Actual source code: ex49.c
1: static char help[] = " Solves the compressible plane strain elasticity equations in 2d on the unit domain using Q1 finite elements. \n\
2: Material properties E (Youngs modulus) and nu (Poisson ratio) may vary as a function of space. \n\
3: The model utilises boundary conditions which produce compression in the x direction. \n\
4: Options: \n"
5: "\
6: -mx : number of elements in x-direction \n\
7: -my : number of elements in y-direction \n\
8: -c_str : structure of the coefficients to use. \n"
9: "\
10: -c_str 0 => isotropic material with constant coefficients. \n\
11: Parameters: \n\
12: -iso_E : Youngs modulus \n\
13: -iso_nu : Poisson ratio \n\
14: -c_str 1 => step function in the material properties in x. \n\
15: Parameters: \n\
16: -step_E0 : Youngs modulus to the left of the step \n\
17: -step_nu0 : Poisson ratio to the left of the step \n\
18: -step_E1 : Youngs modulus to the right of the step \n\
19: -step_n1 : Poisson ratio to the right of the step \n\
20: -step_xc : x coordinate of the step \n"
21: "\
22: -c_str 2 => checkerboard material with alternating properties. \n\
23: Repeats the following pattern throughout the domain. For example with 4 materials specified, we would heve \n\
24: -------------------------\n\
25: | D | A | B | C |\n\
26: ------|-----|-----|------\n\
27: | C | D | A | B |\n\
28: ------|-----|-----|------\n\
29: | B | C | D | A |\n\
30: ------|-----|-----|------\n\
31: | A | B | C | D |\n\
32: -------------------------\n\
33: \n\
34: Parameters: \n\
35: -brick_E : a comma separated list of Young's modulii \n\
36: -brick_nu : a comma separated list of Poisson ratios \n\
37: -brick_span : the number of elements in x and y each brick will span \n\
38: -c_str 3 => sponge-like material with alternating properties. \n\
39: Repeats the following pattern throughout the domain \n"
40: "\
41: -----------------------------\n\
42: | [background] |\n\
43: | E0,nu0 |\n\
44: | ----------------- |\n\
45: | | [inclusion] | |\n\
46: | | E1,nu1 | |\n\
47: | | | |\n\
48: | | <---- w ----> | |\n\
49: | | | |\n\
50: | | | |\n\
51: | ----------------- |\n\
52: | |\n\
53: | |\n\
54: -----------------------------\n\
55: <-------- t + w + t ------->\n\
56: \n\
57: Parameters: \n\
58: -sponge_E0 : Youngs modulus of the surrounding material \n\
59: -sponge_E1 : Youngs modulus of the inclusion \n\
60: -sponge_nu0 : Poisson ratio of the surrounding material \n\
61: -sponge_nu1 : Poisson ratio of the inclusion \n\
62: -sponge_t : the number of elements defining the border around each inclusion \n\
63: -sponge_w : the number of elements in x and y each inclusion will span\n\
64: -use_gp_coords : Evaluate the Youngs modulus, Poisson ratio and the body force at the global coordinates of the quadrature points.\n\
65: By default, E, nu and the body force are evaulated at the element center and applied as a constant over the entire element.\n\
66: -use_nonsymbc : Option to use non-symmetric boundary condition imposition. This choice will use less memory.";
68: /* Contributed by Dave May */
70: #include <petscksp.h>
71: #include <petscdm.h>
72: #include <petscdmda.h>
74: static PetscErrorCode DMDABCApplyCompression(DM,Mat,Vec);
75: static PetscErrorCode DMDABCApplySymmetricCompression(DM elas_da,Mat A,Vec f,IS *dofs,Mat *AA,Vec *ff);
77: #define NSD 2 /* number of spatial dimensions */
78: #define NODES_PER_EL 4 /* nodes per element */
79: #define U_DOFS 2 /* degrees of freedom per displacement node */
80: #define GAUSS_POINTS 4
82: /* cell based evaluation */
83: typedef struct {
84: PetscScalar E,nu,fx,fy;
85: } Coefficients;
87: /* Gauss point based evaluation 8+4+4+4 = 20 */
88: typedef struct {
89: PetscScalar gp_coords[2*GAUSS_POINTS];
90: PetscScalar E[GAUSS_POINTS];
91: PetscScalar nu[GAUSS_POINTS];
92: PetscScalar fx[GAUSS_POINTS];
93: PetscScalar fy[GAUSS_POINTS];
94: } GaussPointCoefficients;
96: typedef struct {
97: PetscScalar ux_dof;
98: PetscScalar uy_dof;
99: } ElasticityDOF;
101: /*
103: D = E/((1+nu)(1-2nu)) * [ 1-nu nu 0 ]
104: [ nu 1-nu 0 ]
105: [ 0 0 0.5*(1-2nu) ]
107: B = [ d_dx 0 ]
108: [ 0 d_dy ]
109: [ d_dy d_dx ]
111: */
113: /* FEM routines */
114: /*
115: Element: Local basis function ordering
116: 1-----2
117: | |
118: | |
119: 0-----3
120: */
121: static void ConstructQ12D_Ni(PetscScalar _xi[],PetscScalar Ni[])
122: {
123: PetscScalar xi = _xi[0];
124: PetscScalar eta = _xi[1];
126: Ni[0] = 0.25*(1.0-xi)*(1.0-eta);
127: Ni[1] = 0.25*(1.0-xi)*(1.0+eta);
128: Ni[2] = 0.25*(1.0+xi)*(1.0+eta);
129: Ni[3] = 0.25*(1.0+xi)*(1.0-eta);
130: }
132: static void ConstructQ12D_GNi(PetscScalar _xi[],PetscScalar GNi[][NODES_PER_EL])
133: {
134: PetscScalar xi = _xi[0];
135: PetscScalar eta = _xi[1];
137: GNi[0][0] = -0.25*(1.0-eta);
138: GNi[0][1] = -0.25*(1.0+eta);
139: GNi[0][2] = 0.25*(1.0+eta);
140: GNi[0][3] = 0.25*(1.0-eta);
142: GNi[1][0] = -0.25*(1.0-xi);
143: GNi[1][1] = 0.25*(1.0-xi);
144: GNi[1][2] = 0.25*(1.0+xi);
145: GNi[1][3] = -0.25*(1.0+xi);
146: }
148: static void ConstructQ12D_GNx(PetscScalar GNi[][NODES_PER_EL],PetscScalar GNx[][NODES_PER_EL],PetscScalar coords[],PetscScalar *det_J)
149: {
150: PetscScalar J00,J01,J10,J11,J;
151: PetscScalar iJ00,iJ01,iJ10,iJ11;
152: PetscInt i;
154: J00 = J01 = J10 = J11 = 0.0;
155: for (i = 0; i < NODES_PER_EL; i++) {
156: PetscScalar cx = coords[2*i+0];
157: PetscScalar cy = coords[2*i+1];
159: J00 = J00+GNi[0][i]*cx; /* J_xx = dx/dxi */
160: J01 = J01+GNi[0][i]*cy; /* J_xy = dy/dxi */
161: J10 = J10+GNi[1][i]*cx; /* J_yx = dx/deta */
162: J11 = J11+GNi[1][i]*cy; /* J_yy = dy/deta */
163: }
164: J = (J00*J11)-(J01*J10);
166: iJ00 = J11/J;
167: iJ01 = -J01/J;
168: iJ10 = -J10/J;
169: iJ11 = J00/J;
171: for (i = 0; i < NODES_PER_EL; i++) {
172: GNx[0][i] = GNi[0][i]*iJ00+GNi[1][i]*iJ01;
173: GNx[1][i] = GNi[0][i]*iJ10+GNi[1][i]*iJ11;
174: }
176: if (det_J) *det_J = J;
177: }
179: static void ConstructGaussQuadrature(PetscInt *ngp,PetscScalar gp_xi[][2],PetscScalar gp_weight[])
180: {
181: *ngp = 4;
182: gp_xi[0][0] = -0.57735026919;gp_xi[0][1] = -0.57735026919;
183: gp_xi[1][0] = -0.57735026919;gp_xi[1][1] = 0.57735026919;
184: gp_xi[2][0] = 0.57735026919;gp_xi[2][1] = 0.57735026919;
185: gp_xi[3][0] = 0.57735026919;gp_xi[3][1] = -0.57735026919;
186: gp_weight[0] = 1.0;
187: gp_weight[1] = 1.0;
188: gp_weight[2] = 1.0;
189: gp_weight[3] = 1.0;
190: }
192: static PetscErrorCode DMDAGetElementOwnershipRanges2d(DM da,PetscInt **_lx,PetscInt **_ly)
193: {
195: PetscMPIInt rank;
196: PetscInt proc_I,proc_J;
197: PetscInt cpu_x,cpu_y;
198: PetscInt local_mx,local_my;
199: Vec vlx,vly;
200: PetscInt *LX,*LY,i;
201: PetscScalar *_a;
202: Vec V_SEQ;
203: VecScatter ctx;
206: MPI_Comm_rank(PETSC_COMM_WORLD,&rank);
208: DMDAGetInfo(da,0,0,0,0,&cpu_x,&cpu_y,0,0,0,0,0,0,0);
210: proc_J = rank/cpu_x;
211: proc_I = rank-cpu_x*proc_J;
213: PetscMalloc1(cpu_x,&LX);
214: PetscMalloc1(cpu_y,&LY);
216: DMDAGetElementsSizes(da,&local_mx,&local_my,NULL);
217: VecCreate(PETSC_COMM_WORLD,&vlx);
218: VecSetSizes(vlx,PETSC_DECIDE,cpu_x);
219: VecSetFromOptions(vlx);
221: VecCreate(PETSC_COMM_WORLD,&vly);
222: VecSetSizes(vly,PETSC_DECIDE,cpu_y);
223: VecSetFromOptions(vly);
225: VecSetValue(vlx,proc_I,(PetscScalar)(local_mx+1.0e-9),INSERT_VALUES);
226: VecSetValue(vly,proc_J,(PetscScalar)(local_my+1.0e-9),INSERT_VALUES);
227: VecAssemblyBegin(vlx);VecAssemblyEnd(vlx);
228: VecAssemblyBegin(vly);VecAssemblyEnd(vly);
230: VecScatterCreateToAll(vlx,&ctx,&V_SEQ);
231: VecScatterBegin(ctx,vlx,V_SEQ,INSERT_VALUES,SCATTER_FORWARD);
232: VecScatterEnd(ctx,vlx,V_SEQ,INSERT_VALUES,SCATTER_FORWARD);
233: VecGetArray(V_SEQ,&_a);
234: for (i = 0; i < cpu_x; i++) LX[i] = (PetscInt)PetscRealPart(_a[i]);
235: VecRestoreArray(V_SEQ,&_a);
236: VecScatterDestroy(&ctx);
237: VecDestroy(&V_SEQ);
239: VecScatterCreateToAll(vly,&ctx,&V_SEQ);
240: VecScatterBegin(ctx,vly,V_SEQ,INSERT_VALUES,SCATTER_FORWARD);
241: VecScatterEnd(ctx,vly,V_SEQ,INSERT_VALUES,SCATTER_FORWARD);
242: VecGetArray(V_SEQ,&_a);
243: for (i = 0; i < cpu_y; i++) LY[i] = (PetscInt)PetscRealPart(_a[i]);
244: VecRestoreArray(V_SEQ,&_a);
245: VecScatterDestroy(&ctx);
246: VecDestroy(&V_SEQ);
248: *_lx = LX;
249: *_ly = LY;
251: VecDestroy(&vlx);
252: VecDestroy(&vly);
253: return(0);
254: }
256: static PetscErrorCode DMDACoordViewGnuplot2d(DM da,const char prefix[])
257: {
258: DM cda;
259: Vec coords;
260: DMDACoor2d **_coords;
261: PetscInt si,sj,nx,ny,i,j;
262: FILE *fp;
263: char fname[PETSC_MAX_PATH_LEN];
264: PetscMPIInt rank;
268: MPI_Comm_rank(PETSC_COMM_WORLD,&rank);
269: PetscSNPrintf(fname,sizeof(fname),"%s-p%1.4d.dat",prefix,rank);
270: PetscFOpen(PETSC_COMM_SELF,fname,"w",&fp);
271: if (!fp) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_USER,"Cannot open file");
272: PetscFPrintf(PETSC_COMM_SELF,fp,"### Element geometry for processor %1.4d ### \n",rank);
274: DMGetCoordinateDM(da,&cda);
275: DMGetCoordinatesLocal(da,&coords);
276: DMDAVecGetArray(cda,coords,&_coords);
277: DMDAGetGhostCorners(cda,&si,&sj,0,&nx,&ny,0);
278: for (j = sj; j < sj+ny-1; j++) {
279: for (i = si; i < si+nx-1; i++) {
280: PetscFPrintf(PETSC_COMM_SELF,fp,"%1.6e %1.6e \n",PetscRealPart(_coords[j][i].x),PetscRealPart(_coords[j][i].y));
281: PetscFPrintf(PETSC_COMM_SELF,fp,"%1.6e %1.6e \n",PetscRealPart(_coords[j+1][i].x),PetscRealPart(_coords[j+1][i].y));
282: PetscFPrintf(PETSC_COMM_SELF,fp,"%1.6e %1.6e \n",PetscRealPart(_coords[j+1][i+1].x),PetscRealPart(_coords[j+1][i+1].y));
283: PetscFPrintf(PETSC_COMM_SELF,fp,"%1.6e %1.6e \n",PetscRealPart(_coords[j][i+1].x),PetscRealPart(_coords[j][i+1].y));
284: PetscFPrintf(PETSC_COMM_SELF,fp,"%1.6e %1.6e \n\n",PetscRealPart(_coords[j][i].x),PetscRealPart(_coords[j][i].y));
285: }
286: }
287: DMDAVecRestoreArray(cda,coords,&_coords);
289: PetscFClose(PETSC_COMM_SELF,fp);
290: return(0);
291: }
293: static PetscErrorCode DMDAViewGnuplot2d(DM da,Vec fields,const char comment[],const char prefix[])
294: {
295: DM cda;
296: Vec coords,local_fields;
297: DMDACoor2d **_coords;
298: FILE *fp;
299: char fname[PETSC_MAX_PATH_LEN];
300: const char *field_name;
301: PetscMPIInt rank;
302: PetscInt si,sj,nx,ny,i,j;
303: PetscInt n_dofs,d;
304: PetscScalar *_fields;
308: MPI_Comm_rank(PETSC_COMM_WORLD,&rank);
309: PetscSNPrintf(fname,sizeof(fname),"%s-p%1.4d.dat",prefix,rank);
310: PetscFOpen(PETSC_COMM_SELF,fname,"w",&fp);
311: if (!fp) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_USER,"Cannot open file");
313: PetscFPrintf(PETSC_COMM_SELF,fp,"### %s (processor %1.4d) ### \n",comment,rank);
314: DMDAGetInfo(da,0,0,0,0,0,0,0,&n_dofs,0,0,0,0,0);
315: PetscFPrintf(PETSC_COMM_SELF,fp,"### x y ");
316: for (d = 0; d < n_dofs; d++) {
317: DMDAGetFieldName(da,d,&field_name);
318: PetscFPrintf(PETSC_COMM_SELF,fp,"%s ",field_name);
319: }
320: PetscFPrintf(PETSC_COMM_SELF,fp,"###\n");
322: DMGetCoordinateDM(da,&cda);
323: DMGetCoordinatesLocal(da,&coords);
324: DMDAVecGetArray(cda,coords,&_coords);
325: DMDAGetGhostCorners(cda,&si,&sj,0,&nx,&ny,0);
327: DMCreateLocalVector(da,&local_fields);
328: DMGlobalToLocalBegin(da,fields,INSERT_VALUES,local_fields);
329: DMGlobalToLocalEnd(da,fields,INSERT_VALUES,local_fields);
330: VecGetArray(local_fields,&_fields);
332: for (j = sj; j < sj+ny; j++) {
333: for (i = si; i < si+nx; i++) {
334: PetscScalar coord_x,coord_y;
335: PetscScalar field_d;
337: coord_x = _coords[j][i].x;
338: coord_y = _coords[j][i].y;
340: PetscFPrintf(PETSC_COMM_SELF,fp,"%1.6e %1.6e ",PetscRealPart(coord_x),PetscRealPart(coord_y));
341: for (d = 0; d < n_dofs; d++) {
342: field_d = _fields[n_dofs*((i-si)+(j-sj)*(nx))+d];
343: PetscFPrintf(PETSC_COMM_SELF,fp,"%1.6e ",PetscRealPart(field_d));
344: }
345: PetscFPrintf(PETSC_COMM_SELF,fp,"\n");
346: }
347: }
348: VecRestoreArray(local_fields,&_fields);
349: VecDestroy(&local_fields);
351: DMDAVecRestoreArray(cda,coords,&_coords);
353: PetscFClose(PETSC_COMM_SELF,fp);
354: return(0);
355: }
357: static PetscErrorCode DMDAViewCoefficientsGnuplot2d(DM da,Vec fields,const char comment[],const char prefix[])
358: {
359: DM cda;
360: Vec local_fields;
361: FILE *fp;
362: char fname[PETSC_MAX_PATH_LEN];
363: const char *field_name;
364: PetscMPIInt rank;
365: PetscInt si,sj,nx,ny,i,j,p;
366: PetscInt n_dofs,d;
367: GaussPointCoefficients **_coefficients;
368: PetscErrorCode ierr;
371: MPI_Comm_rank(PETSC_COMM_WORLD,&rank);
372: PetscSNPrintf(fname,sizeof(fname),"%s-p%1.4d.dat",prefix,rank);
373: PetscFOpen(PETSC_COMM_SELF,fname,"w",&fp);
374: if (!fp) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_USER,"Cannot open file");
376: PetscFPrintf(PETSC_COMM_SELF,fp,"### %s (processor %1.4d) ### \n",comment,rank);
377: DMDAGetInfo(da,0,0,0,0,0,0,0,&n_dofs,0,0,0,0,0);
378: PetscFPrintf(PETSC_COMM_SELF,fp,"### x y ");
379: for (d = 0; d < n_dofs; d++) {
380: DMDAGetFieldName(da,d,&field_name);
381: PetscFPrintf(PETSC_COMM_SELF,fp,"%s ",field_name);
382: }
383: PetscFPrintf(PETSC_COMM_SELF,fp,"###\n");
385: DMGetCoordinateDM(da,&cda);
386: DMDAGetGhostCorners(cda,&si,&sj,0,&nx,&ny,0);
388: DMCreateLocalVector(da,&local_fields);
389: DMGlobalToLocalBegin(da,fields,INSERT_VALUES,local_fields);
390: DMGlobalToLocalEnd(da,fields,INSERT_VALUES,local_fields);
391: DMDAVecGetArray(da,local_fields,&_coefficients);
393: for (j = sj; j < sj+ny; j++) {
394: for (i = si; i < si+nx; i++) {
395: PetscScalar coord_x,coord_y;
397: for (p = 0; p < GAUSS_POINTS; p++) {
398: coord_x = _coefficients[j][i].gp_coords[2*p];
399: coord_y = _coefficients[j][i].gp_coords[2*p+1];
401: PetscFPrintf(PETSC_COMM_SELF,fp,"%1.6e %1.6e ",PetscRealPart(coord_x),PetscRealPart(coord_y));
403: PetscFPrintf(PETSC_COMM_SELF,fp,"%1.6e %1.6e %1.6e %1.6e",
404: PetscRealPart(_coefficients[j][i].E[p]),PetscRealPart(_coefficients[j][i].nu[p]),
405: PetscRealPart(_coefficients[j][i].fx[p]),PetscRealPart(_coefficients[j][i].fy[p]));
406: PetscFPrintf(PETSC_COMM_SELF,fp,"\n");
407: }
408: }
409: }
410: DMDAVecRestoreArray(da,local_fields,&_coefficients);
411: VecDestroy(&local_fields);
413: PetscFClose(PETSC_COMM_SELF,fp);
414: return(0);
415: }
417: static void FormStressOperatorQ1(PetscScalar Ke[],PetscScalar coords[],PetscScalar E[],PetscScalar nu[])
418: {
419: PetscInt ngp;
420: PetscScalar gp_xi[GAUSS_POINTS][2];
421: PetscScalar gp_weight[GAUSS_POINTS];
422: PetscInt p,i,j,k,l;
423: PetscScalar GNi_p[NSD][NODES_PER_EL],GNx_p[NSD][NODES_PER_EL];
424: PetscScalar J_p;
425: PetscScalar B[3][U_DOFS*NODES_PER_EL];
426: PetscScalar prop_E,prop_nu,factor,constit_D[3][3];
428: /* define quadrature rule */
429: ConstructGaussQuadrature(&ngp,gp_xi,gp_weight);
431: /* evaluate integral */
432: for (p = 0; p < ngp; p++) {
433: ConstructQ12D_GNi(gp_xi[p],GNi_p);
434: ConstructQ12D_GNx(GNi_p,GNx_p,coords,&J_p);
436: for (i = 0; i < NODES_PER_EL; i++) {
437: PetscScalar d_dx_i = GNx_p[0][i];
438: PetscScalar d_dy_i = GNx_p[1][i];
440: B[0][2*i] = d_dx_i; B[0][2*i+1] = 0.0;
441: B[1][2*i] = 0.0; B[1][2*i+1] = d_dy_i;
442: B[2][2*i] = d_dy_i; B[2][2*i+1] = d_dx_i;
443: }
445: /* form D for the quadrature point */
446: prop_E = E[p];
447: prop_nu = nu[p];
448: factor = prop_E / ((1.0+prop_nu)*(1.0-2.0*prop_nu));
449: constit_D[0][0] = 1.0-prop_nu; constit_D[0][1] = prop_nu; constit_D[0][2] = 0.0;
450: constit_D[1][0] = prop_nu; constit_D[1][1] = 1.0-prop_nu; constit_D[1][2] = 0.0;
451: constit_D[2][0] = 0.0; constit_D[2][1] = 0.0; constit_D[2][2] = 0.5*(1.0-2.0*prop_nu);
452: for (i = 0; i < 3; i++) {
453: for (j = 0; j < 3; j++) {
454: constit_D[i][j] = factor * constit_D[i][j] * gp_weight[p] * J_p;
455: }
456: }
458: /* form Bt tildeD B */
459: /*
460: Ke_ij = Bt_ik . D_kl . B_lj
461: = B_ki . D_kl . B_lj
462: */
463: for (i = 0; i < 8; i++) {
464: for (j = 0; j < 8; j++) {
465: for (k = 0; k < 3; k++) {
466: for (l = 0; l < 3; l++) {
467: Ke[8*i+j] = Ke[8*i+j] + B[k][i] * constit_D[k][l] * B[l][j];
468: }
469: }
470: }
471: }
473: } /* end quadrature */
474: }
476: static void FormMomentumRhsQ1(PetscScalar Fe[],PetscScalar coords[],PetscScalar fx[],PetscScalar fy[])
477: {
478: PetscInt ngp;
479: PetscScalar gp_xi[GAUSS_POINTS][2];
480: PetscScalar gp_weight[GAUSS_POINTS];
481: PetscInt p,i;
482: PetscScalar Ni_p[NODES_PER_EL];
483: PetscScalar GNi_p[NSD][NODES_PER_EL],GNx_p[NSD][NODES_PER_EL];
484: PetscScalar J_p,fac;
486: /* define quadrature rule */
487: ConstructGaussQuadrature(&ngp,gp_xi,gp_weight);
489: /* evaluate integral */
490: for (p = 0; p < ngp; p++) {
491: ConstructQ12D_Ni(gp_xi[p],Ni_p);
492: ConstructQ12D_GNi(gp_xi[p],GNi_p);
493: ConstructQ12D_GNx(GNi_p,GNx_p,coords,&J_p);
494: fac = gp_weight[p]*J_p;
496: for (i = 0; i < NODES_PER_EL; i++) {
497: Fe[NSD*i] += fac*Ni_p[i]*fx[p];
498: Fe[NSD*i+1] += fac*Ni_p[i]*fy[p];
499: }
500: }
501: }
503: /*
504: i,j are the element indices
505: The unknown is a vector quantity.
506: The s[].c is used to indicate the degree of freedom.
507: */
508: static PetscErrorCode DMDAGetElementEqnums_u(MatStencil s_u[],PetscInt i,PetscInt j)
509: {
511: /* displacement */
512: /* node 0 */
513: s_u[0].i = i;s_u[0].j = j;s_u[0].c = 0; /* Ux0 */
514: s_u[1].i = i;s_u[1].j = j;s_u[1].c = 1; /* Uy0 */
516: /* node 1 */
517: s_u[2].i = i;s_u[2].j = j+1;s_u[2].c = 0; /* Ux1 */
518: s_u[3].i = i;s_u[3].j = j+1;s_u[3].c = 1; /* Uy1 */
520: /* node 2 */
521: s_u[4].i = i+1;s_u[4].j = j+1;s_u[4].c = 0; /* Ux2 */
522: s_u[5].i = i+1;s_u[5].j = j+1;s_u[5].c = 1; /* Uy2 */
524: /* node 3 */
525: s_u[6].i = i+1;s_u[6].j = j;s_u[6].c = 0; /* Ux3 */
526: s_u[7].i = i+1;s_u[7].j = j;s_u[7].c = 1; /* Uy3 */
527: return(0);
528: }
530: static PetscErrorCode GetElementCoords(DMDACoor2d **_coords,PetscInt ei,PetscInt ej,PetscScalar el_coords[])
531: {
533: /* get coords for the element */
534: el_coords[NSD*0+0] = _coords[ej][ei].x; el_coords[NSD*0+1] = _coords[ej][ei].y;
535: el_coords[NSD*1+0] = _coords[ej+1][ei].x; el_coords[NSD*1+1] = _coords[ej+1][ei].y;
536: el_coords[NSD*2+0] = _coords[ej+1][ei+1].x; el_coords[NSD*2+1] = _coords[ej+1][ei+1].y;
537: el_coords[NSD*3+0] = _coords[ej][ei+1].x; el_coords[NSD*3+1] = _coords[ej][ei+1].y;
538: return(0);
539: }
541: static PetscErrorCode AssembleA_Elasticity(Mat A,DM elas_da,DM properties_da,Vec properties)
542: {
543: DM cda;
544: Vec coords;
545: DMDACoor2d **_coords;
546: MatStencil u_eqn[NODES_PER_EL*U_DOFS]; /* 2 degrees of freedom */
547: PetscInt sex,sey,mx,my;
548: PetscInt ei,ej;
549: PetscScalar Ae[NODES_PER_EL*U_DOFS*NODES_PER_EL*U_DOFS];
550: PetscScalar el_coords[NODES_PER_EL*NSD];
551: Vec local_properties;
552: GaussPointCoefficients **props;
553: PetscScalar *prop_E,*prop_nu;
554: PetscErrorCode ierr;
557: /* setup for coords */
558: DMGetCoordinateDM(elas_da,&cda);
559: DMGetCoordinatesLocal(elas_da,&coords);
560: DMDAVecGetArray(cda,coords,&_coords);
562: /* setup for coefficients */
563: DMCreateLocalVector(properties_da,&local_properties);
564: DMGlobalToLocalBegin(properties_da,properties,INSERT_VALUES,local_properties);
565: DMGlobalToLocalEnd(properties_da,properties,INSERT_VALUES,local_properties);
566: DMDAVecGetArray(properties_da,local_properties,&props);
568: DMDAGetElementsCorners(elas_da,&sex,&sey,0);
569: DMDAGetElementsSizes(elas_da,&mx,&my,0);
570: for (ej = sey; ej < sey+my; ej++) {
571: for (ei = sex; ei < sex+mx; ei++) {
572: /* get coords for the element */
573: GetElementCoords(_coords,ei,ej,el_coords);
575: /* get coefficients for the element */
576: prop_E = props[ej][ei].E;
577: prop_nu = props[ej][ei].nu;
579: /* initialise element stiffness matrix */
580: PetscMemzero(Ae,sizeof(Ae));
582: /* form element stiffness matrix */
583: FormStressOperatorQ1(Ae,el_coords,prop_E,prop_nu);
585: /* insert element matrix into global matrix */
586: DMDAGetElementEqnums_u(u_eqn,ei,ej);
587: MatSetValuesStencil(A,NODES_PER_EL*U_DOFS,u_eqn,NODES_PER_EL*U_DOFS,u_eqn,Ae,ADD_VALUES);
588: }
589: }
590: MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);
591: MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);
593: DMDAVecRestoreArray(cda,coords,&_coords);
595: DMDAVecRestoreArray(properties_da,local_properties,&props);
596: VecDestroy(&local_properties);
597: return(0);
598: }
600: static PetscErrorCode DMDASetValuesLocalStencil_ADD_VALUES(ElasticityDOF **fields_F,MatStencil u_eqn[],PetscScalar Fe_u[])
601: {
602: PetscInt n;
605: for (n = 0; n < 4; n++) {
606: fields_F[u_eqn[2*n].j][u_eqn[2*n].i].ux_dof = fields_F[u_eqn[2*n].j][u_eqn[2*n].i].ux_dof+Fe_u[2*n];
607: fields_F[u_eqn[2*n+1].j][u_eqn[2*n+1].i].uy_dof = fields_F[u_eqn[2*n+1].j][u_eqn[2*n+1].i].uy_dof+Fe_u[2*n+1];
608: }
609: return(0);
610: }
612: static PetscErrorCode AssembleF_Elasticity(Vec F,DM elas_da,DM properties_da,Vec properties)
613: {
614: DM cda;
615: Vec coords;
616: DMDACoor2d **_coords;
617: MatStencil u_eqn[NODES_PER_EL*U_DOFS]; /* 2 degrees of freedom */
618: PetscInt sex,sey,mx,my;
619: PetscInt ei,ej;
620: PetscScalar Fe[NODES_PER_EL*U_DOFS];
621: PetscScalar el_coords[NODES_PER_EL*NSD];
622: Vec local_properties;
623: GaussPointCoefficients **props;
624: PetscScalar *prop_fx,*prop_fy;
625: Vec local_F;
626: ElasticityDOF **ff;
627: PetscErrorCode ierr;
630: /* setup for coords */
631: DMGetCoordinateDM(elas_da,&cda);
632: DMGetCoordinatesLocal(elas_da,&coords);
633: DMDAVecGetArray(cda,coords,&_coords);
635: /* setup for coefficients */
636: DMGetLocalVector(properties_da,&local_properties);
637: DMGlobalToLocalBegin(properties_da,properties,INSERT_VALUES,local_properties);
638: DMGlobalToLocalEnd(properties_da,properties,INSERT_VALUES,local_properties);
639: DMDAVecGetArray(properties_da,local_properties,&props);
641: /* get access to the vector */
642: DMGetLocalVector(elas_da,&local_F);
643: VecZeroEntries(local_F);
644: DMDAVecGetArray(elas_da,local_F,&ff);
646: DMDAGetElementsCorners(elas_da,&sex,&sey,0);
647: DMDAGetElementsSizes(elas_da,&mx,&my,0);
648: for (ej = sey; ej < sey+my; ej++) {
649: for (ei = sex; ei < sex+mx; ei++) {
650: /* get coords for the element */
651: GetElementCoords(_coords,ei,ej,el_coords);
653: /* get coefficients for the element */
654: prop_fx = props[ej][ei].fx;
655: prop_fy = props[ej][ei].fy;
657: /* initialise element stiffness matrix */
658: PetscMemzero(Fe,sizeof(Fe));
660: /* form element stiffness matrix */
661: FormMomentumRhsQ1(Fe,el_coords,prop_fx,prop_fy);
663: /* insert element matrix into global matrix */
664: DMDAGetElementEqnums_u(u_eqn,ei,ej);
666: DMDASetValuesLocalStencil_ADD_VALUES(ff,u_eqn,Fe);
667: }
668: }
670: DMDAVecRestoreArray(elas_da,local_F,&ff);
671: DMLocalToGlobalBegin(elas_da,local_F,ADD_VALUES,F);
672: DMLocalToGlobalEnd(elas_da,local_F,ADD_VALUES,F);
673: DMRestoreLocalVector(elas_da,&local_F);
675: DMDAVecRestoreArray(cda,coords,&_coords);
677: DMDAVecRestoreArray(properties_da,local_properties,&props);
678: DMRestoreLocalVector(properties_da,&local_properties);
679: return(0);
680: }
682: static PetscErrorCode solve_elasticity_2d(PetscInt mx,PetscInt my)
683: {
684: DM elas_da,da_prop;
685: PetscInt u_dof,dof,stencil_width;
686: Mat A;
687: PetscInt mxl,myl;
688: DM prop_cda,vel_cda;
689: Vec prop_coords,vel_coords;
690: PetscInt si,sj,nx,ny,i,j,p;
691: Vec f,X;
692: PetscInt prop_dof,prop_stencil_width;
693: Vec properties,l_properties;
694: MatNullSpace matnull;
695: PetscReal dx,dy;
696: PetscInt M,N;
697: DMDACoor2d **_prop_coords,**_vel_coords;
698: GaussPointCoefficients **element_props;
699: KSP ksp_E;
700: PetscInt coefficient_structure = 0;
701: PetscInt cpu_x,cpu_y,*lx = NULL,*ly = NULL;
702: PetscBool use_gp_coords = PETSC_FALSE;
703: PetscBool use_nonsymbc = PETSC_FALSE;
704: PetscBool no_view = PETSC_FALSE;
705: PetscBool flg;
706: PetscErrorCode ierr;
709: /* Generate the da for velocity and pressure */
710: /*
711: We use Q1 elements for the temperature.
712: FEM has a 9-point stencil (BOX) or connectivity pattern
713: Num nodes in each direction is mx+1, my+1
714: */
715: u_dof = U_DOFS; /* Vx, Vy - velocities */
716: dof = u_dof;
717: stencil_width = 1;
718: DMDACreate2d(PETSC_COMM_WORLD, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE,DMDA_STENCIL_BOX,mx+1,my+1,PETSC_DECIDE,PETSC_DECIDE,dof,stencil_width,NULL,NULL,&elas_da);
720: DMSetMatType(elas_da,MATAIJ);
721: DMSetFromOptions(elas_da);
722: DMSetUp(elas_da);
724: DMDASetFieldName(elas_da,0,"Ux");
725: DMDASetFieldName(elas_da,1,"Uy");
727: /* unit box [0,1] x [0,1] */
728: DMDASetUniformCoordinates(elas_da,0.0,1.0,0.0,1.0,0.0,1.0);
730: /* Generate element properties, we will assume all material properties are constant over the element */
731: /* local number of elements */
732: DMDAGetElementsSizes(elas_da,&mxl,&myl,NULL);
734: /* !!! IN PARALLEL WE MUST MAKE SURE THE TWO DMDA's ALIGN !!! */
735: DMDAGetInfo(elas_da,0,0,0,0,&cpu_x,&cpu_y,0,0,0,0,0,0,0);
736: DMDAGetElementOwnershipRanges2d(elas_da,&lx,&ly);
738: prop_dof = (PetscInt)(sizeof(GaussPointCoefficients)/sizeof(PetscScalar)); /* gauss point setup */
739: prop_stencil_width = 0;
740: DMDACreate2d(PETSC_COMM_WORLD, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE,DMDA_STENCIL_BOX,mx,my,cpu_x,cpu_y,prop_dof,prop_stencil_width,lx,ly,&da_prop);
741: DMSetFromOptions(da_prop);
742: DMSetUp(da_prop);
744: PetscFree(lx);
745: PetscFree(ly);
747: /* define centroid positions */
748: DMDAGetInfo(da_prop,0,&M,&N,0,0,0,0,0,0,0,0,0,0);
749: dx = 1.0/((PetscReal)(M));
750: dy = 1.0/((PetscReal)(N));
752: DMDASetUniformCoordinates(da_prop,0.0+0.5*dx,1.0-0.5*dx,0.0+0.5*dy,1.0-0.5*dy,0.0,1.0);
754: /* define coefficients */
755: PetscOptionsGetInt(NULL,NULL,"-c_str",&coefficient_structure,NULL);
757: DMCreateGlobalVector(da_prop,&properties);
758: DMCreateLocalVector(da_prop,&l_properties);
759: DMDAVecGetArray(da_prop,l_properties,&element_props);
761: DMGetCoordinateDM(da_prop,&prop_cda);
762: DMGetCoordinatesLocal(da_prop,&prop_coords);
763: DMDAVecGetArray(prop_cda,prop_coords,&_prop_coords);
765: DMDAGetGhostCorners(prop_cda,&si,&sj,0,&nx,&ny,0);
767: DMGetCoordinateDM(elas_da,&vel_cda);
768: DMGetCoordinatesLocal(elas_da,&vel_coords);
769: DMDAVecGetArray(vel_cda,vel_coords,&_vel_coords);
771: /* interpolate the coordinates */
772: for (j = sj; j < sj+ny; j++) {
773: for (i = si; i < si+nx; i++) {
774: PetscInt ngp;
775: PetscScalar gp_xi[GAUSS_POINTS][2],gp_weight[GAUSS_POINTS];
776: PetscScalar el_coords[8];
778: GetElementCoords(_vel_coords,i,j,el_coords);
779: ConstructGaussQuadrature(&ngp,gp_xi,gp_weight);
781: for (p = 0; p < GAUSS_POINTS; p++) {
782: PetscScalar gp_x,gp_y;
783: PetscInt n;
784: PetscScalar xi_p[2],Ni_p[4];
786: xi_p[0] = gp_xi[p][0];
787: xi_p[1] = gp_xi[p][1];
788: ConstructQ12D_Ni(xi_p,Ni_p);
790: gp_x = 0.0;
791: gp_y = 0.0;
792: for (n = 0; n < NODES_PER_EL; n++) {
793: gp_x = gp_x+Ni_p[n]*el_coords[2*n];
794: gp_y = gp_y+Ni_p[n]*el_coords[2*n+1];
795: }
796: element_props[j][i].gp_coords[2*p] = gp_x;
797: element_props[j][i].gp_coords[2*p+1] = gp_y;
798: }
799: }
800: }
802: /* define the coefficients */
803: PetscOptionsGetBool(NULL,NULL,"-use_gp_coords",&use_gp_coords,&flg);
805: for (j = sj; j < sj+ny; j++) {
806: for (i = si; i < si+nx; i++) {
807: PetscScalar centroid_x = _prop_coords[j][i].x; /* centroids of cell */
808: PetscScalar centroid_y = _prop_coords[j][i].y;
809: PETSC_UNUSED PetscScalar coord_x,coord_y;
811: if (coefficient_structure == 0) { /* isotropic */
812: PetscScalar opts_E,opts_nu;
814: opts_E = 1.0;
815: opts_nu = 0.33;
816: PetscOptionsGetScalar(NULL,NULL,"-iso_E",&opts_E,&flg);
817: PetscOptionsGetScalar(NULL,NULL,"-iso_nu",&opts_nu,&flg);
819: for (p = 0; p < GAUSS_POINTS; p++) {
820: element_props[j][i].E[p] = opts_E;
821: element_props[j][i].nu[p] = opts_nu;
823: element_props[j][i].fx[p] = 0.0;
824: element_props[j][i].fy[p] = 0.0;
825: }
826: } else if (coefficient_structure == 1) { /* step */
827: PetscScalar opts_E0,opts_nu0,opts_xc;
828: PetscScalar opts_E1,opts_nu1;
830: opts_E0 = opts_E1 = 1.0;
831: opts_nu0 = opts_nu1 = 0.333;
832: opts_xc = 0.5;
833: PetscOptionsGetScalar(NULL,NULL,"-step_E0",&opts_E0,&flg);
834: PetscOptionsGetScalar(NULL,NULL,"-step_nu0",&opts_nu0,&flg);
835: PetscOptionsGetScalar(NULL,NULL,"-step_E1",&opts_E1,&flg);
836: PetscOptionsGetScalar(NULL,NULL,"-step_nu1",&opts_nu1,&flg);
837: PetscOptionsGetScalar(NULL,NULL,"-step_xc",&opts_xc,&flg);
839: for (p = 0; p < GAUSS_POINTS; p++) {
840: coord_x = centroid_x;
841: coord_y = centroid_y;
842: if (use_gp_coords) {
843: coord_x = element_props[j][i].gp_coords[2*p];
844: coord_y = element_props[j][i].gp_coords[2*p+1];
845: }
847: element_props[j][i].E[p] = opts_E0;
848: element_props[j][i].nu[p] = opts_nu0;
849: if (PetscRealPart(coord_x) > PetscRealPart(opts_xc)) {
850: element_props[j][i].E[p] = opts_E1;
851: element_props[j][i].nu[p] = opts_nu1;
852: }
854: element_props[j][i].fx[p] = 0.0;
855: element_props[j][i].fy[p] = 0.0;
856: }
857: } else if (coefficient_structure == 2) { /* brick */
858: PetscReal values_E[10];
859: PetscReal values_nu[10];
860: PetscInt nbricks,maxnbricks;
861: PetscInt index,span;
862: PetscInt jj;
864: flg = PETSC_FALSE;
865: maxnbricks = 10;
866: PetscOptionsGetRealArray(NULL,NULL, "-brick_E",values_E,&maxnbricks,&flg);
867: nbricks = maxnbricks;
868: if (!flg) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_USER,"User must supply a list of E values for each brick");
870: flg = PETSC_FALSE;
871: maxnbricks = 10;
872: PetscOptionsGetRealArray(NULL,NULL, "-brick_nu",values_nu,&maxnbricks,&flg);
873: if (!flg) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_USER,"User must supply a list of nu values for each brick");
874: if (maxnbricks != nbricks) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_USER,"User must supply equal numbers of values for E and nu");
876: span = 1;
877: PetscOptionsGetInt(NULL,NULL,"-brick_span",&span,&flg);
879: /* cycle through the indices so that no two material properties are repeated in lines of x or y */
880: jj = (j/span)%nbricks;
881: index = (jj+i/span)%nbricks;
882: /*printf("j=%d: index = %d \n", j,index); */
884: for (p = 0; p < GAUSS_POINTS; p++) {
885: element_props[j][i].E[p] = values_E[index];
886: element_props[j][i].nu[p] = values_nu[index];
887: }
888: } else if (coefficient_structure == 3) { /* sponge */
889: PetscScalar opts_E0,opts_nu0;
890: PetscScalar opts_E1,opts_nu1;
891: PetscInt opts_t,opts_w;
892: PetscInt ii,jj,ci,cj;
894: opts_E0 = opts_E1 = 1.0;
895: opts_nu0 = opts_nu1 = 0.333;
896: PetscOptionsGetScalar(NULL,NULL,"-sponge_E0",&opts_E0,&flg);
897: PetscOptionsGetScalar(NULL,NULL,"-sponge_nu0",&opts_nu0,&flg);
898: PetscOptionsGetScalar(NULL,NULL,"-sponge_E1",&opts_E1,&flg);
899: PetscOptionsGetScalar(NULL,NULL,"-sponge_nu1",&opts_nu1,&flg);
901: opts_t = opts_w = 1;
902: PetscOptionsGetInt(NULL,NULL,"-sponge_t",&opts_t,&flg);
903: PetscOptionsGetInt(NULL,NULL,"-sponge_w",&opts_w,&flg);
905: ii = (i)/(opts_t+opts_w+opts_t);
906: jj = (j)/(opts_t+opts_w+opts_t);
908: ci = i - ii*(opts_t+opts_w+opts_t);
909: cj = j - jj*(opts_t+opts_w+opts_t);
911: for (p = 0; p < GAUSS_POINTS; p++) {
912: element_props[j][i].E[p] = opts_E0;
913: element_props[j][i].nu[p] = opts_nu0;
914: }
915: if ((ci >= opts_t) && (ci < opts_t+opts_w)) {
916: if ((cj >= opts_t) && (cj < opts_t+opts_w)) {
917: for (p = 0; p < GAUSS_POINTS; p++) {
918: element_props[j][i].E[p] = opts_E1;
919: element_props[j][i].nu[p] = opts_nu1;
920: }
921: }
922: }
923: } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_USER,"Unknown coefficient_structure");
924: }
925: }
926: DMDAVecRestoreArray(prop_cda,prop_coords,&_prop_coords);
928: DMDAVecRestoreArray(vel_cda,vel_coords,&_vel_coords);
930: DMDAVecRestoreArray(da_prop,l_properties,&element_props);
931: DMLocalToGlobalBegin(da_prop,l_properties,ADD_VALUES,properties);
932: DMLocalToGlobalEnd(da_prop,l_properties,ADD_VALUES,properties);
934: PetscOptionsGetBool(NULL,NULL,"-no_view",&no_view,NULL);
935: if (!no_view) {
936: DMDAViewCoefficientsGnuplot2d(da_prop,properties,"Coeffcients for elasticity eqn.","properties");
937: DMDACoordViewGnuplot2d(elas_da,"mesh");
938: }
940: /* Generate a matrix with the correct non-zero pattern of type AIJ. This will work in parallel and serial */
941: DMCreateMatrix(elas_da,&A);
942: DMGetCoordinates(elas_da,&vel_coords);
943: MatNullSpaceCreateRigidBody(vel_coords,&matnull);
944: MatSetNearNullSpace(A,matnull);
945: MatNullSpaceDestroy(&matnull);
946: MatCreateVecs(A,&f,&X);
948: /* assemble A11 */
949: MatZeroEntries(A);
950: VecZeroEntries(f);
952: AssembleA_Elasticity(A,elas_da,da_prop,properties);
953: /* build force vector */
954: AssembleF_Elasticity(f,elas_da,da_prop,properties);
956: KSPCreate(PETSC_COMM_WORLD,&ksp_E);
957: KSPSetOptionsPrefix(ksp_E,"elas_"); /* elasticity */
959: PetscOptionsGetBool(NULL,NULL,"-use_nonsymbc",&use_nonsymbc,&flg);
960: /* solve */
961: if (!use_nonsymbc) {
962: Mat AA;
963: Vec ff,XX;
964: IS is;
965: VecScatter scat;
967: DMDABCApplySymmetricCompression(elas_da,A,f,&is,&AA,&ff);
968: VecDuplicate(ff,&XX);
970: KSPSetOperators(ksp_E,AA,AA);
971: KSPSetFromOptions(ksp_E);
973: KSPSolve(ksp_E,ff,XX);
975: /* push XX back into X */
976: DMDABCApplyCompression(elas_da,NULL,X);
978: VecScatterCreate(XX,NULL,X,is,&scat);
979: VecScatterBegin(scat,XX,X,INSERT_VALUES,SCATTER_FORWARD);
980: VecScatterEnd(scat,XX,X,INSERT_VALUES,SCATTER_FORWARD);
981: VecScatterDestroy(&scat);
983: MatDestroy(&AA);
984: VecDestroy(&ff);
985: VecDestroy(&XX);
986: ISDestroy(&is);
987: } else {
988: DMDABCApplyCompression(elas_da,A,f);
990: KSPSetOperators(ksp_E,A,A);
991: KSPSetFromOptions(ksp_E);
993: KSPSolve(ksp_E,f,X);
994: }
996: if (!no_view) {DMDAViewGnuplot2d(elas_da,X,"Displacement solution for elasticity eqn.","X");}
997: KSPDestroy(&ksp_E);
999: VecDestroy(&X);
1000: VecDestroy(&f);
1001: MatDestroy(&A);
1003: DMDestroy(&elas_da);
1004: DMDestroy(&da_prop);
1006: VecDestroy(&properties);
1007: VecDestroy(&l_properties);
1008: return(0);
1009: }
1011: int main(int argc,char **args)
1012: {
1014: PetscInt mx,my;
1016: PetscInitialize(&argc,&args,(char*)0,help);if (ierr) return ierr;
1017: mx = my = 10;
1018: PetscOptionsGetInt(NULL,NULL,"-mx",&mx,NULL);
1019: PetscOptionsGetInt(NULL,NULL,"-my",&my,NULL);
1020: solve_elasticity_2d(mx,my);
1021: PetscFinalize();
1022: return ierr;
1023: }
1025: /* -------------------------- helpers for boundary conditions -------------------------------- */
1027: static PetscErrorCode BCApply_EAST(DM da,PetscInt d_idx,PetscScalar bc_val,Mat A,Vec b)
1028: {
1029: DM cda;
1030: Vec coords;
1031: PetscInt si,sj,nx,ny,i,j;
1032: PetscInt M,N;
1033: DMDACoor2d **_coords;
1034: const PetscInt *g_idx;
1035: PetscInt *bc_global_ids;
1036: PetscScalar *bc_vals;
1037: PetscInt nbcs;
1038: PetscInt n_dofs;
1039: PetscErrorCode ierr;
1040: ISLocalToGlobalMapping ltogm;
1043: /* enforce bc's */
1044: DMGetLocalToGlobalMapping(da,<ogm);
1045: ISLocalToGlobalMappingGetIndices(ltogm,&g_idx);
1047: DMGetCoordinateDM(da,&cda);
1048: DMGetCoordinatesLocal(da,&coords);
1049: DMDAVecGetArray(cda,coords,&_coords);
1050: DMDAGetGhostCorners(cda,&si,&sj,0,&nx,&ny,0);
1051: DMDAGetInfo(da,0,&M,&N,0,0,0,0,&n_dofs,0,0,0,0,0);
1053: /* --- */
1055: PetscMalloc1(ny*n_dofs,&bc_global_ids);
1056: PetscMalloc1(ny*n_dofs,&bc_vals);
1058: /* init the entries to -1 so VecSetValues will ignore them */
1059: for (i = 0; i < ny*n_dofs; i++) bc_global_ids[i] = -1;
1061: i = nx-1;
1062: for (j = 0; j < ny; j++) {
1063: PetscInt local_id;
1064: PETSC_UNUSED PetscScalar coordx,coordy;
1066: local_id = i+j*nx;
1068: bc_global_ids[j] = g_idx[n_dofs*local_id+d_idx];
1070: coordx = _coords[j+sj][i+si].x;
1071: coordy = _coords[j+sj][i+si].y;
1073: bc_vals[j] = bc_val;
1074: }
1075: ISLocalToGlobalMappingRestoreIndices(ltogm,&g_idx);
1076: nbcs = 0;
1077: if ((si+nx) == (M)) nbcs = ny;
1079: if (b) {
1080: VecSetValues(b,nbcs,bc_global_ids,bc_vals,INSERT_VALUES);
1081: VecAssemblyBegin(b);
1082: VecAssemblyEnd(b);
1083: }
1084: if (A) {
1085: MatZeroRows(A,nbcs,bc_global_ids,1.0,0,0);
1086: }
1088: PetscFree(bc_vals);
1089: PetscFree(bc_global_ids);
1091: DMDAVecRestoreArray(cda,coords,&_coords);
1092: return(0);
1093: }
1095: static PetscErrorCode BCApply_WEST(DM da,PetscInt d_idx,PetscScalar bc_val,Mat A,Vec b)
1096: {
1097: DM cda;
1098: Vec coords;
1099: PetscInt si,sj,nx,ny,i,j;
1100: PetscInt M,N;
1101: DMDACoor2d **_coords;
1102: const PetscInt *g_idx;
1103: PetscInt *bc_global_ids;
1104: PetscScalar *bc_vals;
1105: PetscInt nbcs;
1106: PetscInt n_dofs;
1107: PetscErrorCode ierr;
1108: ISLocalToGlobalMapping ltogm;
1111: /* enforce bc's */
1112: DMGetLocalToGlobalMapping(da,<ogm);
1113: ISLocalToGlobalMappingGetIndices(ltogm,&g_idx);
1115: DMGetCoordinateDM(da,&cda);
1116: DMGetCoordinatesLocal(da,&coords);
1117: DMDAVecGetArray(cda,coords,&_coords);
1118: DMDAGetGhostCorners(cda,&si,&sj,0,&nx,&ny,0);
1119: DMDAGetInfo(da,0,&M,&N,0,0,0,0,&n_dofs,0,0,0,0,0);
1121: /* --- */
1123: PetscMalloc1(ny*n_dofs,&bc_global_ids);
1124: PetscMalloc1(ny*n_dofs,&bc_vals);
1126: /* init the entries to -1 so VecSetValues will ignore them */
1127: for (i = 0; i < ny*n_dofs; i++) bc_global_ids[i] = -1;
1129: i = 0;
1130: for (j = 0; j < ny; j++) {
1131: PetscInt local_id;
1132: PETSC_UNUSED PetscScalar coordx,coordy;
1134: local_id = i+j*nx;
1136: bc_global_ids[j] = g_idx[n_dofs*local_id+d_idx];
1138: coordx = _coords[j+sj][i+si].x;
1139: coordy = _coords[j+sj][i+si].y;
1141: bc_vals[j] = bc_val;
1142: }
1143: ISLocalToGlobalMappingRestoreIndices(ltogm,&g_idx);
1144: nbcs = 0;
1145: if (si == 0) nbcs = ny;
1147: if (b) {
1148: VecSetValues(b,nbcs,bc_global_ids,bc_vals,INSERT_VALUES);
1149: VecAssemblyBegin(b);
1150: VecAssemblyEnd(b);
1151: }
1152: if (A) {
1153: MatZeroRows(A,nbcs,bc_global_ids,1.0,0,0);
1154: }
1156: PetscFree(bc_vals);
1157: PetscFree(bc_global_ids);
1159: DMDAVecRestoreArray(cda,coords,&_coords);
1160: return(0);
1161: }
1163: static PetscErrorCode DMDABCApplyCompression(DM elas_da,Mat A,Vec f)
1164: {
1168: BCApply_EAST(elas_da,0,-1.0,A,f);
1169: BCApply_EAST(elas_da,1, 0.0,A,f);
1170: BCApply_WEST(elas_da,0,1.0,A,f);
1171: BCApply_WEST(elas_da,1,0.0,A,f);
1172: return(0);
1173: }
1175: static PetscErrorCode Orthogonalize(PetscInt n,Vec *vecs)
1176: {
1177: PetscInt i,j;
1178: PetscScalar dot;
1182: for (i=0; i<n; i++) {
1183: VecNormalize(vecs[i],NULL);
1184: for (j=i+1; j<n; j++) {
1185: VecDot(vecs[i],vecs[j],&dot);
1186: VecAXPY(vecs[j],-dot,vecs[i]);
1187: }
1188: }
1189: return(0);
1190: }
1192: static PetscErrorCode DMDABCApplySymmetricCompression(DM elas_da,Mat A,Vec f,IS *dofs,Mat *AA,Vec *ff)
1193: {
1195: PetscInt start,end,m;
1196: PetscInt *unconstrained;
1197: PetscInt cnt,i;
1198: Vec x;
1199: PetscScalar *_x;
1200: IS is;
1201: VecScatter scat;
1204: /* push bc's into f and A */
1205: VecDuplicate(f,&x);
1206: BCApply_EAST(elas_da,0,-1.0,A,x);
1207: BCApply_EAST(elas_da,1, 0.0,A,x);
1208: BCApply_WEST(elas_da,0,1.0,A,x);
1209: BCApply_WEST(elas_da,1,0.0,A,x);
1211: /* define which dofs are not constrained */
1212: VecGetLocalSize(x,&m);
1213: PetscMalloc1(m,&unconstrained);
1214: VecGetOwnershipRange(x,&start,&end);
1215: VecGetArray(x,&_x);
1216: cnt = 0;
1217: for (i = 0; i < m; i+=2) {
1218: PetscReal val1,val2;
1220: val1 = PetscRealPart(_x[i]);
1221: val2 = PetscRealPart(_x[i+1]);
1222: if (PetscAbs(val1) < 0.1 && PetscAbs(val2) < 0.1) {
1223: unconstrained[cnt] = start + i;
1224: cnt++;
1225: unconstrained[cnt] = start + i + 1;
1226: cnt++;
1227: }
1228: }
1229: VecRestoreArray(x,&_x);
1231: ISCreateGeneral(PETSC_COMM_WORLD,cnt,unconstrained,PETSC_COPY_VALUES,&is);
1232: PetscFree(unconstrained);
1233: ISSetBlockSize(is,2);
1235: /* define correction for dirichlet in the rhs */
1236: MatMult(A,x,f);
1237: VecScale(f,-1.0);
1239: /* get new matrix */
1240: MatCreateSubMatrix(A,is,is,MAT_INITIAL_MATRIX,AA);
1241: /* get new vector */
1242: MatCreateVecs(*AA,NULL,ff);
1244: VecScatterCreate(f,is,*ff,NULL,&scat);
1245: VecScatterBegin(scat,f,*ff,INSERT_VALUES,SCATTER_FORWARD);
1246: VecScatterEnd(scat,f,*ff,INSERT_VALUES,SCATTER_FORWARD);
1248: { /* Constrain near-null space */
1249: PetscInt nvecs;
1250: const Vec *vecs;
1251: Vec *uvecs;
1252: PetscBool has_const;
1253: MatNullSpace mnull,unull;
1255: MatGetNearNullSpace(A,&mnull);
1256: MatNullSpaceGetVecs(mnull,&has_const,&nvecs,&vecs);
1257: VecDuplicateVecs(*ff,nvecs,&uvecs);
1258: for (i=0; i<nvecs; i++) {
1259: VecScatterBegin(scat,vecs[i],uvecs[i],INSERT_VALUES,SCATTER_FORWARD);
1260: VecScatterEnd(scat,vecs[i],uvecs[i],INSERT_VALUES,SCATTER_FORWARD);
1261: }
1262: Orthogonalize(nvecs,uvecs);
1263: MatNullSpaceCreate(PetscObjectComm((PetscObject)A),PETSC_FALSE,nvecs,uvecs,&unull);
1264: MatSetNearNullSpace(*AA,unull);
1265: MatNullSpaceDestroy(&unull);
1266: VecDestroyVecs(nvecs,&uvecs);
1267: }
1269: VecScatterDestroy(&scat);
1271: *dofs = is;
1272: VecDestroy(&x);
1273: return(0);
1274: }
1276: /*TEST
1278: build:
1279: requires: !complex !single
1281: test:
1282: args: -mx 20 -my 30 -elas_ksp_monitor_short -no_view -c_str 3 -sponge_E0 1 -sponge_E1 1000 -sponge_nu0 0.4 -sponge_nu1 0.2 -sponge_t 1 -sponge_w 8 -elas_ksp_rtol 5e-3 -elas_ksp_view
1283: output_file: output/ex49_1.out
1285: test:
1286: suffix: 2
1287: nsize: 4
1288: args: -mx 20 -my 30 -elas_ksp_monitor_short -no_view -c_str 3 -sponge_E0 1 -sponge_E1 1000 -sponge_nu0 0.4 -sponge_nu1 0.2 -sponge_t 1 -sponge_w 8 -elas_ksp_type gcr -elas_pc_type asm -elas_sub_pc_type lu -elas_ksp_rtol 5e-3
1290: test:
1291: suffix: 3
1292: nsize: 4
1293: args: -mx 20 -my 30 -elas_ksp_monitor_short -no_view -c_str 2 -brick_E 1,10,1000,100 -brick_nu 0.4,0.2,0.3,0.1 -brick_span 3 -elas_pc_type asm -elas_sub_pc_type lu -elas_ksp_rtol 5e-3
1295: test:
1296: suffix: 4
1297: nsize: 4
1298: args: -elas_ksp_monitor_short -elas_ksp_converged_reason -elas_ksp_type cg -elas_ksp_norm_type unpreconditioned -mx 40 -my 40 -c_str 2 -brick_E 1,1e-6,1e-2 -brick_nu .3,.2,.4 -brick_span 8 -elas_mg_levels_ksp_type chebyshev -elas_pc_type ml -elas_mg_levels_ksp_chebyshev_esteig 0,0.2,0,1.1 -elas_mg_levels_pc_type pbjacobi -elas_mg_levels_ksp_max_it 3 -use_nonsymbc -elas_pc_ml_nullspace user
1299: requires: ml
1301: test:
1302: suffix: 5
1303: nsize: 3
1304: args: -elas_ksp_monitor_short -elas_ksp_converged_reason -elas_ksp_type cg -elas_ksp_norm_type natural -mx 22 -my 22 -c_str 2 -brick_E 1,1e-6,1e-2 -brick_nu .3,.2,.4 -brick_span 8 -elas_pc_type gamg -elas_mg_levels_ksp_type chebyshev -elas_mg_levels_ksp_max_it 1 -elas_mg_levels_ksp_chebyshev_esteig 0.2,1.1 -elas_mg_levels_pc_type jacobi
1306: test:
1307: suffix: 6
1308: nsize: 4
1309: args: -mx 20 -my 30 -elas_ksp_monitor_short -no_view -c_str 3 -sponge_E0 1 -sponge_E1 1000 -sponge_nu0 0.4 -sponge_nu1 0.2 -sponge_t 1 -sponge_w 8 -elas_ksp_type pipegcr -elas_pc_type asm -elas_sub_pc_type lu
1311: test:
1312: suffix: 7
1313: nsize: 4
1314: args: -mx 20 -my 30 -elas_ksp_monitor_short -no_view -c_str 3 -sponge_E0 1 -sponge_E1 1000 -sponge_nu0 0.4 -sponge_nu1 0.2 -sponge_t 1 -sponge_w 8 -elas_ksp_type pipegcr -elas_pc_type asm -elas_sub_pc_type ksp -elas_sub_ksp_ksp_type cg -elas_sub_ksp_ksp_max_it 15
1316: test:
1317: suffix: 8
1318: nsize: 4
1319: args: -mx 20 -my 30 -elas_ksp_monitor_short -no_view -c_str 3 -sponge_E0 1 -sponge_E1 1000 -sponge_nu0 0.4 -sponge_nu1 0.2 -sponge_t 1 -sponge_w 8 -elas_ksp_type pipefgmres -elas_pc_type asm -elas_sub_pc_type ksp -elas_sub_ksp_ksp_type cg -elas_sub_ksp_ksp_max_it 15
1321: test:
1322: suffix: hypre_nullspace
1323: requires: hypre !defined(PETSC_HAVE_HYPRE_DEVICE)
1324: args: -elas_ksp_monitor_short -elas_ksp_converged_reason -elas_ksp_type cg -elas_ksp_norm_type natural -mx 22 -my 22 -c_str 2 -brick_E 1,1e-6,1e-2 -brick_nu .3,.2,.4 -brick_span 8 -elas_pc_type hypre -elas_pc_hypre_boomeramg_nodal_coarsen 6 -elas_pc_hypre_boomeramg_vec_interp_variant 3 -elas_pc_hypre_boomeramg_interp_type ext+i -elas_ksp_view
1326: test:
1327: nsize: 4
1328: suffix: bddc
1329: args: -elas_ksp_monitor_short -no_view -elas_ksp_converged_reason -elas_ksp_type cg -elas_ksp_norm_type natural -mx 22 -my 22 -dm_mat_type is -elas_pc_type bddc -elas_pc_bddc_monolithic
1331: test:
1332: nsize: 4
1333: suffix: bddc_unsym
1334: args: -elas_ksp_monitor_short -no_view -elas_ksp_converged_reason -elas_ksp_type cg -elas_ksp_norm_type natural -mx 22 -my 22 -dm_mat_type is -elas_pc_type bddc -elas_pc_bddc_monolithic -use_nonsymbc -elas_pc_bddc_symmetric 0
1336: test:
1337: nsize: 4
1338: suffix: bddc_unsym_deluxe
1339: args: -elas_ksp_monitor_short -no_view -elas_ksp_converged_reason -elas_ksp_type cg -elas_ksp_norm_type natural -mx 22 -my 22 -dm_mat_type is -elas_pc_type bddc -elas_pc_bddc_monolithic -use_nonsymbc -elas_pc_bddc_symmetric 0 -elas_pc_bddc_use_deluxe_scaling -elas_sub_schurs_symmetric 0
1341: test:
1342: nsize: 4
1343: suffix: fetidp_unsym_deluxe
1344: args: -elas_ksp_monitor_short -no_view -elas_ksp_converged_reason -elas_ksp_type fetidp -elas_fetidp_ksp_type cg -elas_ksp_norm_type natural -mx 22 -my 22 -dm_mat_type is -elas_fetidp_bddc_pc_bddc_monolithic -use_nonsymbc -elas_fetidp_bddc_pc_bddc_use_deluxe_scaling -elas_fetidp_bddc_sub_schurs_symmetric 0 -elas_fetidp_bddc_pc_bddc_deluxe_singlemat
1346: test:
1347: nsize: 4
1348: suffix: bddc_layerjump
1349: args: -mx 40 -my 40 -elas_ksp_monitor_short -no_view -c_str 3 -sponge_E0 1 -sponge_E1 1000 -sponge_nu0 0.4 -sponge_nu1 0.2 -sponge_t 1 -sponge_w 8 -elas_ksp_type cg -elas_pc_type bddc -elas_pc_bddc_monolithic -dm_mat_type is -elas_ksp_norm_type natural
1351: test:
1352: nsize: 4
1353: suffix: bddc_subdomainjump
1354: args: -mx 40 -my 40 -elas_ksp_monitor_short -no_view -c_str 2 -brick_E 1,1000 -brick_nu 0.4,0.2 -brick_span 20 -elas_ksp_type cg -elas_pc_type bddc -elas_pc_bddc_monolithic -dm_mat_type is -elas_pc_is_use_stiffness_scaling -elas_ksp_norm_type natural
1356: test:
1357: nsize: 9
1358: suffix: bddc_subdomainjump_deluxe
1359: args: -mx 30 -my 30 -elas_ksp_monitor_short -no_view -c_str 2 -brick_E 1,1000 -brick_nu 0.4,0.2 -brick_span 10 -elas_ksp_type cg -elas_pc_type bddc -elas_pc_bddc_monolithic -dm_mat_type is -elas_pc_bddc_use_deluxe_scaling -elas_ksp_norm_type natural -elas_pc_bddc_schur_layers 1
1360: TEST*/