: K = u_eqn[NSD*n].k;
492: fields_F[K][J][II].u_dof = fields_F[K][J][II].u_dof+Fe_u[NSD*n];
494: II = u_eqn[NSD*n+1].i;
495: J = u_eqn[NSD*n+1].j;
496: K = u_eqn[NSD*n+1].k;
498: fields_F[K][J][II].v_dof = fields_F[K][J][II].v_dof+Fe_u[NSD*n+1];
500: II = u_eqn[NSD*n+2].i;
501: J = u_eqn[NSD*n+2].j;
502: K = u_eqn[NSD*n+2].k;
503: fields_F[K][J][II].w_dof = fields_F[K][J][II].w_dof+Fe_u[NSD*n+2];
505: II = p_eqn[n].i;
506: J = p_eqn[n].j;
507: K = p_eqn[n].k;
509: fields_F[K][J][II].p_dof = fields_F[K][J][II].p_dof+Fe_p[n];
511: }
512: return(0);
513: }
515: static void FormStressOperatorQ13D(PetscScalar Ke[],PetscScalar coords[],PetscScalar eta[])
516: {
517: PetscInt ngp;
518: PetscScalar gp_xi[GAUSS_POINTS][NSD];
519: PetscScalar gp_weight[GAUSS_POINTS];
520: PetscInt p,i,j,k;
521: PetscScalar GNi_p[NSD][NODES_PER_EL],GNx_p[NSD][NODES_PER_EL];
522: PetscScalar J_p,tildeD[6];
523: PetscScalar B[6][U_DOFS*NODES_PER_EL];
524: const PetscInt nvdof = U_DOFS*NODES_PER_EL;
526: /* define quadrature rule */
527: ConstructGaussQuadrature3D(&ngp,gp_xi,gp_weight);
529: /* evaluate integral */
530: for (p = 0; p < ngp; p++) {
531: ShapeFunctionQ13D_Evaluate_dxi(gp_xi[p],GNi_p);
532: ShapeFunctionQ13D_Evaluate_dx(GNi_p,GNx_p,coords,&J_p);
534: for (i = 0; i < NODES_PER_EL; i++) {
535: PetscScalar d_dx_i = GNx_p[0][i];
536: PetscScalar d_dy_i = GNx_p[1][i];
537: PetscScalar d_dz_i = GNx_p[2][i];
539: B[0][3*i] = d_dx_i; B[0][3*i+1] = 0.0; B[0][3*i+2] = 0.0;
540: B[1][3*i] = 0.0; B[1][3*i+1] = d_dy_i; B[1][3*i+2] = 0.0;
541: B[2][3*i] = 0.0; B[2][3*i+1] = 0.0; B[2][3*i+2] = d_dz_i;
543: B[3][3*i] = d_dy_i; B[3][3*i+1] = d_dx_i; B[3][3*i+2] = 0.0; /* e_xy */
544: B[4][3*i] = d_dz_i; B[4][3*i+1] = 0.0; B[4][3*i+2] = d_dx_i; /* e_xz */
545: B[5][3*i] = 0.0; B[5][3*i+1] = d_dz_i; B[5][3*i+2] = d_dy_i; /* e_yz */
546: }
549: tildeD[0] = 2.0*gp_weight[p]*J_p*eta[p];
550: tildeD[1] = 2.0*gp_weight[p]*J_p*eta[p];
551: tildeD[2] = 2.0*gp_weight[p]*J_p*eta[p];
553: tildeD[3] = gp_weight[p]*J_p*eta[p];
554: tildeD[4] = gp_weight[p]*J_p*eta[p];
555: tildeD[5] = gp_weight[p]*J_p*eta[p];
557: /* form Bt tildeD B */
558: /*
559: Ke_ij = Bt_ik . D_kl . B_lj
560: = B_ki . D_kl . B_lj
561: = B_ki . D_kk . B_kj
562: */
563: for (i = 0; i < nvdof; i++) {
564: for (j = i; j < nvdof; j++) {
565: for (k = 0; k < 6; k++) {
566: Ke[i*nvdof+j] += B[k][i]*tildeD[k]*B[k][j];
567: }
568: }
569: }
571: }
572: /* fill lower triangular part */
573: #if defined(ASSEMBLE_LOWER_TRIANGULAR)
574: for (i = 0; i < nvdof; i++) {
575: for (j = i; j < nvdof; j++) {
576: Ke[j*nvdof+i] = Ke[i*nvdof+j];
577: }
578: }
579: #endif
580: }
582: static void FormGradientOperatorQ13D(PetscScalar Ke[],PetscScalar coords[])
583: {
584: PetscInt ngp;
585: PetscScalar gp_xi[GAUSS_POINTS][NSD];
586: PetscScalar gp_weight[GAUSS_POINTS];
587: PetscInt p,i,j,di;
588: PetscScalar Ni_p[NODES_PER_EL];
589: PetscScalar GNi_p[NSD][NODES_PER_EL],GNx_p[NSD][NODES_PER_EL];
590: PetscScalar J_p,fac;
592: /* define quadrature rule */
593: ConstructGaussQuadrature3D(&ngp,gp_xi,gp_weight);
595: /* evaluate integral */
596: for (p = 0; p < ngp; p++) {
597: ShapeFunctionQ13D_Evaluate(gp_xi[p],Ni_p);
598: ShapeFunctionQ13D_Evaluate_dxi(gp_xi[p],GNi_p);
599: ShapeFunctionQ13D_Evaluate_dx(GNi_p,GNx_p,coords,&J_p);
600: fac = gp_weight[p]*J_p;
602: for (i = 0; i < NODES_PER_EL; i++) { /* u nodes */
603: for (di = 0; di < NSD; di++) { /* u dofs */
604: for (j = 0; j < NODES_PER_EL; j++) { /* p nodes, p dofs = 1 (ie no loop) */
605: PetscInt IJ;
606: IJ = ASS_MAP_wIwDI_uJuDJ(i,di,NODES_PER_EL,3,j,0,NODES_PER_EL,1);
608: Ke[IJ] = Ke[IJ]-GNx_p[di][i]*Ni_p[j]*fac;
609: }
610: }
611: }
612: }
613: }
615: static void FormDivergenceOperatorQ13D(PetscScalar De[],PetscScalar coords[])
616: {
617: PetscScalar Ge[U_DOFS*NODES_PER_EL*P_DOFS*NODES_PER_EL];
618: PetscInt i,j;
619: PetscInt nr_g,nc_g;
621: PetscMemzero(Ge,sizeof(PetscScalar)*U_DOFS*NODES_PER_EL*P_DOFS*NODES_PER_EL);
622: FormGradientOperatorQ13D(Ge,coords);
624: nr_g = U_DOFS*NODES_PER_EL;
625: nc_g = P_DOFS*NODES_PER_EL;
627: for (i = 0; i < nr_g; i++) {
628: for (j = 0; j < nc_g; j++) {
629: De[nr_g*j+i] = Ge[nc_g*i+j];
630: }
631: }
632: }
634: static void FormStabilisationOperatorQ13D(PetscScalar Ke[],PetscScalar coords[],PetscScalar eta[])
635: {
636: PetscInt ngp;
637: PetscScalar gp_xi[GAUSS_POINTS][NSD];
638: PetscScalar gp_weight[GAUSS_POINTS];
639: PetscInt p,i,j;
640: PetscScalar Ni_p[NODES_PER_EL];
641: PetscScalar GNi_p[NSD][NODES_PER_EL],GNx_p[NSD][NODES_PER_EL];
642: PetscScalar J_p,fac,eta_avg;
644: /* define quadrature rule */
645: ConstructGaussQuadrature3D(&ngp,gp_xi,gp_weight);
647: /* evaluate integral */
648: for (p = 0; p < ngp; p++) {
649: ShapeFunctionQ13D_Evaluate(gp_xi[p],Ni_p);
650: ShapeFunctionQ13D_Evaluate_dxi(gp_xi[p],GNi_p);
651: ShapeFunctionQ13D_Evaluate_dx(GNi_p,GNx_p,coords,&J_p);
652: fac = gp_weight[p]*J_p;
653: /*
654: for (i = 0; i < NODES_PER_EL; i++) {
655: for (j = i; j < NODES_PER_EL; j++) {
656: Ke[NODES_PER_EL*i+j] -= fac*(Ni_p[i]*Ni_p[j]-0.015625);
657: }
658: }
659: */
661: for (i = 0; i < NODES_PER_EL; i++) {
662: for (j = 0; j < NODES_PER_EL; j++) {
663: Ke[NODES_PER_EL*i+j] -= fac*(Ni_p[i]*Ni_p[j]-0.015625);
664: }
665: }
666: }
668: /* scale */
669: eta_avg = 0.0;
670: for (p = 0; p < ngp; p++) eta_avg += eta[p];
671: eta_avg = (1.0/((PetscScalar)ngp))*eta_avg;
672: fac = 1.0/eta_avg;
674: /*
675: for (i = 0; i < NODES_PER_EL; i++) {
676: for (j = i; j < NODES_PER_EL; j++) {
677: Ke[NODES_PER_EL*i+j] = fac*Ke[NODES_PER_EL*i+j];
678: #if defined(ASSEMBLE_LOWER_TRIANGULAR)
679: Ke[NODES_PER_EL*j+i] = Ke[NODES_PER_EL*i+j];
680: #endif
681: }
682: }
683: */
685: for (i = 0; i < NODES_PER_EL; i++) {
686: for (j = 0; j < NODES_PER_EL; j++) {
687: Ke[NODES_PER_EL*i+j] = fac*Ke[NODES_PER_EL*i+j];
688: }
689: }
690: }
692: static void FormScaledMassMatrixOperatorQ13D(PetscScalar Ke[],PetscScalar coords[],PetscScalar eta[])
693: {
694: PetscInt ngp;
695: PetscScalar gp_xi[GAUSS_POINTS][NSD];
696: PetscScalar gp_weight[GAUSS_POINTS];
697: PetscInt p,i,j;
698: PetscScalar Ni_p[NODES_PER_EL];
699: PetscScalar GNi_p[NSD][NODES_PER_EL],GNx_p[NSD][NODES_PER_EL];
700: PetscScalar J_p,fac,eta_avg;
702: /* define quadrature rule */
703: ConstructGaussQuadrature3D(&ngp,gp_xi,gp_weight);
705: /* evaluate integral */
706: for (p = 0; p < ngp; p++) {
707: ShapeFunctionQ13D_Evaluate(gp_xi[p],Ni_p);
708: ShapeFunctionQ13D_Evaluate_dxi(gp_xi[p],GNi_p);
709: ShapeFunctionQ13D_Evaluate_dx(GNi_p,GNx_p,coords,&J_p);
710: fac = gp_weight[p]*J_p;
712: /*
713: for (i = 0; i < NODES_PER_EL; i++) {
714: for (j = i; j < NODES_PER_EL; j++) {
715: Ke[NODES_PER_EL*i+j] = Ke[NODES_PER_EL*i+j]-fac*Ni_p[i]*Ni_p[j];
716: }
717: }
718: */
720: for (i = 0; i < NODES_PER_EL; i++) {
721: for (j = 0; j < NODES_PER_EL; j++) {
722: Ke[NODES_PER_EL*i+j] = Ke[NODES_PER_EL*i+j]-fac*Ni_p[i]*Ni_p[j];
723: }
724: }
725: }
727: /* scale */
728: eta_avg = 0.0;
729: for (p = 0; p < ngp; p++) eta_avg += eta[p];
730: eta_avg = (1.0/((PetscScalar)ngp))*eta_avg;
731: fac = 1.0/eta_avg;
732: /*
733: for (i = 0; i < NODES_PER_EL; i++) {
734: for (j = i; j < NODES_PER_EL; j++) {
735: Ke[NODES_PER_EL*i+j] = fac*Ke[NODES_PER_EL*i+j];
736: #if defined(ASSEMBLE_LOWER_TRIANGULAR)
737: Ke[NODES_PER_EL*j+i] = Ke[NODES_PER_EL*i+j];
738: #endif
739: }
740: }
741: */
743: for (i = 0; i < NODES_PER_EL; i++) {
744: for (j = 0; j < NODES_PER_EL; j++) {
745: Ke[NODES_PER_EL*i+j] = fac*Ke[NODES_PER_EL*i+j];
746: }
747: }
748: }
750: static void FormMomentumRhsQ13D(PetscScalar Fe[],PetscScalar coords[],PetscScalar fx[],PetscScalar fy[],PetscScalar fz[])
751: {
752: PetscInt ngp;
753: PetscScalar gp_xi[GAUSS_POINTS][NSD];
754: PetscScalar gp_weight[GAUSS_POINTS];
755: PetscInt p,i;
756: PetscScalar Ni_p[NODES_PER_EL];
757: PetscScalar GNi_p[NSD][NODES_PER_EL],GNx_p[NSD][NODES_PER_EL];
758: PetscScalar J_p,fac;
760: /* define quadrature rule */
761: ConstructGaussQuadrature3D(&ngp,gp_xi,gp_weight);
763: /* evaluate integral */
764: for (p = 0; p < ngp; p++) {
765: ShapeFunctionQ13D_Evaluate(gp_xi[p],Ni_p);
766: ShapeFunctionQ13D_Evaluate_dxi(gp_xi[p],GNi_p);
767: ShapeFunctionQ13D_Evaluate_dx(GNi_p,GNx_p,coords,&J_p);
768: fac = gp_weight[p]*J_p;
770: for (i = 0; i < NODES_PER_EL; i++) {
771: Fe[NSD*i] -= fac*Ni_p[i]*fx[p];
772: Fe[NSD*i+1] -= fac*Ni_p[i]*fy[p];
773: Fe[NSD*i+2] -= fac*Ni_p[i]*fz[p];
774: }
775: }
776: }
778: static void FormContinuityRhsQ13D(PetscScalar Fe[],PetscScalar coords[],PetscScalar hc[])
779: {
780: PetscInt ngp;
781: PetscScalar gp_xi[GAUSS_POINTS][NSD];
782: PetscScalar gp_weight[GAUSS_POINTS];
783: PetscInt p,i;
784: PetscScalar Ni_p[NODES_PER_EL];
785: PetscScalar GNi_p[NSD][NODES_PER_EL],GNx_p[NSD][NODES_PER_EL];
786: PetscScalar J_p,fac;
788: /* define quadrature rule */
789: ConstructGaussQuadrature3D(&ngp,gp_xi,gp_weight);
791: /* evaluate integral */
792: for (p = 0; p < ngp; p++) {
793: ShapeFunctionQ13D_Evaluate(gp_xi[p],Ni_p);
794: ShapeFunctionQ13D_Evaluate_dxi(gp_xi[p],GNi_p);
795: ShapeFunctionQ13D_Evaluate_dx(GNi_p,GNx_p,coords,&J_p);
796: fac = gp_weight[p]*J_p;
798: for (i = 0; i < NODES_PER_EL; i++) Fe[i] -= fac*Ni_p[i]*hc[p];
799: }
800: }
802: #define _ZERO_ROWCOL_i(A,i) { \
803: PetscInt KK; \
804: PetscScalar tmp = A[24*(i)+(i)]; \
805: for (KK=0;KK<24;KK++) A[24*(i)+KK]=0.0; \
806: for (KK=0;KK<24;KK++) A[24*KK+(i)]=0.0; \
807: A[24*(i)+(i)] = tmp;} \
809: #define _ZERO_ROW_i(A,i) { \
810: PetscInt KK; \
811: for (KK=0;KK<8;KK++) A[8*(i)+KK]=0.0;}
813: #define _ZERO_COL_i(A,i) { \
814: PetscInt KK; \
815: for (KK=0;KK<8;KK++) A[24*KK+(i)]=0.0;}
819: static PetscErrorCode AssembleA_Stokes(Mat A,DM stokes_da,CellProperties cell_properties)
820: {
821: DM cda;
822: Vec coords;
823: DMDACoor3d ***_coords;
824: MatStencil u_eqn[NODES_PER_EL*U_DOFS];
825: MatStencil p_eqn[NODES_PER_EL*P_DOFS];
826: PetscInt sex,sey,sez,mx,my,mz;
827: PetscInt ei,ej,ek;
828: PetscScalar Ae[NODES_PER_EL*U_DOFS*NODES_PER_EL*U_DOFS];
829: PetscScalar Ge[NODES_PER_EL*U_DOFS*NODES_PER_EL*P_DOFS];
830: PetscScalar De[NODES_PER_EL*P_DOFS*NODES_PER_EL*U_DOFS];
831: PetscScalar Ce[NODES_PER_EL*P_DOFS*NODES_PER_EL*P_DOFS];
832: PetscScalar el_coords[NODES_PER_EL*NSD];
833: GaussPointCoefficients *props;
834: PetscScalar *prop_eta;
835: PetscInt n,M,N,P;
836: PetscErrorCode ierr;
839: DMDAGetInfo(stokes_da,0,&M,&N,&P,0,0,0, 0,0,0,0,0,0);
840: /* setup for coords */
841: DMGetCoordinateDM(stokes_da,&cda);
842: DMGetCoordinatesLocal(stokes_da,&coords);
843: DMDAVecGetArray(cda,coords,&_coords);
845: DMDAGetElementCorners(stokes_da,&sex,&sey,&sez,&mx,&my,&mz);
846: for (ek = sez; ek < sez+mz; ek++) {
847: for (ej = sey; ej < sey+my; ej++) {
848: for (ei = sex; ei < sex+mx; ei++) {
849: /* get coords for the element */
850: GetElementCoords3D(_coords,ei,ej,ek,el_coords);
851: /* get cell properties */
852: CellPropertiesGetCell(cell_properties,ei,ej,ek,&props);
853: /* get coefficients for the element */
854: prop_eta = props->eta;
856: /* initialise element stiffness matrix */
857: PetscMemzero(Ae,sizeof(PetscScalar)*NODES_PER_EL*U_DOFS*NODES_PER_EL*U_DOFS);
858: PetscMemzero(Ge,sizeof(PetscScalar)*NODES_PER_EL*U_DOFS*NODES_PER_EL*P_DOFS);
859: PetscMemzero(De,sizeof(PetscScalar)*NODES_PER_EL*P_DOFS*NODES_PER_EL*U_DOFS);
860: PetscMemzero(Ce,sizeof(PetscScalar)*NODES_PER_EL*P_DOFS*NODES_PER_EL*P_DOFS);
862: /* form element stiffness matrix */
863: FormStressOperatorQ13D(Ae,el_coords,prop_eta);
864: FormGradientOperatorQ13D(Ge,el_coords);
865: /*#if defined(ASSEMBLE_LOWER_TRIANGULAR)*/
866: FormDivergenceOperatorQ13D(De,el_coords);
867: /*#endif*/
868: FormStabilisationOperatorQ13D(Ce,el_coords,prop_eta);
870: /* insert element matrix into global matrix */
871: DMDAGetElementEqnums3D_up(u_eqn,p_eqn,ei,ej,ek);
873: for (n=0; n<NODES_PER_EL; n++) {
874: if ((u_eqn[3*n].i == 0) || (u_eqn[3*n].i == M-1)) {
875: _ZERO_ROWCOL_i(Ae,3*n);
876: _ZERO_ROW_i (Ge,3*n);
877: _ZERO_COL_i (De,3*n);
878: }
880: if ((u_eqn[3*n+1].j == 0) || (u_eqn[3*n+1].j == N-1)) {
881: _ZERO_ROWCOL_i(Ae,3*n+1);
882: _ZERO_ROW_i (Ge,3*n+1);
883: _ZERO_COL_i (De,3*n+1);
884: }
886: if ((u_eqn[3*n+2].k == 0) || (u_eqn[3*n+2].k == P-1)) {
887: _ZERO_ROWCOL_i(Ae,3*n+2);
888: _ZERO_ROW_i (Ge,3*n+2);
889: _ZERO_COL_i (De,3*n+2);
890: }
891: }
892: MatSetValuesStencil(A,NODES_PER_EL*U_DOFS,u_eqn,NODES_PER_EL*U_DOFS,u_eqn,Ae,ADD_VALUES);
893: MatSetValuesStencil(A,NODES_PER_EL*U_DOFS,u_eqn,NODES_PER_EL*P_DOFS,p_eqn,Ge,ADD_VALUES);
894: MatSetValuesStencil(A,NODES_PER_EL*P_DOFS,p_eqn,NODES_PER_EL*U_DOFS,u_eqn,De,ADD_VALUES);
895: MatSetValuesStencil(A,NODES_PER_EL*P_DOFS,p_eqn,NODES_PER_EL*P_DOFS,p_eqn,Ce,ADD_VALUES);
896: }
897: }
898: }
899: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
900: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
902: DMDAVecRestoreArray(cda,coords,&_coords);
904: return(0);
905: }
909: static PetscErrorCode AssembleA_PCStokes(Mat A,DM stokes_da,CellProperties cell_properties)
910: {
911: DM cda;
912: Vec coords;
913: DMDACoor3d ***_coords;
914: MatStencil u_eqn[NODES_PER_EL*U_DOFS];
915: MatStencil p_eqn[NODES_PER_EL*P_DOFS];
916: PetscInt sex,sey,sez,mx,my,mz;
917: PetscInt ei,ej,ek;
918: PetscScalar Ae[NODES_PER_EL*U_DOFS*NODES_PER_EL*U_DOFS];
919: PetscScalar Ge[NODES_PER_EL*U_DOFS*NODES_PER_EL*P_DOFS];
920: PetscScalar De[NODES_PER_EL*P_DOFS*NODES_PER_EL*U_DOFS];
921: PetscScalar Ce[NODES_PER_EL*P_DOFS*NODES_PER_EL*P_DOFS];
922: PetscScalar el_coords[NODES_PER_EL*NSD];
923: GaussPointCoefficients *props;
924: PetscScalar *prop_eta;
925: PetscInt n,M,N,P;
926: PetscErrorCode ierr;
929: DMDAGetInfo(stokes_da,0,&M,&N,&P,0,0,0, 0,0,0,0,0,0);
930: /* setup for coords */
931: DMGetCoordinateDM(stokes_da,&cda);
932: DMGetCoordinatesLocal(stokes_da,&coords);
933: DMDAVecGetArray(cda,coords,&_coords);
935: DMDAGetElementCorners(stokes_da,&sex,&sey,&sez,&mx,&my,&mz);
936: for (ek = sez; ek < sez+mz; ek++) {
937: for (ej = sey; ej < sey+my; ej++) {
938: for (ei = sex; ei < sex+mx; ei++) {
939: /* get coords for the element */
940: GetElementCoords3D(_coords,ei,ej,ek,el_coords);
941: /* get cell properties */
942: CellPropertiesGetCell(cell_properties,ei,ej,ek,&props);
943: /* get coefficients for the element */
944: prop_eta = props->eta;
946: /* initialise element stiffness matrix */
947: PetscMemzero(Ae,sizeof(PetscScalar)*NODES_PER_EL*U_DOFS*NODES_PER_EL*U_DOFS);
948: PetscMemzero(Ge,sizeof(PetscScalar)*NODES_PER_EL*U_DOFS*NODES_PER_EL*P_DOFS);
949: PetscMemzero(De,sizeof(PetscScalar)*NODES_PER_EL*P_DOFS*NODES_PER_EL*U_DOFS);
950: PetscMemzero(Ce,sizeof(PetscScalar)*NODES_PER_EL*P_DOFS*NODES_PER_EL*P_DOFS);
952: /* form element stiffness matrix */
953: FormStressOperatorQ13D(Ae,el_coords,prop_eta);
954: FormGradientOperatorQ13D(Ge,el_coords);
955: /* FormDivergenceOperatorQ13D(De,el_coords); */
956: FormScaledMassMatrixOperatorQ13D(Ce,el_coords,prop_eta);
958: /* insert element matrix into global matrix */
959: DMDAGetElementEqnums3D_up(u_eqn,p_eqn,ei,ej,ek);
961: for (n=0; n<NODES_PER_EL; n++) {
962: if ((u_eqn[3*n].i == 0) || (u_eqn[3*n].i == M-1)) {
963: _ZERO_ROWCOL_i(Ae,3*n);
964: _ZERO_ROW_i (Ge,3*n);
965: _ZERO_COL_i (De,3*n);
966: }
968: if ((u_eqn[3*n+1].j == 0) || (u_eqn[3*n+1].j == N-1)) {
969: _ZERO_ROWCOL_i(Ae,3*n+1);
970: _ZERO_ROW_i (Ge,3*n+1);
971: _ZERO_COL_i (De,3*n+1);
972: }
974: if ((u_eqn[3*n+2].k == 0) || (u_eqn[3*n+2].k == P-1)) {
975: _ZERO_ROWCOL_i(Ae,3*n+2);
976: _ZERO_ROW_i (Ge,3*n+2);
977: _ZERO_COL_i (De,3*n+2);
978: }
979: }
980: MatSetValuesStencil(A,NODES_PER_EL*U_DOFS,u_eqn,NODES_PER_EL*U_DOFS,u_eqn,Ae,ADD_VALUES);
981: MatSetValuesStencil(A,NODES_PER_EL*U_DOFS,u_eqn,NODES_PER_EL*P_DOFS,p_eqn,Ge,ADD_VALUES);
982: /*MatSetValuesStencil(A,NODES_PER_EL*P_DOFS,p_eqn,NODES_PER_EL*U_DOFS,u_eqn,De,ADD_VALUES);*/
983: MatSetValuesStencil(A,NODES_PER_EL*P_DOFS,p_eqn,NODES_PER_EL*P_DOFS,p_eqn,Ce,ADD_VALUES);
984: }
985: }
986: }
987: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
988: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
990: DMDAVecRestoreArray(cda,coords,&_coords);
991: return(0);
992: }
996: static PetscErrorCode AssembleF_Stokes(Vec F,DM stokes_da,CellProperties cell_properties)
997: {
998: DM cda;
999: Vec coords;
1000: DMDACoor3d ***_coords;
1001: MatStencil u_eqn[NODES_PER_EL*U_DOFS];
1002: MatStencil p_eqn[NODES_PER_EL*P_DOFS];
1003: PetscInt sex,sey,sez,mx,my,mz;
1004: PetscInt ei,ej,ek;
1005: PetscScalar Fe[NODES_PER_EL*U_DOFS];
1006: PetscScalar He[NODES_PER_EL*P_DOFS];
1007: PetscScalar el_coords[NODES_PER_EL*NSD];
1008: GaussPointCoefficients *props;
1009: PetscScalar *prop_fx,*prop_fy,*prop_fz,*prop_hc;
1010: Vec local_F;
1011: StokesDOF ***ff;
1012: PetscInt n,M,N,P;
1013: PetscErrorCode ierr;
1016: DMDAGetInfo(stokes_da,0,&M,&N,&P,0,0,0, 0,0,0,0,0,0);
1017: /* setup for coords */
1018: DMGetCoordinateDM(stokes_da,&cda);
1019: DMGetCoordinatesLocal(stokes_da,&coords);
1020: DMDAVecGetArray(cda,coords,&_coords);
1022: /* get acces to the vector */
1023: DMGetLocalVector(stokes_da,&local_F);
1024: VecZeroEntries(local_F);
1025: DMDAVecGetArray(stokes_da,local_F,&ff);
1027: DMDAGetElementCorners(stokes_da,&sex,&sey,&sez,&mx,&my,&mz);
1028: for (ek = sez; ek < sez+mz; ek++) {
1029: for (ej = sey; ej < sey+my; ej++) {
1030: for (ei = sex; ei < sex+mx; ei++) {
1031: /* get coords for the element */
1032: GetElementCoords3D(_coords,ei,ej,ek,el_coords);
1033: /* get cell properties */
1034: CellPropertiesGetCell(cell_properties,ei,ej,ek,&props);
1035: /* get coefficients for the element */
1036: prop_fx = props->fx;
1037: prop_fy = props->fy;
1038: prop_fz = props->fz;
1039: prop_hc = props->hc;
1041: /* initialise element stiffness matrix */
1042: PetscMemzero(Fe,sizeof(PetscScalar)*NODES_PER_EL*U_DOFS);
1043: PetscMemzero(He,sizeof(PetscScalar)*NODES_PER_EL*P_DOFS);
1045: /* form element stiffness matrix */
1046: FormMomentumRhsQ13D(Fe,el_coords,prop_fx,prop_fy,prop_fz);
1047: FormContinuityRhsQ13D(He,el_coords,prop_hc);
1049: /* insert element matrix into global matrix */
1050: DMDAGetElementEqnums3D_up(u_eqn,p_eqn,ei,ej,ek);
1052: for (n=0; n<NODES_PER_EL; n++) {
1053: if ((u_eqn[3*n].i == 0) || (u_eqn[3*n].i == M-1)) Fe[3*n] = 0.0;
1055: if ((u_eqn[3*n+1].j == 0) || (u_eqn[3*n+1].j == N-1)) Fe[3*n+1] = 0.0;
1057: if ((u_eqn[3*n+2].k == 0) || (u_eqn[3*n+2].k == P-1)) Fe[3*n+2] = 0.0;
1058: }
1060: DMDASetValuesLocalStencil3D_ADD_VALUES(ff,u_eqn,p_eqn,Fe,He);
1061: }
1062: }
1063: }
1064: DMDAVecRestoreArray(stokes_da,local_F,&ff);
1065: DMLocalToGlobalBegin(stokes_da,local_F,ADD_VALUES,F);
1066: DMLocalToGlobalEnd(stokes_da,local_F,ADD_VALUES,F);
1067: DMRestoreLocalVector(stokes_da,&local_F);
1069: DMDAVecRestoreArray(cda,coords,&_coords);
1070: return(0);
1071: }
1073: static void evaluate_MS_FrankKamentski_constants(PetscReal *theta,PetscReal *MX,PetscReal *MY,PetscReal *MZ)
1074: {
1075: *theta = 0.0;
1076: *MX = 2.0 * PETSC_PI;
1077: *MY = 2.0 * PETSC_PI;
1078: *MZ = 2.0 * PETSC_PI;
1079: }
1080: static void evaluate_MS_FrankKamentski(PetscReal pos[],PetscReal v[],PetscReal *p,PetscReal *eta,PetscReal Fm[],PetscReal *Fc)
1081: {
1082: PetscReal x,y,z;
1083: PetscReal theta,MX,MY,MZ;
1085: evaluate_MS_FrankKamentski_constants(&theta,&MX,&MY,&MZ);
1086: x = pos[0];
1087: y = pos[1];
1088: z = pos[2];
1089: if (v) {
1090: /*
1091: v[0] = PetscPowRealInt(z,3)*PetscExpReal(y)*PetscSinReal(PETSC_PI*x);
1092: v[1] = z*cos(2.0*PETSC_PI*x)*PetscExpReal(-y)*PetscSinReal(PETSC_PI*y);
1093: v[2] = -(PetscPowRealInt(x,3) + PetscPowRealInt(y,3))*PetscSinReal(2.0*PETSC_PI*z);
1094: */
1095: /*
1096: v[0] = PetscSinReal(PETSC_PI*x);
1097: v[1] = PetscSinReal(PETSC_PI*y);
1098: v[2] = PetscSinReal(PETSC_PI*z);
1099: */
1100: v[0] = PetscPowRealInt(z,3)*PetscExpReal(y)*PetscSinReal(PETSC_PI*x);
1101: v[1] = z*PetscCosReal(2.0*PETSC_PI*x)*PetscExpReal(-y)*PetscSinReal(PETSC_PI*y);
1102: v[2] = PetscPowRealInt(z,2)*(PetscCosReal(2.0*PETSC_PI*x)*PetscExpReal(-y)*PetscSinReal(PETSC_PI*y)/2 - PETSC_PI*PetscCosReal(PETSC_PI*y)*PetscCosReal(2.0*PETSC_PI*x)*PetscExpReal(-y)/2) - PETSC_PI*PetscPowRealInt(z,4)*PetscCosReal(PETSC_PI*x)*PetscExpReal(y)/4;
1103: }
1104: if (p) *p = PetscPowRealInt(x,2) + PetscPowRealInt(y,2) + PetscPowRealInt(z,2);
1105: if (eta) {
1106: /**eta = PetscExpReal(-theta*(1.0 - y - 0.1*PetscCosReal(MX*x)*PetscCosReal(MZ*z)*PetscSinReal(MY*y)));*/
1107: *eta = 1.0;
1108: }
1109: if (Fm) {
1110: /*
1111: Fm[0] = -2*x - 2.0*PetscPowRealInt(PETSC_PI,2)*PetscPowRealInt(z,3)*PetscExpReal(y)*PetscExpReal(-theta*(1 - y - 0.1*PetscCosReal(MX*x)*PetscCosReal(MZ*z)*PetscSinReal(MY*y)))*PetscSinReal(PETSC_PI*x) - 0.2*MZ*theta*(-1.5*PetscPowRealInt(x,2)*PetscSinReal(2.0*PETSC_PI*z) + 1.5*PetscPowRealInt(z,2)*PetscExpReal(y)*PetscSinReal(PETSC_PI*x))*PetscCosReal(MX*x)*PetscExpReal(-theta*(1 - y - 0.1*PetscCosReal(MX*x)*PetscCosReal(MZ*z)*PetscSinReal(MY*y)))*PetscSinReal(MY*y)*PetscSinReal(MZ*z) - 0.2*PETSC_PI*MX*theta*PetscPowRealInt(z,3)*PetscCosReal(PETSC_PI*x)*PetscCosReal(MZ*z)*PetscExpReal(y)*PetscExpReal(-theta*(1 - y - 0.1*PetscCosReal(MX*x)*PetscCosReal(MZ*z)*PetscSinReal(MY*y)))*PetscSinReal(MX*x)*PetscSinReal(MY*y) + 2.0*(3.0*z*PetscExpReal(y)*PetscSinReal(PETSC_PI*x) - 3.0*PETSC_PI*PetscPowRealInt(x,2)*PetscCosReal(2.0*PETSC_PI*z))*PetscExpReal(-theta*(1 - y - 0.1*PetscCosReal(MX*x)*PetscCosReal(MZ*z)*PetscSinReal(MY*y))) + 2.0*(0.5*PetscPowRealInt(z,3)*PetscExpReal(y)*PetscSinReal(PETSC_PI*x) + PETSC_PI*z*PetscExpReal(-y)*PetscSinReal(PETSC_PI*y)*PetscSinReal(2.0*PETSC_PI*x) - 1.0*z*PetscPowRealInt(PETSC_PI,2)*PetscCosReal(PETSC_PI*y)*PetscExpReal(-y)*PetscSinReal(2.0*PETSC_PI*x))*PetscExpReal(-theta*(1 - y - 0.1*PetscCosReal(MX*x)*PetscCosReal(MZ*z)*PetscSinReal(MY*y))) + 2.0*theta*(1 + 0.1*MY*PetscCosReal(MX*x)*PetscCosReal(MY*y)*PetscCosReal(MZ*z))*(0.5*PetscPowRealInt(z,3)*PetscExpReal(y)*PetscSinReal(PETSC_PI*x) - 1.0*PETSC_PI*z*PetscExpReal(-y)*PetscSinReal(PETSC_PI*y)*PetscSinReal(2.0*PETSC_PI*x))*PetscExpReal(-theta*(1 - y - 0.1*PetscCosReal(MX*x)*PetscCosReal(MZ*z)*PetscSinReal(MY*y))) ;
1112: Fm[1] = -2*y - 0.2*MX*theta*(0.5*PetscPowRealInt(z,3)*PetscExpReal(y)*PetscSinReal(PETSC_PI*x) - 1.0*PETSC_PI*z*PetscExpReal(-y)*PetscSinReal(PETSC_PI*y)*PetscSinReal(2.0*PETSC_PI*x))*PetscCosReal(MZ*z)*PetscExpReal(-theta*(1 - y - 0.1*PetscCosReal(MX*x)*PetscCosReal(MZ*z)*PetscSinReal(MY*y)))*PetscSinReal(MX*x)*PetscSinReal(MY*y) - 0.2*MZ*theta*(-1.5*PetscPowRealInt(y,2)*PetscSinReal(2.0*PETSC_PI*z) + 0.5*PetscCosReal(2.0*PETSC_PI*x)*PetscExpReal(-y)*PetscSinReal(PETSC_PI*y))*PetscCosReal(MX*x)*PetscExpReal(-theta*(1 - y - 0.1*PetscCosReal(MX*x)*PetscCosReal(MZ*z)*PetscSinReal(MY*y)))*PetscSinReal(MY*y)*PetscSinReal(MZ*z) + 2.0*(-2.0*z*PetscPowRealInt(PETSC_PI,2)*PetscCosReal(2.0*PETSC_PI*x)*PetscExpReal(-y)*PetscSinReal(PETSC_PI*y) + 0.5*PETSC_PI*PetscPowRealInt(z,3)*PetscCosReal(PETSC_PI*x)*PetscExpReal(y))*PetscExpReal(-theta*(1 - y - 0.1*PetscCosReal(MX*x)*PetscCosReal(MZ*z)*PetscSinReal(MY*y))) + 2.0*(z*PetscCosReal(2.0*PETSC_PI*x)*PetscExpReal(-y)*PetscSinReal(PETSC_PI*y) - z*PetscPowRealInt(PETSC_PI,2)*PetscCosReal(2.0*PETSC_PI*x)*PetscExpReal(-y)*PetscSinReal(PETSC_PI*y) - 2*PETSC_PI*z*PetscCosReal(PETSC_PI*y)*PetscCosReal(2.0*PETSC_PI*x)*PetscExpReal(-y))*PetscExpReal(-theta*(1 - y - 0.1*PetscCosReal(MX*x)*PetscCosReal(MZ*z)*PetscSinReal(MY*y))) + 2.0*theta*(1 + 0.1*MY*PetscCosReal(MX*x)*PetscCosReal(MY*y)*PetscCosReal(MZ*z))*(-z*PetscCosReal(2.0*PETSC_PI*x)*PetscExpReal(-y)*PetscSinReal(PETSC_PI*y) + PETSC_PI*z*PetscCosReal(PETSC_PI*y)*PetscCosReal(2.0*PETSC_PI*x)*PetscExpReal(-y))*PetscExpReal(-theta*(1 - y - 0.1*PetscCosReal(MX*x)*PetscCosReal(MZ*z)*PetscSinReal(MY*y))) - 6.0*PETSC_PI*PetscPowRealInt(y,2)*PetscCosReal(2.0*PETSC_PI*z)*PetscExpReal(-theta*(1 - y - 0.1*PetscCosReal(MX*x)*PetscCosReal(MZ*z)*PetscSinReal(MY*y)));
1113: Fm[2] = -2*z + 8.0*PetscPowRealInt(PETSC_PI,2)*(PetscPowRealInt(x,3) + PetscPowRealInt(y,3))*PetscExpReal(-theta*(1 - y - 0.1*PetscCosReal(MX*x)*PetscCosReal(MZ*z)*PetscSinReal(MY*y)))*PetscSinReal(2.0*PETSC_PI*z) - 0.2*MX*theta*(-1.5*PetscPowRealInt(x,2)*PetscSinReal(2.0*PETSC_PI*z) + 1.5*PetscPowRealInt(z,2)*PetscExpReal(y)*PetscSinReal(PETSC_PI*x))*PetscCosReal(MZ*z)*PetscExpReal(-theta*(1 - y - 0.1*PetscCosReal(MX*x)*PetscCosReal(MZ*z)*PetscSinReal(MY*y)))*PetscSinReal(MX*x)*PetscSinReal(MY*y) + 0.4*PETSC_PI*MZ*theta*(PetscPowRealInt(x,3) + PetscPowRealInt(y,3))*PetscCosReal(MX*x)*PetscCosReal(2.0*PETSC_PI*z)*PetscExpReal(-theta*(1 - y - 0.1*PetscCosReal(MX*x)*PetscCosReal(MZ*z)*PetscSinReal(MY*y)))*PetscSinReal(MY*y)*PetscSinReal(MZ*z) + 2.0*(-3.0*x*PetscSinReal(2.0*PETSC_PI*z) + 1.5*PETSC_PI*PetscPowRealInt(z,2)*PetscCosReal(PETSC_PI*x)*PetscExpReal(y))*PetscExpReal(-theta*(1 - y - 0.1*PetscCosReal(MX*x)*PetscCosReal(MZ*z)*PetscSinReal(MY*y))) + 2.0*(-3.0*y*PetscSinReal(2.0*PETSC_PI*z) - 0.5*PetscCosReal(2.0*PETSC_PI*x)*PetscExpReal(-y)*PetscSinReal(PETSC_PI*y) + 0.5*PETSC_PI*PetscCosReal(PETSC_PI*y)*PetscCosReal(2.0*PETSC_PI*x)*PetscExpReal(-y))*PetscExpReal(-theta*(1 - y - 0.1*PetscCosReal(MX*x)*PetscCosReal(MZ*z)*PetscSinReal(MY*y))) + 2.0*theta*(1 + 0.1*MY*PetscCosReal(MX*x)*PetscCosReal(MY*y)*PetscCosReal(MZ*z))*(-1.5*PetscPowRealInt(y,2)*PetscSinReal(2.0*PETSC_PI*z) + 0.5*PetscCosReal(2.0*PETSC_PI*x)*PetscExpReal(-y)*PetscSinReal(PETSC_PI*y))*PetscExpReal(-theta*(1 - y - 0.1*PetscCosReal(MX*x)*PetscCosReal(MZ*z)*PetscSinReal(MY*y))) ;
1114: */
1115: /*
1116: Fm[0]=-2*x - 2.0*PetscPowRealInt(PETSC_PI,2)*PetscSinReal(PETSC_PI*x);
1117: Fm[1]=-2*y - 2.0*PetscPowRealInt(PETSC_PI,2)*PetscSinReal(PETSC_PI*y);
1118: Fm[2]=-2*z - 2.0*PetscPowRealInt(PETSC_PI,2)*PetscSinReal(PETSC_PI*z);
1119: */
1120: /*
1121: Fm[0] = -2*x + PetscPowRealInt(z,3)*PetscExpReal(y)*PetscSinReal(PETSC_PI*x) + 6.0*z*PetscExpReal(y)*PetscSinReal(PETSC_PI*x) - 6.0*PETSC_PI*PetscPowRealInt(x,2)*PetscCosReal(2.0*PETSC_PI*z) - 2.0*PetscPowRealInt(PETSC_PI,2)*PetscPowRealInt(z,3)*PetscExpReal(y)*PetscSinReal(PETSC_PI*x) + 2.0*PETSC_PI*z*PetscExpReal(-y)*PetscSinReal(PETSC_PI*y)*PetscSinReal(2.0*PETSC_PI*x) - 2.0*z*PetscPowRealInt(PETSC_PI,2)*PetscCosReal(PETSC_PI*y)*PetscExpReal(-y)*PetscSinReal(2.0*PETSC_PI*x) ;
1122: Fm[1] = -2*y - 6.0*PETSC_PI*PetscPowRealInt(y,2)*PetscCosReal(2.0*PETSC_PI*z) + 2.0*z*PetscCosReal(2.0*PETSC_PI*x)*PetscExpReal(-y)*PetscSinReal(PETSC_PI*y) - 6.0*z*PetscPowRealInt(PETSC_PI,2)*PetscCosReal(2.0*PETSC_PI*x)*PetscExpReal(-y)*PetscSinReal(PETSC_PI*y) + PETSC_PI*PetscPowRealInt(z,3)*PetscCosReal(PETSC_PI*x)*PetscExpReal(y) - 4.0*PETSC_PI*z*PetscCosReal(PETSC_PI*y)*PetscCosReal(2.0*PETSC_PI*x)*PetscExpReal(-y);
1123: Fm[2] = -2*z - 6.0*x*PetscSinReal(2.0*PETSC_PI*z) - 6.0*y*PetscSinReal(2.0*PETSC_PI*z) - PetscCosReal(2.0*PETSC_PI*x)*PetscExpReal(-y)*PetscSinReal(PETSC_PI*y) + 8.0*PetscPowRealInt(PETSC_PI,2)*(PetscPowRealInt(x,3) + PetscPowRealInt(y,3))*PetscSinReal(2.0*PETSC_PI*z) + 3.0*PETSC_PI*PetscPowRealInt(z,2)*PetscCosReal(PETSC_PI*x)*PetscExpReal(y) + PETSC_PI*PetscCosReal(PETSC_PI*y)*PetscCosReal(2.0*PETSC_PI*x)*PetscExpReal(-y) ;
1124: */
1125: Fm[0] = -2*x + 2*z*(PetscPowRealInt(PETSC_PI,2)*PetscCosReal(PETSC_PI*y)*PetscExpReal(-y)*PetscSinReal(2.0*PETSC_PI*x) - 1.0*PETSC_PI*PetscExpReal(-y)*PetscSinReal(PETSC_PI*y)*PetscSinReal(2.0*PETSC_PI*x)) + PetscPowRealInt(z,3)*PetscExpReal(y)*PetscSinReal(PETSC_PI*x) + 6.0*z*PetscExpReal(y)*PetscSinReal(PETSC_PI*x) - 1.0*PetscPowRealInt(PETSC_PI,2)*PetscPowRealInt(z,3)*PetscExpReal(y)*PetscSinReal(PETSC_PI*x) + 2.0*PETSC_PI*z*PetscExpReal(-y)*PetscSinReal(PETSC_PI*y)*PetscSinReal(2.0*PETSC_PI*x) - 2.0*z*PetscPowRealInt(PETSC_PI,2)*PetscCosReal(PETSC_PI*y)*PetscExpReal(-y)*PetscSinReal(2.0*PETSC_PI*x);
1126: Fm[1] = -2*y + 2*z*(-PetscCosReal(2.0*PETSC_PI*x)*PetscExpReal(-y)*PetscSinReal(PETSC_PI*y)/2 + PetscPowRealInt(PETSC_PI,2)*PetscCosReal(2.0*PETSC_PI*x)*PetscExpReal(-y)*PetscSinReal(PETSC_PI*y)/2 + PETSC_PI*PetscCosReal(PETSC_PI*y)*PetscCosReal(2.0*PETSC_PI*x)*PetscExpReal(-y)) + 2.0*z*PetscCosReal(2.0*PETSC_PI *x)*PetscExpReal(-y)*PetscSinReal(PETSC_PI*y) - 6.0*z*PetscPowRealInt(PETSC_PI,2)*PetscCosReal(2.0*PETSC_PI*x)*PetscExpReal(-y)*PetscSinReal(PETSC_PI*y) - 4.0*PETSC_PI*z*PetscCosReal(PETSC_PI *y)*PetscCosReal(2.0*PETSC_PI*x)*PetscExpReal(-y);
1127: Fm[2] = -2*z + PetscPowRealInt(z,2)*(-2.0*PetscPowRealInt(PETSC_PI,2)*PetscCosReal(2.0*PETSC_PI*x)*PetscExpReal(-y)*PetscSinReal(PETSC_PI*y) + 2.0*PetscPowRealInt(PETSC_PI,3)*PetscCosReal(PETSC_PI*y)*PetscCosReal(2.0*PETSC_PI*x)*PetscExpReal(-y)) + PetscPowRealInt(z,2)*(PetscCosReal(2.0*PETSC_PI*x)*PetscExpReal(-y)*PetscSinReal(PETSC_PI*y)/2 - 3*PetscPowRealInt(PETSC_PI,2)*PetscCosReal(2.0*PETSC_PI*x)*PetscExpReal(-y)*PetscSinReal(PETSC_PI*y)/2 + PetscPowRealInt(PETSC_PI,3)*PetscCosReal(PETSC_PI*y)*PetscCosReal(2.0*PETSC_PI*x)*PetscExpReal(-y)/2 - 3*PETSC_PI*PetscCosReal(PETSC_PI*y)*PetscCosReal(2.0*PETSC_PI*x)*PetscExpReal(-y)/2) + 1.0*PetscCosReal(2.0*PETSC_PI*x)*PetscExpReal(-y)*PetscSinReal(PETSC_PI*y) + 0.25*PetscPowRealInt(PETSC_PI,3)*PetscPowRealInt(z,4)*PetscCosReal(PETSC_PI*x)*PetscExpReal(y) - 0.25*PETSC_PI*PetscPowRealInt(z,4)*PetscCosReal(PETSC_PI*x)*PetscExpReal(y) - 3.0*PETSC_PI*PetscPowRealInt(z,2)*PetscCosReal(PETSC_PI*x)*PetscExpReal(y) - 1.0*PETSC_PI*PetscCosReal(PETSC_PI *y)*PetscCosReal(2.0*PETSC_PI*x)*PetscExpReal(-y);
1128: }
1129: if (Fc) {
1130: /**Fc = -2.0*PETSC_PI*(PetscPowRealInt(x,3) + PetscPowRealInt(y,3))*PetscCosReal(2.0*PETSC_PI*z) - z*PetscCosReal(2.0*PETSC_PI*x)*PetscExpReal(-y)*PetscSinReal(PETSC_PI*y) + PETSC_PI*PetscPowRealInt(z,3)*PetscCosReal(PETSC_PI*x)*PetscExpReal(y) + PETSC_PI*z*PetscCosReal(PETSC_PI*y)*PetscCosReal(2.0*PETSC_PI*x)*PetscExpReal(-y) ;*/
1131: /**Fc = PETSC_PI*PetscCosReal(PETSC_PI*x) + PETSC_PI*PetscCosReal(PETSC_PI*y) + PETSC_PI*PetscCosReal(PETSC_PI*z);*/
1132: /**Fc = -2.0*PETSC_PI*(PetscPowRealInt(x,3) + PetscPowRealInt(y,3))*PetscCosReal(2.0*PETSC_PI*z) - z*PetscCosReal(2.0*PETSC_PI*x)*PetscExpReal(-y)*PetscSinReal(PETSC_PI*y) + PETSC_PI*PetscPowRealInt(z,3)*PetscCosReal(PETSC_PI*x)*PetscExpReal(y) + PETSC_PI*z*PetscCosReal(PETSC_PI*y)*PetscCosReal(2.0*PETSC_PI*x)*PetscExpReal(-y);*/
1133: *Fc = 0.0;
1134: }
1135: }
1139: static PetscErrorCode DMDACreateManufacturedSolution(PetscInt mx,PetscInt my,PetscInt mz,DM *_da,Vec *_X)
1140: {
1141: DM da,cda;
1142: Vec X;
1143: StokesDOF ***_stokes;
1144: Vec coords;
1145: DMDACoor3d ***_coords;
1146: PetscInt si,sj,sk,ei,ej,ek,i,j,k;
1150: DMDACreate3d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE,DM_BOUNDARY_NONE,DM_BOUNDARY_NONE,DMDA_STENCIL_BOX,
1151: mx+1,my+1,mz+1,PETSC_DECIDE,PETSC_DECIDE,PETSC_DECIDE,4,1,NULL,NULL,NULL,&da);
1152: DMDASetFieldName(da,0,"anlytic_Vx");
1153: DMDASetFieldName(da,1,"anlytic_Vy");
1154: DMDASetFieldName(da,2,"anlytic_Vz");
1155: DMDASetFieldName(da,3,"analytic_P");
1157: DMDASetUniformCoordinates(da,0.0,1.0,0.0,1.0,0.0,1.0);
1159: DMGetCoordinatesLocal(da,&coords);
1160: DMGetCoordinateDM(da,&cda);
1161: DMDAVecGetArray(cda,coords,&_coords);
1163: DMCreateGlobalVector(da,&X);
1164: DMDAVecGetArray(da,X,&_stokes);
1166: DMDAGetCorners(da,&si,&sj,&sk,&ei,&ej,&ek);
1167: for (k = sk; k < sk+ek; k++) {
1168: for (j = sj; j < sj+ej; j++) {
1169: for (i = si; i < si+ei; i++) {
1170: PetscReal pos[NSD],pressure,vel[NSD];
1172: pos[0] = PetscRealPart(_coords[k][j][i].x);
1173: pos[1] = PetscRealPart(_coords[k][j][i].y);
1174: pos[2] = PetscRealPart(_coords[k][j][i].z);
1176: evaluate_MS_FrankKamentski(pos,vel,&pressure,NULL,NULL,NULL);
1178: _stokes[k][j][i].u_dof = vel[0];
1179: _stokes[k][j][i].v_dof = vel[1];
1180: _stokes[k][j][i].w_dof = vel[2];
1181: _stokes[k][j][i].p_dof = pressure;
1182: }
1183: }
1184: }
1185: DMDAVecRestoreArray(da,X,&_stokes);
1186: DMDAVecRestoreArray(cda,coords,&_coords);
1188: *_da = da;
1189: *_X = X;
1190: return(0);
1191: }
1195: static PetscErrorCode DMDAIntegrateErrors3D(DM stokes_da,Vec X,Vec X_analytic)
1196: {
1197: DM cda;
1198: Vec coords,X_analytic_local,X_local;
1199: DMDACoor3d ***_coords;
1200: PetscInt sex,sey,sez,mx,my,mz;
1201: PetscInt ei,ej,ek;
1202: PetscScalar el_coords[NODES_PER_EL*NSD];
1203: StokesDOF ***stokes_analytic,***stokes;
1204: StokesDOF stokes_analytic_e[NODES_PER_EL],stokes_e[NODES_PER_EL];
1206: PetscScalar GNi_p[NSD][NODES_PER_EL],GNx_p[NSD][NODES_PER_EL];
1207: PetscScalar Ni_p[NODES_PER_EL];
1208: PetscInt ngp;
1209: PetscScalar gp_xi[GAUSS_POINTS][NSD];
1210: PetscScalar gp_weight[GAUSS_POINTS];
1211: PetscInt p,i;
1212: PetscScalar J_p,fac;
1213: PetscScalar h,p_e_L2,u_e_L2,u_e_H1,p_L2,u_L2,u_H1,tp_L2,tu_L2,tu_H1;
1214: PetscScalar tint_p_ms,tint_p,int_p_ms,int_p;
1215: PetscInt M;
1216: PetscReal xymin[NSD],xymax[NSD];
1220: /* define quadrature rule */
1221: ConstructGaussQuadrature3D(&ngp,gp_xi,gp_weight);
1223: /* setup for coords */
1224: DMGetCoordinateDM(stokes_da,&cda);
1225: DMGetCoordinatesLocal(stokes_da,&coords);
1226: DMDAVecGetArray(cda,coords,&_coords);
1228: /* setup for analytic */
1229: DMCreateLocalVector(stokes_da,&X_analytic_local);
1230: DMGlobalToLocalBegin(stokes_da,X_analytic,INSERT_VALUES,X_analytic_local);
1231: DMGlobalToLocalEnd(stokes_da,X_analytic,INSERT_VALUES,X_analytic_local);
1232: DMDAVecGetArray(stokes_da,X_analytic_local,&stokes_analytic);
1234: /* setup for solution */
1235: DMCreateLocalVector(stokes_da,&X_local);
1236: DMGlobalToLocalBegin(stokes_da,X,INSERT_VALUES,X_local);
1237: DMGlobalToLocalEnd(stokes_da,X,INSERT_VALUES,X_local);
1238: DMDAVecGetArray(stokes_da,X_local,&stokes);
1240: DMDAGetInfo(stokes_da,0,&M,0,0,0,0,0,0,0,0,0,0,0);
1241: DMDAGetBoundingBox(stokes_da,xymin,xymax);
1243: h = (xymax[0]-xymin[0])/((PetscReal)(M-1));
1245: tp_L2 = tu_L2 = tu_H1 = 0.0;
1246: tint_p_ms = tint_p = 0.0;
1248: DMDAGetElementCorners(stokes_da,&sex,&sey,&sez,&mx,&my,&mz);
1250: for (ek = sez; ek < sez+mz; ek++) {
1251: for (ej = sey; ej < sey+my; ej++) {
1252: for (ei = sex; ei < sex+mx; ei++) {
1253: /* get coords for the element */
1254: GetElementCoords3D(_coords,ei,ej,ek,el_coords);
1255: StokesDAGetNodalFields3D(stokes,ei,ej,ek,stokes_e);
1256: StokesDAGetNodalFields3D(stokes_analytic,ei,ej,ek,stokes_analytic_e);
1258: /* evaluate integral */
1259: for (p = 0; p < ngp; p++) {
1260: ShapeFunctionQ13D_Evaluate(gp_xi[p],Ni_p);
1261: ShapeFunctionQ13D_Evaluate_dxi(gp_xi[p],GNi_p);
1262: ShapeFunctionQ13D_Evaluate_dx(GNi_p,GNx_p,el_coords,&J_p);
1263: fac = gp_weight[p]*J_p;
1265: for (i = 0; i < NODES_PER_EL; i++) {
1266: tint_p_ms = tint_p_ms+fac*Ni_p[i]*stokes_analytic_e[i].p_dof;
1267: tint_p = tint_p +fac*Ni_p[i]*stokes_e[i].p_dof;
1268: }
1269: }
1270: }
1271: }
1272: }
1273: MPI_Allreduce(&tint_p_ms,&int_p_ms,1,MPIU_SCALAR,MPIU_SUM,PETSC_COMM_WORLD);
1274: MPI_Allreduce(&tint_p,&int_p,1,MPIU_SCALAR,MPIU_SUM,PETSC_COMM_WORLD);
1276: PetscPrintf(PETSC_COMM_WORLD,"\\int P dv %1.4e (h) %1.4e (ms)\n",PetscRealPart(int_p),PetscRealPart(int_p_ms));
1278: /* remove mine and add manufacture one */
1279: DMDAVecRestoreArray(stokes_da,X_analytic_local,&stokes_analytic);
1280: DMDAVecRestoreArray(stokes_da,X_local,&stokes);
1282: {
1283: PetscInt k,L,dof;
1284: PetscScalar *fields;
1285: DMDAGetInfo(stokes_da,0, 0,0,0, 0,0,0, &dof,0,0,0,0,0);
1287: VecGetLocalSize(X_local,&L);
1288: VecGetArray(X_local,&fields);
1289: for (k=0; k<L/dof; k++) fields[dof*k+3] = fields[dof*k+3] - int_p + int_p_ms;
1290: VecRestoreArray(X_local,&fields);
1292: VecGetLocalSize(X,&L);
1293: VecGetArray(X,&fields);
1294: for (k=0; k<L/dof; k++) fields[dof*k+3] = fields[dof*k+3] - int_p + int_p_ms;
1295: VecRestoreArray(X,&fields);
1296: }
1298: DMDAVecGetArray(stokes_da,X_local,&stokes);
1299: DMDAVecGetArray(stokes_da,X_analytic_local,&stokes_analytic);
1301: for (ek = sez; ek < sez+mz; ek++) {
1302: for (ej = sey; ej < sey+my; ej++) {
1303: for (ei = sex; ei < sex+mx; ei++) {
1304: /* get coords for the element */
1305: GetElementCoords3D(_coords,ei,ej,ek,el_coords);
1306: StokesDAGetNodalFields3D(stokes,ei,ej,ek,stokes_e);
1307: StokesDAGetNodalFields3D(stokes_analytic,ei,ej,ek,stokes_analytic_e);
1309: /* evaluate integral */
1310: p_e_L2 = 0.0;
1311: u_e_L2 = 0.0;
1312: u_e_H1 = 0.0;
1313: for (p = 0; p < ngp; p++) {
1314: ShapeFunctionQ13D_Evaluate(gp_xi[p],Ni_p);
1315: ShapeFunctionQ13D_Evaluate_dxi(gp_xi[p],GNi_p);
1316: ShapeFunctionQ13D_Evaluate_dx(GNi_p,GNx_p,el_coords,&J_p);
1317: fac = gp_weight[p]*J_p;
1319: for (i = 0; i < NODES_PER_EL; i++) {
1320: PetscScalar u_error,v_error,w_error;
1322: p_e_L2 = p_e_L2+fac*Ni_p[i]*(stokes_e[i].p_dof-stokes_analytic_e[i].p_dof)*(stokes_e[i].p_dof-stokes_analytic_e[i].p_dof);
1324: u_error = stokes_e[i].u_dof-stokes_analytic_e[i].u_dof;
1325: v_error = stokes_e[i].v_dof-stokes_analytic_e[i].v_dof;
1326: w_error = stokes_e[i].w_dof-stokes_analytic_e[i].w_dof;
1327: /*
1328: if (p==0) {
1329: printf("p=0: %d %d %d %1.4e,%1.4e,%1.4e \n", ei,ej,ek,u_error,v_error,w_error);
1330: }
1331: */
1332: u_e_L2 += fac*Ni_p[i]*(u_error*u_error+v_error*v_error+w_error*w_error);
1334: u_e_H1 = u_e_H1+fac*(GNx_p[0][i]*u_error*GNx_p[0][i]*u_error /* du/dx */
1335: +GNx_p[1][i]*u_error*GNx_p[1][i]*u_error
1336: +GNx_p[2][i]*u_error*GNx_p[2][i]*u_error
1337: +GNx_p[0][i]*v_error*GNx_p[0][i]*v_error /* dv/dx */
1338: +GNx_p[1][i]*v_error*GNx_p[1][i]*v_error
1339: +GNx_p[2][i]*v_error*GNx_p[2][i]*v_error
1340: +GNx_p[0][i]*w_error*GNx_p[0][i]*w_error /* dw/dx */
1341: +GNx_p[1][i]*w_error*GNx_p[1][i]*w_error
1342: +GNx_p[2][i]*w_error*GNx_p[2][i]*w_error);
1343: }
1344: }
1346: tp_L2 += p_e_L2;
1347: tu_L2 += u_e_L2;
1348: tu_H1 += u_e_H1;
1349: }
1350: }
1351: }
1352: MPI_Allreduce(&tp_L2,&p_L2,1,MPIU_SCALAR,MPIU_SUM,PETSC_COMM_WORLD);
1353: MPI_Allreduce(&tu_L2,&u_L2,1,MPIU_SCALAR,MPIU_SUM,PETSC_COMM_WORLD);
1354: MPI_Allreduce(&tu_H1,&u_H1,1,MPIU_SCALAR,MPIU_SUM,PETSC_COMM_WORLD);
1355: p_L2 = PetscSqrtScalar(p_L2);
1356: u_L2 = PetscSqrtScalar(u_L2);
1357: u_H1 = PetscSqrtScalar(u_H1);
1359: PetscPrintf(PETSC_COMM_WORLD,"%1.4e %1.4e %1.4e %1.4e \n",PetscRealPart(h),PetscRealPart(p_L2),PetscRealPart(u_L2),PetscRealPart(u_H1));
1362: DMDAVecRestoreArray(cda,coords,&_coords);
1364: DMDAVecRestoreArray(stokes_da,X_analytic_local,&stokes_analytic);
1365: VecDestroy(&X_analytic_local);
1366: DMDAVecRestoreArray(stokes_da,X_local,&stokes);
1367: VecDestroy(&X_local);
1368: return(0);
1369: }
1373: PetscErrorCode DAView_3DVTK_StructuredGrid_appended(DM da,Vec FIELD,const char file_prefix[])
1374: {
1375: char vtk_filename[PETSC_MAX_PATH_LEN];
1376: PetscMPIInt rank;
1377: MPI_Comm comm;
1378: FILE *vtk_fp = NULL;
1379: PetscInt si,sj,sk,nx,ny,nz,i;
1380: PetscInt f,n_fields,N;
1381: DM cda;
1382: Vec coords;
1383: Vec l_FIELD;
1384: PetscScalar *_L_FIELD;
1385: PetscInt memory_offset;
1386: PetscScalar *buffer;
1391: /* create file name */
1392: PetscObjectGetComm((PetscObject)da,&comm);
1393: MPI_Comm_rank(comm,&rank);
1394: PetscSNPrintf(vtk_filename,sizeof(vtk_filename),"subdomain-%s-p%1.4d.vts",file_prefix,rank);
1396: /* open file and write header */
1397: vtk_fp = fopen(vtk_filename,"w");
1398: if (!vtk_fp) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SYS,"Cannot open file = %s \n",vtk_filename);
1400: PetscFPrintf(PETSC_COMM_SELF,vtk_fp,"<?xml version=\"1.0\"?>\n");
1402: /* coords */
1403: DMDAGetGhostCorners(da,&si,&sj,&sk,&nx,&ny,&nz);
1404: N = nx * ny * nz;
1406: #if defined(PETSC_WORDS_BIGENDIAN)
1407: PetscFPrintf(PETSC_COMM_SELF,vtk_fp,"<VTKFile type=\"StructuredGrid\" version=\"0.1\" byte_order=\"BigEndian\">\n");
1408: #else
1409: PetscFPrintf(PETSC_COMM_SELF,vtk_fp,"<VTKFile type=\"StructuredGrid\" version=\"0.1\" byte_order=\"LittleEndian\">\n");
1410: #endif
1411: PetscFPrintf(PETSC_COMM_SELF,vtk_fp," <StructuredGrid WholeExtent=\"%D %D %D %D %D %D\">\n",si,si+nx-1,sj,sj+ny-1,sk,sk+nz-1);
1412: PetscFPrintf(PETSC_COMM_SELF,vtk_fp," <Piece Extent=\"%D %D %D %D %D %D\">\n",si,si+nx-1,sj,sj+ny-1,sk,sk+nz-1);
1414: memory_offset = 0;
1416: PetscFPrintf(PETSC_COMM_SELF,vtk_fp," <CellData></CellData>\n");
1418: PetscFPrintf(PETSC_COMM_SELF,vtk_fp," <Points>\n");
1420: /* copy coordinates */
1421: DMGetCoordinateDM(da,&cda);
1422: DMGetCoordinatesLocal(da,&coords);
1423: PetscFPrintf(PETSC_COMM_SELF,vtk_fp," <DataArray type=\"Float64\" NumberOfComponents=\"3\" format=\"appended\" offset=\"%d\" />\n",memory_offset);
1424: memory_offset = memory_offset + sizeof(PetscInt) + sizeof(PetscScalar)*N*3;
1426: PetscFPrintf(PETSC_COMM_SELF,vtk_fp," </Points>\n");
1428: PetscFPrintf(PETSC_COMM_SELF,vtk_fp," <PointData Scalars=\" ");
1429: DMDAGetInfo(da,0,0,0,0,0,0,0,&n_fields,0,0,0,0,0);
1430: for (f=0; f<n_fields; f++) {
1431: const char *field_name;
1432: DMDAGetFieldName(da,f,&field_name);
1433: PetscFPrintf(PETSC_COMM_SELF,vtk_fp,"%s ",field_name);
1434: }
1435: PetscFPrintf(PETSC_COMM_SELF,vtk_fp,"\">\n");
1437: for (f=0; f<n_fields; f++) {
1438: const char *field_name;
1440: DMDAGetFieldName(da,f,&field_name);
1441: PetscFPrintf(PETSC_COMM_SELF,vtk_fp," <DataArray type=\"Float64\" Name=\"%s\" format=\"appended\" offset=\"%d\"/>\n", field_name,memory_offset);
1442: memory_offset = memory_offset + sizeof(PetscInt) + sizeof(PetscScalar)*N;
1443: }
1445: PetscFPrintf(PETSC_COMM_SELF,vtk_fp," </PointData>\n");
1446: PetscFPrintf(PETSC_COMM_SELF,vtk_fp," </Piece>\n");
1447: PetscFPrintf(PETSC_COMM_SELF,vtk_fp," </StructuredGrid>\n");
1449: PetscMalloc1(N,&buffer);
1450: DMGetLocalVector(da,&l_FIELD);
1451: DMGlobalToLocalBegin(da, FIELD,INSERT_VALUES,l_FIELD);
1452: DMGlobalToLocalEnd(da,FIELD,INSERT_VALUES,l_FIELD);
1453: VecGetArray(l_FIELD,&_L_FIELD);
1455: PetscFPrintf(PETSC_COMM_SELF,vtk_fp," <AppendedData encoding=\"raw\">\n");
1456: PetscFPrintf(PETSC_COMM_SELF,vtk_fp,"_");
1458: /* write coordinates */
1459: {
1460: int length = sizeof(PetscScalar)*N*3;
1461: PetscScalar *allcoords;
1463: fwrite(&length,sizeof(int),1,vtk_fp);
1464: VecGetArray(coords,&allcoords);
1465: fwrite(allcoords,sizeof(PetscScalar),3*N,vtk_fp);
1466: VecRestoreArray(coords,&allcoords);
1467: }
1468: /* write fields */
1469: for (f=0; f<n_fields; f++) {
1470: int length = sizeof(PetscScalar)*N;
1471: fwrite(&length,sizeof(int),1,vtk_fp);
1472: /* load */
1473: for (i=0; i<N; i++) buffer[i] = _L_FIELD[n_fields*i + f];
1475: /* write */
1476: fwrite(buffer,sizeof(PetscScalar),N,vtk_fp);
1477: }
1478: PetscFPrintf(PETSC_COMM_SELF,vtk_fp,"\n </AppendedData>\n");
1480: PetscFPrintf(PETSC_COMM_SELF,vtk_fp,"</VTKFile>\n");
1482: PetscFree(buffer);
1483: VecRestoreArray(l_FIELD,&_L_FIELD);
1484: DMRestoreLocalVector(da,&l_FIELD);
1486: if (vtk_fp) {
1487: fclose(vtk_fp);
1488: vtk_fp = NULL;
1489: }
1491: return(0);
1492: }
1496: PetscErrorCode DAViewVTK_write_PieceExtend(FILE *vtk_fp,PetscInt indent_level,DM da,const char local_file_prefix[])
1497: {
1498: PetscMPIInt size,rank;
1499: MPI_Comm comm;
1500: const PetscInt *lx,*ly,*lz;
1501: PetscInt M,N,P,pM,pN,pP,sum,*olx,*oly,*olz;
1502: PetscInt *osx,*osy,*osz,*oex,*oey,*oez;
1503: PetscInt i,j,k,II,stencil;
1507: /* create file name */
1508: PetscObjectGetComm((PetscObject)da,&comm);
1509: MPI_Comm_size(comm,&size);
1510: MPI_Comm_rank(comm,&rank);
1512: DMDAGetInfo(da,0,&M,&N,&P,&pM,&pN,&pP,0,&stencil,0,0,0,0);
1513: DMDAGetOwnershipRanges(da,&lx,&ly,&lz);
1515: /* generate start,end list */
1516: PetscMalloc1(pM+1,&olx);
1517: PetscMalloc1(pN+1,&oly);
1518: PetscMalloc1(pP+1,&olz);
1519: sum = 0;
1520: for (i=0; i<pM; i++) {
1521: olx[i] = sum;
1522: sum = sum + lx[i];
1523: }
1524: olx[pM] = sum;
1525: sum = 0;
1526: for (i=0; i<pN; i++) {
1527: oly[i] = sum;
1528: sum = sum + ly[i];
1529: }
1530: oly[pN] = sum;
1531: sum = 0;
1532: for (i=0; i<pP; i++) {
1533: olz[i] = sum;
1534: sum = sum + lz[i];
1535: }
1536: olz[pP] = sum;
1538: PetscMalloc1(pM,&osx);
1539: PetscMalloc1(pN,&osy);
1540: PetscMalloc1(pP,&osz);
1541: PetscMalloc1(pM,&oex);
1542: PetscMalloc1(pN,&oey);
1543: PetscMalloc1(pP,&oez);
1544: for (i=0; i<pM; i++) {
1545: osx[i] = olx[i] - stencil;
1546: oex[i] = olx[i] + lx[i] + stencil;
1547: if (osx[i]<0) osx[i]=0;
1548: if (oex[i]>M) oex[i]=M;
1549: }
1551: for (i=0; i<pN; i++) {
1552: osy[i] = oly[i] - stencil;
1553: oey[i] = oly[i] + ly[i] + stencil;
1554: if (osy[i]<0)osy[i]=0;
1555: if (oey[i]>M)oey[i]=N;
1556: }
1557: for (i=0; i<pP; i++) {
1558: osz[i] = olz[i] - stencil;
1559: oez[i] = olz[i] + lz[i] + stencil;
1560: if (osz[i]<0) osz[i]=0;
1561: if (oez[i]>P) oez[i]=P;
1562: }
1564: for (k=0; k<pP; k++) {
1565: for (j=0; j<pN; j++) {
1566: for (i=0; i<pM; i++) {
1567: char name[PETSC_MAX_PATH_LEN];
1568: PetscInt procid = i + j*pM + k*pM*pN; /* convert proc(i,j,k) to pid */
1569: PetscSNPrintf(name,sizeof(name),"subdomain-%s-p%1.4d.vts",local_file_prefix,procid);
1570: for (II=0; II<indent_level; II++) PetscFPrintf(PETSC_COMM_SELF,vtk_fp," ");
1572: PetscFPrintf(PETSC_COMM_SELF,vtk_fp,"<Piece Extent=\"%d %d %d %d %d %d\" Source=\"%s\"/>\n",
1573: osx[i],oex[i]-1,
1574: osy[j],oey[j]-1,
1575: osz[k],oez[k]-1,name);
1576: }
1577: }
1578: }
1579: PetscFree(olx);
1580: PetscFree(oly);
1581: PetscFree(olz);
1582: PetscFree(osx);
1583: PetscFree(osy);
1584: PetscFree(osz);
1585: PetscFree(oex);
1586: PetscFree(oey);
1587: PetscFree(oez);
1588: return(0);
1589: }
1593: PetscErrorCode DAView_3DVTK_PStructuredGrid(DM da,const char file_prefix[],const char local_file_prefix[])
1594: {
1595: MPI_Comm comm;
1596: PetscMPIInt size,rank;
1597: char vtk_filename[PETSC_MAX_PATH_LEN];
1598: FILE *vtk_fp = NULL;
1599: PetscInt M,N,P,si,sj,sk,nx,ny,nz;
1600: PetscInt i,dofs;
1604: /* only master generates this file */
1605: PetscObjectGetComm((PetscObject)da,&comm);
1606: MPI_Comm_size(comm,&size);
1607: MPI_Comm_rank(comm,&rank);
1609: if (rank != 0) return(0);
1611: /* create file name */
1612: PetscSNPrintf(vtk_filename,sizeof(vtk_filename),"%s.pvts",file_prefix);
1613: vtk_fp = fopen(vtk_filename,"w");
1614: if (!vtk_fp) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SYS,"Cannot open file = %s \n",vtk_filename);
1616: /* (VTK) generate pvts header */
1617: PetscFPrintf(PETSC_COMM_SELF,vtk_fp,"<?xml version=\"1.0\"?>\n");
1619: #if defined(PETSC_WORDS_BIGENDIAN)
1620: PetscFPrintf(PETSC_COMM_SELF,vtk_fp,"<VTKFile type=\"PStructuredGrid\" version=\"0.1\" byte_order=\"BigEndian\">\n");
1621: #else
1622: PetscFPrintf(PETSC_COMM_SELF,vtk_fp,"<VTKFile type=\"PStructuredGrid\" version=\"0.1\" byte_order=\"LittleEndian\">\n");
1623: #endif
1625: /* define size of the nodal mesh based on the cell DM */
1626: DMDAGetInfo(da,0,&M,&N,&P,0,0,0,&dofs,0,0,0,0,0);
1627: DMDAGetGhostCorners(da,&si,&sj,&sk,&nx,&ny,&nz);
1628: PetscFPrintf(PETSC_COMM_SELF,vtk_fp," <PStructuredGrid GhostLevel=\"1\" WholeExtent=\"%d %d %d %d %d %d\">\n",0,M-1,0,N-1,0,P-1); /* note overlap = 1 for Q1 */
1630: /* DUMP THE CELL REFERENCES */
1631: PetscFPrintf(PETSC_COMM_SELF,vtk_fp," <PCellData>\n");
1632: PetscFPrintf(PETSC_COMM_SELF,vtk_fp," </PCellData>\n");
1634: PetscFPrintf(PETSC_COMM_SELF,vtk_fp," <PPoints>\n");
1635: PetscFPrintf(PETSC_COMM_SELF,vtk_fp," <PDataArray type=\"Float64\" Name=\"Points\" NumberOfComponents=\"%d\"/>\n",NSD);
1636: PetscFPrintf(PETSC_COMM_SELF,vtk_fp," </PPoints>\n");
1638: PetscFPrintf(PETSC_COMM_SELF,vtk_fp," <PPointData>\n");
1639: for (i=0; i<dofs; i++) {
1640: const char *fieldname;
1641: DMDAGetFieldName(da,i,&fieldname);
1642: PetscFPrintf(PETSC_COMM_SELF,vtk_fp," <PDataArray type=\"Float64\" Name=\"%s\" NumberOfComponents=\"1\"/>\n",fieldname);
1643: }
1644: PetscFPrintf(PETSC_COMM_SELF,vtk_fp," </PPointData>\n");
1646: /* write out the parallel information */
1647: DAViewVTK_write_PieceExtend(vtk_fp,2,da,local_file_prefix);
1649: /* close the file */
1650: PetscFPrintf(PETSC_COMM_SELF,vtk_fp," </PStructuredGrid>\n");
1651: PetscFPrintf(PETSC_COMM_SELF,vtk_fp,"</VTKFile>\n");
1653: if (vtk_fp) {
1654: fclose(vtk_fp);
1655: vtk_fp = NULL;
1656: }
1657: return(0);
1658: }
1662: PetscErrorCode DAView3DPVTS(DM da, Vec x,const char NAME[])
1663: {
1664: char vts_filename[PETSC_MAX_PATH_LEN];
1665: char pvts_filename[PETSC_MAX_PATH_LEN];
1669: PetscSNPrintf(vts_filename,sizeof(vts_filename),"%s-mesh",NAME);
1670: DAView_3DVTK_StructuredGrid_appended(da,x,vts_filename);
1672: PetscSNPrintf(pvts_filename,sizeof(pvts_filename),"%s-mesh",NAME);
1673: DAView_3DVTK_PStructuredGrid(da,pvts_filename,vts_filename);
1674: return(0);
1675: }
1679: PetscErrorCode KSPMonitorStokesBlocks(KSP ksp,PetscInt n,PetscReal rnorm,void *dummy)
1680: {
1682: PetscReal norms[4];
1683: Vec Br,v,w;
1684: Mat A;
1687: KSPGetOperators(ksp,&A,NULL);
1688: MatCreateVecs(A,&w,&v);
1690: KSPBuildResidual(ksp,v,w,&Br);
1692: VecStrideNorm(Br,0,NORM_2,&norms[0]);
1693: VecStrideNorm(Br,1,NORM_2,&norms[1]);
1694: VecStrideNorm(Br,2,NORM_2,&norms[2]);
1695: VecStrideNorm(Br,3,NORM_2,&norms[3]);
1697: VecDestroy(&v);
1698: VecDestroy(&w);
1700: PetscPrintf(PETSC_COMM_WORLD,"%3D KSP Component U,V,W,P residual norm [ %1.12e, %1.12e, %1.12e, %1.12e ]\n",n,norms[0],norms[1],norms[2],norms[3]);
1701: return(0);
1702: }
1706: static PetscErrorCode PCMGSetupViaCoarsen(PC pc,DM da_fine)
1707: {
1708: PetscInt nlevels,k;
1709: PETSC_UNUSED PetscInt finest;
1710: DM *da_list,*daclist;
1711: Mat R;
1712: PetscErrorCode ierr;
1715: nlevels = 1;
1716: PetscOptionsGetInt(NULL,NULL,"-levels",&nlevels,0);
1718: PetscMalloc1(nlevels,&da_list);
1719: for (k=0; k<nlevels; k++) da_list[k] = NULL;
1720: PetscMalloc1(nlevels,&daclist);
1721: for (k=0; k<nlevels; k++) daclist[k] = NULL;
1723: /* finest grid is nlevels - 1 */
1724: finest = nlevels - 1;
1725: daclist[0] = da_fine;
1726: PetscObjectReference((PetscObject)da_fine);
1727: DMCoarsenHierarchy(da_fine,nlevels-1,&daclist[1]);
1728: for (k=0; k<nlevels; k++) {
1729: da_list[k] = daclist[nlevels-1-k];
1730: DMDASetUniformCoordinates(da_list[k],0.0,1.0,0.0,1.0,0.0,1.0);
1731: }
1733: PCMGSetLevels(pc,nlevels,NULL);
1734: PCMGSetType(pc,PC_MG_MULTIPLICATIVE);
1735: PCMGSetGalerkin(pc,PETSC_TRUE);
1737: for (k=1; k<nlevels; k++) {
1738: DMCreateInterpolation(da_list[k-1],da_list[k],&R,NULL);
1739: PCMGSetInterpolation(pc,k,R);
1740: MatDestroy(&R);
1741: }
1743: /* tidy up */
1744: for (k=0; k<nlevels; k++) {
1745: DMDestroy(&da_list[k]);
1746: }
1747: PetscFree(da_list);
1748: PetscFree(daclist);
1749: return(0);
1750: }
1754: static PetscErrorCode solve_stokes_3d_coupled(PetscInt mx,PetscInt my,PetscInt mz)
1755: {
1756: DM da_Stokes;
1757: PetscInt u_dof,p_dof,dof,stencil_width;
1758: Mat A,B;
1759: PetscInt mxl,myl,mzl;
1760: DM vel_cda;
1761: Vec vel_coords;
1762: PetscInt p;
1763: Vec f,X;
1764: DMDACoor3d ***_vel_coords;
1765: PetscInt its;
1766: KSP ksp_S;
1767: PetscInt model_definition = 0;
1768: PetscInt ei,ej,ek,sex,sey,sez,Imx,Jmy,Kmz;
1769: CellProperties cell_properties;
1770: PetscBool write_output = PETSC_FALSE;
1774: /* Generate the da for velocity and pressure */
1775: /* Num nodes in each direction is mx+1, my+1, mz+1 */
1776: u_dof = U_DOFS; /* Vx, Vy - velocities */
1777: p_dof = P_DOFS; /* p - pressure */
1778: dof = u_dof+p_dof;
1779: stencil_width = 1;
1780: DMDACreate3d(PETSC_COMM_WORLD,DM_BOUNDARY_NONE,DM_BOUNDARY_NONE,DM_BOUNDARY_NONE,DMDA_STENCIL_BOX,
1781: mx+1,my+1,mz+1,PETSC_DECIDE,PETSC_DECIDE,PETSC_DECIDE,dof,stencil_width,NULL,NULL,NULL,&da_Stokes);
1782: DMDASetFieldName(da_Stokes,0,"Vx");
1783: DMDASetFieldName(da_Stokes,1,"Vy");
1784: DMDASetFieldName(da_Stokes,2,"Vz");
1785: DMDASetFieldName(da_Stokes,3,"P");
1787: /* unit box [0,1] x [0,1] x [0,1] */
1788: DMDASetUniformCoordinates(da_Stokes,0.0,1.0,0.0,1.0,0.0,1.0);
1790: /* local number of elements */
1791: DMDAGetLocalElementSize(da_Stokes,&mxl,&myl,&mzl);
1793: /* create quadrature point info for PDE coefficients */
1794: CellPropertiesCreate(da_Stokes,&cell_properties);
1796: /* interpolate the coordinates to quadrature points */
1797: DMGetCoordinateDM(da_Stokes,&vel_cda);
1798: DMGetCoordinatesLocal(da_Stokes,&vel_coords);
1799: DMDAVecGetArray(vel_cda,vel_coords,&_vel_coords);
1800: DMDAGetElementCorners(da_Stokes,&sex,&sey,&sez,&Imx,&Jmy,&Kmz);
1801: for (ek = sez; ek < sez+Kmz; ek++) {
1802: for (ej = sey; ej < sey+Jmy; ej++) {
1803: for (ei = sex; ei < sex+Imx; ei++) {
1804: /* get coords for the element */
1805: PetscInt ngp;
1806: PetscScalar gp_xi[GAUSS_POINTS][NSD],gp_weight[GAUSS_POINTS];
1807: PetscScalar el_coords[NSD*NODES_PER_EL];
1808: GaussPointCoefficients *cell;
1810: CellPropertiesGetCell(cell_properties,ei,ej,ek,&cell);
1811: GetElementCoords3D(_vel_coords,ei,ej,ek,el_coords);
1812: ConstructGaussQuadrature3D(&ngp,gp_xi,gp_weight);
1814: for (p = 0; p < GAUSS_POINTS; p++) {
1815: PetscScalar xi_p[NSD],Ni_p[NODES_PER_EL];
1816: PetscScalar gp_x,gp_y,gp_z;
1817: PetscInt n;
1819: xi_p[0] = gp_xi[p][0];
1820: xi_p[1] = gp_xi[p][1];
1821: xi_p[2] = gp_xi[p][2];
1822: ShapeFunctionQ13D_Evaluate(xi_p,Ni_p);
1824: gp_x = gp_y = gp_z = 0.0;
1825: for (n = 0; n < NODES_PER_EL; n++) {
1826: gp_x = gp_x+Ni_p[n]*el_coords[NSD*n];
1827: gp_y = gp_y+Ni_p[n]*el_coords[NSD*n+1];
1828: gp_z = gp_z+Ni_p[n]*el_coords[NSD*n+2];
1829: }
1830: cell->gp_coords[NSD*p] = gp_x;
1831: cell->gp_coords[NSD*p+1] = gp_y;
1832: cell->gp_coords[NSD*p+2] = gp_z;
1833: }
1834: }
1835: }
1836: }
1838: PetscOptionsGetInt(NULL,NULL,"-model",&model_definition,NULL);
1840: switch (model_definition) {
1841: case 0: /* isoviscous */
1842: for (ek = sez; ek < sez+Kmz; ek++) {
1843: for (ej = sey; ej < sey+Jmy; ej++) {
1844: for (ei = sex; ei < sex+Imx; ei++) {
1845: GaussPointCoefficients *cell;
1847: CellPropertiesGetCell(cell_properties,ei,ej,ek,&cell);
1848: for (p = 0; p < GAUSS_POINTS; p++) {
1849: PetscReal coord_x = PetscRealPart(cell->gp_coords[NSD*p]);
1850: PetscReal coord_y = PetscRealPart(cell->gp_coords[NSD*p+1]);
1851: PetscReal coord_z = PetscRealPart(cell->gp_coords[NSD*p+2]);
1853: cell->eta[p] = 1.0;
1855: cell->fx[p] = 0.0*coord_x;
1856: cell->fy[p] = -PetscSinReal(2.2*PETSC_PI*coord_y)*PetscCosReal(1.0*PETSC_PI*coord_x);
1857: cell->fz[p] = 0.0*coord_z;
1858: cell->hc[p] = 0.0;
1859: }
1860: }
1861: }
1862: }
1863: break;
1865: case 1: /* manufactured */
1866: for (ek = sez; ek < sez+Kmz; ek++) {
1867: for (ej = sey; ej < sey+Jmy; ej++) {
1868: for (ei = sex; ei < sex+Imx; ei++) {
1869: PetscReal eta,Fm[NSD],Fc,pos[NSD];
1870: GaussPointCoefficients *cell;
1872: CellPropertiesGetCell(cell_properties,ei,ej,ek,&cell);
1873: for (p = 0; p < GAUSS_POINTS; p++) {
1874: PetscReal coord_x = PetscRealPart(cell->gp_coords[NSD*p]);
1875: PetscReal coord_y = PetscRealPart(cell->gp_coords[NSD*p+1]);
1876: PetscReal coord_z = PetscRealPart(cell->gp_coords[NSD*p+2]);
1878: pos[0] = coord_x;
1879: pos[1] = coord_y;
1880: pos[2] = coord_z;
1882: evaluate_MS_FrankKamentski(pos,NULL,NULL,&eta,Fm,&Fc);
1883: cell->eta[p] = eta;
1885: cell->fx[p] = Fm[0];
1886: cell->fy[p] = Fm[1];
1887: cell->fz[p] = Fm[2];
1888: cell->hc[p] = Fc;
1889: }
1890: }
1891: }
1892: }
1893: break;
1895: case 2: /* solcx */
1896: for (ek = sez; ek < sez+Kmz; ek++) {
1897: for (ej = sey; ej < sey+Jmy; ej++) {
1898: for (ei = sex; ei < sex+Imx; ei++) {
1899: GaussPointCoefficients *cell;
1901: CellPropertiesGetCell(cell_properties,ei,ej,ek,&cell);
1902: for (p = 0; p < GAUSS_POINTS; p++) {
1903: PetscReal coord_x = PetscRealPart(cell->gp_coords[NSD*p]);
1904: PetscReal coord_y = PetscRealPart(cell->gp_coords[NSD*p+1]);
1905: PetscReal coord_z = PetscRealPart(cell->gp_coords[NSD*p+2]);
1907: cell->eta[p] = 1.0;
1909: cell->fx[p] = 0.0;
1910: cell->fy[p] = -PetscSinReal(3.0*PETSC_PI*coord_y)*PetscCosReal(1.0*PETSC_PI*coord_x);
1911: cell->fz[p] = 0.0*coord_z;
1912: cell->hc[p] = 0.0;
1913: }
1914: }
1915: }
1916: }
1917: break;
1919: case 3: /* sinker */
1920: for (ek = sez; ek < sez+Kmz; ek++) {
1921: for (ej = sey; ej < sey+Jmy; ej++) {
1922: for (ei = sex; ei < sex+Imx; ei++) {
1923: GaussPointCoefficients *cell;
1925: CellPropertiesGetCell(cell_properties,ei,ej,ek,&cell);
1926: for (p = 0; p < GAUSS_POINTS; p++) {
1927: PetscReal xp = PetscRealPart(cell->gp_coords[NSD*p]);
1928: PetscReal yp = PetscRealPart(cell->gp_coords[NSD*p+1]);
1929: PetscReal zp = PetscRealPart(cell->gp_coords[NSD*p+2]);
1931: cell->eta[p] = 1.0e-2;
1932: cell->fx[p] = 0.0;
1933: cell->fy[p] = 0.0;
1934: cell->fz[p] = 0.0;
1935: cell->hc[p] = 0.0;
1937: if ((fabs(xp-0.5) < 0.2) &&
1938: (fabs(yp-0.5) < 0.2) &&
1939: (fabs(zp-0.5) < 0.2)) {
1940: cell->eta[p] = 1.0;
1941: cell->fz[p] = 1.0;
1942: }
1944: }
1945: }
1946: }
1947: }
1948: break;
1950: default:
1951: SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP,"No default model is supported. Choose either -model {0,1,2,3}");
1952: break;
1953: }
1955: DMDAVecRestoreArray(vel_cda,vel_coords,&_vel_coords);
1957: /* Generate a matrix with the correct non-zero pattern of type AIJ. This will work in parallel and serial */
1958: DMSetMatType(da_Stokes,MATAIJ);
1959: DMCreateMatrix(da_Stokes,&A);
1960: DMCreateMatrix(da_Stokes,&B);
1961: DMCreateGlobalVector(da_Stokes,&X);
1962: DMCreateGlobalVector(da_Stokes,&f);
1964: /* assemble A11 */
1965: MatZeroEntries(A);
1966: MatZeroEntries(B);
1967: VecZeroEntries(f);
1969: AssembleA_Stokes(A,da_Stokes,cell_properties);
1970: AssembleA_PCStokes(B,da_Stokes,cell_properties);
1971: /* build force vector */
1972: AssembleF_Stokes(f,da_Stokes,cell_properties);
1974: /* SOLVE */
1975: KSPCreate(PETSC_COMM_WORLD,&ksp_S);
1976: KSPSetOptionsPrefix(ksp_S,"stokes_"); /* stokes */
1977: KSPSetOperators(ksp_S,A,B);
1978: KSPSetFromOptions(ksp_S);
1980: {
1981: PC pc;
1982: const PetscInt ufields[] = {0,1,2},pfields[] = {3};
1983: KSPGetPC(ksp_S,&pc);
1984: PCFieldSplitSetBlockSize(pc,4);
1985: PCFieldSplitSetFields(pc,"u",3,ufields,ufields);
1986: PCFieldSplitSetFields(pc,"p",1,pfields,pfields);
1987: }
1989: {
1990: PC pc;
1991: PetscBool same = PETSC_FALSE;
1992: KSPGetPC(ksp_S,&pc);
1993: PetscObjectTypeCompare((PetscObject)pc,PCMG,&same);
1994: if (same) {
1995: PCMGSetupViaCoarsen(pc,da_Stokes);
1996: }
1997: }
1999: {
2000: PetscBool stokes_monitor = PETSC_FALSE;
2001: PetscOptionsGetBool(NULL,NULL,"-stokes_ksp_monitor_blocks",&stokes_monitor,0);
2002: if (stokes_monitor) {
2003: KSPMonitorSet(ksp_S,KSPMonitorStokesBlocks,NULL,NULL);
2004: }
2005: }
2006: KSPSolve(ksp_S,f,X);
2008: PetscOptionsGetBool(NULL,NULL,"-write_pvts",&write_output,NULL);
2009: if (write_output) {DAView3DPVTS(da_Stokes,X,"up");}
2010: {
2011: PetscBool flg = PETSC_FALSE;
2012: char filename[PETSC_MAX_PATH_LEN];
2013: PetscOptionsGetString(NULL,NULL,"-write_binary",filename,sizeof(filename),&flg);
2014: if (flg) {
2015: PetscViewer viewer;
2016: /* PetscViewerBinaryOpen(PETSC_COMM_WORLD,filename[0]?filename:"ex42-binaryoutput",FILE_MODE_WRITE,&viewer); */
2017: PetscViewerVTKOpen(PETSC_COMM_WORLD,"ex42.vts",FILE_MODE_WRITE,&viewer);
2018: VecView(X,viewer);
2019: PetscViewerDestroy(&viewer);
2020: }
2021: }
2022: KSPGetIterationNumber(ksp_S,&its);
2024: /* verify */
2025: if (model_definition == 1) {
2026: DM da_Stokes_analytic;
2027: Vec X_analytic;
2029: DMDACreateManufacturedSolution(mx,my,mz,&da_Stokes_analytic,&X_analytic);
2030: if (write_output) {
2031: DAView3DPVTS(da_Stokes_analytic,X_analytic,"ms");
2032: }
2033: DMDAIntegrateErrors3D(da_Stokes_analytic,X,X_analytic);
2034: if (write_output) {
2035: DAView3DPVTS(da_Stokes,X,"up2");
2036: }
2037: DMDestroy(&da_Stokes_analytic);
2038: VecDestroy(&X_analytic);
2039: }
2041: KSPDestroy(&ksp_S);
2042: VecDestroy(&X);
2043: VecDestroy(&f);
2044: MatDestroy(&A);
2045: MatDestroy(&B);
2047: CellPropertiesDestroy(&cell_properties);
2048: DMDestroy(&da_Stokes);
2049: return(0);
2050: }
2054: int main(int argc,char **args)
2055: {
2057: PetscInt mx,my,mz;
2059: PetscInitialize(&argc,&args,(char*)0,help);
2061: mx = my = mz = 10;
2062: PetscOptionsGetInt(NULL,NULL,"-mx",&mx,NULL);
2063: my = mx; mz = mx;
2064: PetscOptionsGetInt(NULL,NULL,"-my",&my,NULL);
2065: PetscOptionsGetInt(NULL,NULL,"-mz",&mz,NULL);
2067: solve_stokes_3d_coupled(mx,my,mz);
2069: PetscFinalize();
2070: return 0;
2071: }