1 2 static char help[] = "Time-dependent PDE in 2d. Modified from ex13.c for illustrating how to solve DAEs. \n"; 3 /* 4 u_t = uxx + uyy 5 0 < x < 1, 0 < y < 1; 6 At t=0: u(x,y) = exp(c*r*r*r), if r=PetscSqrtReal((x-.5)*(x-.5) + (y-.5)*(y-.5)) < .125 7 u(x,y) = 0.0 if r >= .125 8 9 10 Boundary conditions: 11 Drichlet BC: 12 At x=0, x=1, y=0, y=1: u = 0.0 13 14 Neumann BC: 15 At x=0, x=1: du(x,y,t)/dx = 0 16 At y=0, y=1: du(x,y,t)/dy = 0 17 18 mpiexec -n 2 ./ex15 -da_grid_x 40 -da_grid_y 40 -ts_max_steps 2 -snes_monitor -ksp_monitor 19 ./ex15 -da_grid_x 40 -da_grid_y 40 -draw_pause .1 -boundary 1 -ts_monitor_draw_solution 20 ./ex15 -da_grid_x 40 -da_grid_y 40 -draw_pause .1 -boundary 1 -Jtype 2 -nstencilpts 9 21 22 */ 23 24 #include <petscdm.h> 25 #include <petscdmda.h> 26 #include <petscts.h> 27 28 /* 29 User-defined data structures and routines 30 */ 31 32 /* AppCtx: used by FormIFunction() and FormIJacobian() */ 33 typedef struct { 34 DM da; 35 PetscInt nstencilpts; /* number of stencil points: 5 or 9 */ 36 PetscReal c; 37 PetscInt boundary; /* Type of boundary condition */ 38 PetscBool viewJacobian; 39 } AppCtx; 40 41 extern PetscErrorCode FormIFunction(TS,PetscReal,Vec,Vec,Vec,void*); 42 extern PetscErrorCode FormIJacobian(TS,PetscReal,Vec,Vec,PetscReal,Mat,Mat,void*); 43 extern PetscErrorCode FormInitialSolution(Vec,void*); 44 45 int main(int argc,char **argv) 46 { 47 TS ts; /* nonlinear solver */ 48 Vec u,r; /* solution, residual vectors */ 49 Mat J,Jmf = NULL; /* Jacobian matrices */ 50 PetscErrorCode ierr; 51 DM da; 52 PetscReal dt; 53 AppCtx user; /* user-defined work context */ 54 SNES snes; 55 PetscInt Jtype; /* Jacobian type 56 0: user provide Jacobian; 57 1: slow finite difference; 58 2: fd with coloring; */ 59 60 ierr = PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr; 61 /* Initialize user application context */ 62 user.da = NULL; 63 user.nstencilpts = 5; 64 user.c = -30.0; 65 user.boundary = 0; /* 0: Drichlet BC; 1: Neumann BC */ 66 user.viewJacobian = PETSC_FALSE; 67 68 ierr = PetscOptionsGetInt(NULL,NULL,"-nstencilpts",&user.nstencilpts,NULL);CHKERRQ(ierr); 69 ierr = PetscOptionsGetInt(NULL,NULL,"-boundary",&user.boundary,NULL);CHKERRQ(ierr); 70 ierr = PetscOptionsHasName(NULL,NULL,"-viewJacobian",&user.viewJacobian);CHKERRQ(ierr); 71 72 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 73 Create distributed array (DMDA) to manage parallel grid and vectors 74 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 75 if (user.nstencilpts == 5) { 76 ierr = DMDACreate2d(PETSC_COMM_WORLD, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE,DMDA_STENCIL_STAR,11,11,PETSC_DECIDE,PETSC_DECIDE,1,1,NULL,NULL,&da);CHKERRQ(ierr); 77 } else if (user.nstencilpts == 9) { 78 ierr = DMDACreate2d(PETSC_COMM_WORLD, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE,DMDA_STENCIL_BOX,11,11,PETSC_DECIDE,PETSC_DECIDE,1,1,NULL,NULL,&da);CHKERRQ(ierr); 79 } else SETERRQ1(PETSC_COMM_WORLD,PETSC_ERR_SUP,"nstencilpts %d is not supported",user.nstencilpts); 80 ierr = DMSetFromOptions(da);CHKERRQ(ierr); 81 ierr = DMSetUp(da);CHKERRQ(ierr); 82 user.da = da; 83 84 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 85 Extract global vectors from DMDA; 86 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 87 ierr = DMCreateGlobalVector(da,&u);CHKERRQ(ierr); 88 ierr = VecDuplicate(u,&r);CHKERRQ(ierr); 89 90 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 91 Create timestepping solver context 92 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 93 ierr = TSCreate(PETSC_COMM_WORLD,&ts);CHKERRQ(ierr); 94 ierr = TSSetProblemType(ts,TS_NONLINEAR);CHKERRQ(ierr); 95 ierr = TSSetType(ts,TSBEULER);CHKERRQ(ierr); 96 ierr = TSSetDM(ts,da);CHKERRQ(ierr); 97 ierr = TSSetIFunction(ts,r,FormIFunction,&user);CHKERRQ(ierr); 98 ierr = TSSetMaxTime(ts,1.0);CHKERRQ(ierr); 99 ierr = TSSetExactFinalTime(ts,TS_EXACTFINALTIME_STEPOVER);CHKERRQ(ierr); 100 101 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 102 Set initial conditions 103 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 104 ierr = FormInitialSolution(u,&user);CHKERRQ(ierr); 105 ierr = TSSetSolution(ts,u);CHKERRQ(ierr); 106 dt = .01; 107 ierr = TSSetTimeStep(ts,dt);CHKERRQ(ierr); 108 109 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 110 Set Jacobian evaluation routine 111 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 112 ierr = DMSetMatType(da,MATAIJ);CHKERRQ(ierr); 113 ierr = DMCreateMatrix(da,&J);CHKERRQ(ierr); 114 Jtype = 0; 115 ierr = PetscOptionsGetInt(NULL,NULL, "-Jtype",&Jtype,NULL);CHKERRQ(ierr); 116 if (Jtype == 0) { /* use user provided Jacobian evaluation routine */ 117 if (user.nstencilpts != 5) SETERRQ1(PETSC_COMM_WORLD,PETSC_ERR_SUP,"user Jacobian routine FormIJacobian() does not support nstencilpts=%D",user.nstencilpts); 118 ierr = TSSetIJacobian(ts,J,J,FormIJacobian,&user);CHKERRQ(ierr); 119 } else { /* use finite difference Jacobian J as preconditioner and '-snes_mf_operator' for Mat*vec */ 120 ierr = TSGetSNES(ts,&snes);CHKERRQ(ierr); 121 ierr = MatCreateSNESMF(snes,&Jmf);CHKERRQ(ierr); 122 if (Jtype == 1) { /* slow finite difference J; */ 123 ierr = SNESSetJacobian(snes,Jmf,J,SNESComputeJacobianDefault,NULL);CHKERRQ(ierr); 124 } else if (Jtype == 2) { /* Use coloring to compute finite difference J efficiently */ 125 ierr = SNESSetJacobian(snes,Jmf,J,SNESComputeJacobianDefaultColor,0);CHKERRQ(ierr); 126 } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Jtype is not supported"); 127 } 128 129 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 130 Sets various TS parameters from user options 131 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 132 ierr = TSSetFromOptions(ts);CHKERRQ(ierr); 133 134 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 135 Solve nonlinear system 136 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 137 ierr = TSSolve(ts,u);CHKERRQ(ierr); 138 139 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 140 Free work space. 141 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 142 ierr = MatDestroy(&J);CHKERRQ(ierr); 143 ierr = MatDestroy(&Jmf);CHKERRQ(ierr); 144 ierr = VecDestroy(&u);CHKERRQ(ierr); 145 ierr = VecDestroy(&r);CHKERRQ(ierr); 146 ierr = TSDestroy(&ts);CHKERRQ(ierr); 147 ierr = DMDestroy(&da);CHKERRQ(ierr); 148 149 ierr = PetscFinalize(); 150 return ierr; 151 } 152 153 /* --------------------------------------------------------------------- */ 154 /* 155 FormIFunction = Udot - RHSFunction 156 */ 157 PetscErrorCode FormIFunction(TS ts,PetscReal t,Vec U,Vec Udot,Vec F,void *ctx) 158 { 159 PetscErrorCode ierr; 160 AppCtx *user=(AppCtx*)ctx; 161 DM da = (DM)user->da; 162 PetscInt i,j,Mx,My,xs,ys,xm,ym; 163 PetscReal hx,hy,sx,sy; 164 PetscScalar u,uxx,uyy,**uarray,**f,**udot; 165 Vec localU; 166 167 PetscFunctionBeginUser; 168 ierr = DMGetLocalVector(da,&localU);CHKERRQ(ierr); 169 ierr = DMDAGetInfo(da,PETSC_IGNORE,&Mx,&My,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE);CHKERRQ(ierr); 170 171 hx = 1.0/(PetscReal)(Mx-1); sx = 1.0/(hx*hx); 172 hy = 1.0/(PetscReal)(My-1); sy = 1.0/(hy*hy); 173 if (user->nstencilpts == 9 && hx != hy) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP,"hx must equal hy when nstencilpts = 9 for this example"); 174 175 /* 176 Scatter ghost points to local vector,using the 2-step process 177 DMGlobalToLocalBegin(),DMGlobalToLocalEnd(). 178 By placing code between these two statements, computations can be 179 done while messages are in transition. 180 */ 181 ierr = DMGlobalToLocalBegin(da,U,INSERT_VALUES,localU);CHKERRQ(ierr); 182 ierr = DMGlobalToLocalEnd(da,U,INSERT_VALUES,localU);CHKERRQ(ierr); 183 184 /* Get pointers to vector data */ 185 ierr = DMDAVecGetArrayRead(da,localU,&uarray);CHKERRQ(ierr); 186 ierr = DMDAVecGetArray(da,F,&f);CHKERRQ(ierr); 187 ierr = DMDAVecGetArray(da,Udot,&udot);CHKERRQ(ierr); 188 189 /* Get local grid boundaries */ 190 ierr = DMDAGetCorners(da,&xs,&ys,NULL,&xm,&ym,NULL);CHKERRQ(ierr); 191 192 /* Compute function over the locally owned part of the grid */ 193 for (j=ys; j<ys+ym; j++) { 194 for (i=xs; i<xs+xm; i++) { 195 /* Boundary conditions */ 196 if (i == 0 || j == 0 || i == Mx-1 || j == My-1) { 197 if (user->boundary == 0) { /* Drichlet BC */ 198 f[j][i] = uarray[j][i]; /* F = U */ 199 } else { /* Neumann BC */ 200 if (i == 0 && j == 0) { /* SW corner */ 201 f[j][i] = uarray[j][i] - uarray[j+1][i+1]; 202 } else if (i == Mx-1 && j == 0) { /* SE corner */ 203 f[j][i] = uarray[j][i] - uarray[j+1][i-1]; 204 } else if (i == 0 && j == My-1) { /* NW corner */ 205 f[j][i] = uarray[j][i] - uarray[j-1][i+1]; 206 } else if (i == Mx-1 && j == My-1) { /* NE corner */ 207 f[j][i] = uarray[j][i] - uarray[j-1][i-1]; 208 } else if (i == 0) { /* Left */ 209 f[j][i] = uarray[j][i] - uarray[j][i+1]; 210 } else if (i == Mx-1) { /* Right */ 211 f[j][i] = uarray[j][i] - uarray[j][i-1]; 212 } else if (j == 0) { /* Bottom */ 213 f[j][i] = uarray[j][i] - uarray[j+1][i]; 214 } else if (j == My-1) { /* Top */ 215 f[j][i] = uarray[j][i] - uarray[j-1][i]; 216 } 217 } 218 } else { /* Interior */ 219 u = uarray[j][i]; 220 /* 5-point stencil */ 221 uxx = (-2.0*u + uarray[j][i-1] + uarray[j][i+1]); 222 uyy = (-2.0*u + uarray[j-1][i] + uarray[j+1][i]); 223 if (user->nstencilpts == 9) { 224 /* 9-point stencil: assume hx=hy */ 225 uxx = 2.0*uxx/3.0 + (0.5*(uarray[j-1][i-1]+uarray[j-1][i+1]+uarray[j+1][i-1]+uarray[j+1][i+1]) - 2.0*u)/6.0; 226 uyy = 2.0*uyy/3.0 + (0.5*(uarray[j-1][i-1]+uarray[j-1][i+1]+uarray[j+1][i-1]+uarray[j+1][i+1]) - 2.0*u)/6.0; 227 } 228 f[j][i] = udot[j][i] - (uxx*sx + uyy*sy); 229 } 230 } 231 } 232 233 /* Restore vectors */ 234 ierr = DMDAVecRestoreArrayRead(da,localU,&uarray);CHKERRQ(ierr); 235 ierr = DMDAVecRestoreArray(da,F,&f);CHKERRQ(ierr); 236 ierr = DMDAVecRestoreArray(da,Udot,&udot);CHKERRQ(ierr); 237 ierr = DMRestoreLocalVector(da,&localU);CHKERRQ(ierr); 238 ierr = PetscLogFlops(11.0*ym*xm);CHKERRQ(ierr); 239 PetscFunctionReturn(0); 240 } 241 242 /* --------------------------------------------------------------------- */ 243 /* 244 FormIJacobian() - Compute IJacobian = dF/dU + a dF/dUdot 245 This routine is not used with option '-use_coloring' 246 */ 247 PetscErrorCode FormIJacobian(TS ts,PetscReal t,Vec U,Vec Udot,PetscReal a,Mat J,Mat Jpre,void *ctx) 248 { 249 PetscErrorCode ierr; 250 PetscInt i,j,Mx,My,xs,ys,xm,ym,nc; 251 AppCtx *user = (AppCtx*)ctx; 252 DM da = (DM)user->da; 253 MatStencil col[5],row; 254 PetscScalar vals[5],hx,hy,sx,sy; 255 256 PetscFunctionBeginUser; 257 ierr = DMDAGetInfo(da,PETSC_IGNORE,&Mx,&My,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE);CHKERRQ(ierr); 258 ierr = DMDAGetCorners(da,&xs,&ys,NULL,&xm,&ym,NULL);CHKERRQ(ierr); 259 260 hx = 1.0/(PetscReal)(Mx-1); sx = 1.0/(hx*hx); 261 hy = 1.0/(PetscReal)(My-1); sy = 1.0/(hy*hy); 262 263 for (j=ys; j<ys+ym; j++) { 264 for (i=xs; i<xs+xm; i++) { 265 nc = 0; 266 row.j = j; row.i = i; 267 if (user->boundary == 0 && (i == 0 || i == Mx-1 || j == 0 || j == My-1)) { 268 col[nc].j = j; col[nc].i = i; vals[nc++] = 1.0; 269 270 } else if (user->boundary > 0 && i == 0) { /* Left Neumann */ 271 col[nc].j = j; col[nc].i = i; vals[nc++] = 1.0; 272 col[nc].j = j; col[nc].i = i+1; vals[nc++] = -1.0; 273 } else if (user->boundary > 0 && i == Mx-1) { /* Right Neumann */ 274 col[nc].j = j; col[nc].i = i; vals[nc++] = 1.0; 275 col[nc].j = j; col[nc].i = i-1; vals[nc++] = -1.0; 276 } else if (user->boundary > 0 && j == 0) { /* Bottom Neumann */ 277 col[nc].j = j; col[nc].i = i; vals[nc++] = 1.0; 278 col[nc].j = j+1; col[nc].i = i; vals[nc++] = -1.0; 279 } else if (user->boundary > 0 && j == My-1) { /* Top Neumann */ 280 col[nc].j = j; col[nc].i = i; vals[nc++] = 1.0; 281 col[nc].j = j-1; col[nc].i = i; vals[nc++] = -1.0; 282 } else { /* Interior */ 283 col[nc].j = j-1; col[nc].i = i; vals[nc++] = -sy; 284 col[nc].j = j; col[nc].i = i-1; vals[nc++] = -sx; 285 col[nc].j = j; col[nc].i = i; vals[nc++] = 2.0*(sx + sy) + a; 286 col[nc].j = j; col[nc].i = i+1; vals[nc++] = -sx; 287 col[nc].j = j+1; col[nc].i = i; vals[nc++] = -sy; 288 } 289 ierr = MatSetValuesStencil(Jpre,1,&row,nc,col,vals,INSERT_VALUES);CHKERRQ(ierr); 290 } 291 } 292 ierr = MatAssemblyBegin(Jpre,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 293 ierr = MatAssemblyEnd(Jpre,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 294 if (J != Jpre) { 295 ierr = MatAssemblyBegin(J,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 296 ierr = MatAssemblyEnd(J,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 297 } 298 299 if (user->viewJacobian) { 300 ierr = PetscPrintf(PetscObjectComm((PetscObject)Jpre),"Jpre:\n");CHKERRQ(ierr); 301 ierr = MatView(Jpre,PETSC_VIEWER_STDOUT_WORLD);CHKERRQ(ierr); 302 } 303 PetscFunctionReturn(0); 304 } 305 306 /* ------------------------------------------------------------------- */ 307 PetscErrorCode FormInitialSolution(Vec U,void *ptr) 308 { 309 AppCtx *user=(AppCtx*)ptr; 310 DM da =user->da; 311 PetscReal c =user->c; 312 PetscErrorCode ierr; 313 PetscInt i,j,xs,ys,xm,ym,Mx,My; 314 PetscScalar **u; 315 PetscReal hx,hy,x,y,r; 316 317 PetscFunctionBeginUser; 318 ierr = DMDAGetInfo(da,PETSC_IGNORE,&Mx,&My,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE,PETSC_IGNORE);CHKERRQ(ierr); 319 320 hx = 1.0/(PetscReal)(Mx-1); 321 hy = 1.0/(PetscReal)(My-1); 322 323 /* Get pointers to vector data */ 324 ierr = DMDAVecGetArray(da,U,&u);CHKERRQ(ierr); 325 326 /* Get local grid boundaries */ 327 ierr = DMDAGetCorners(da,&xs,&ys,NULL,&xm,&ym,NULL);CHKERRQ(ierr); 328 329 /* Compute function over the locally owned part of the grid */ 330 for (j=ys; j<ys+ym; j++) { 331 y = j*hy; 332 for (i=xs; i<xs+xm; i++) { 333 x = i*hx; 334 r = PetscSqrtReal((x-.5)*(x-.5) + (y-.5)*(y-.5)); 335 if (r < .125) u[j][i] = PetscExpReal(c*r*r*r); 336 else u[j][i] = 0.0; 337 } 338 } 339 340 /* Restore vectors */ 341 ierr = DMDAVecRestoreArray(da,U,&u);CHKERRQ(ierr); 342 PetscFunctionReturn(0); 343 } 344 345 /*TEST 346 347 test: 348 args: -da_grid_x 20 -da_grid_y 20 -boundary 0 -ts_max_steps 10 -ts_monitor 349 350 test: 351 suffix: 2 352 args: -da_grid_x 20 -da_grid_y 20 -boundary 0 -ts_max_steps 10 -Jtype 2 -ts_monitor 353 354 test: 355 suffix: 3 356 requires: !single 357 args: -da_grid_x 20 -da_grid_y 20 -boundary 1 -ts_max_steps 10 -ts_monitor 358 359 test: 360 suffix: 4 361 requires: !single 362 nsize: 2 363 args: -da_grid_x 20 -da_grid_y 20 -boundary 1 -ts_max_steps 10 -ts_monitor 364 365 test: 366 suffix: 5 367 nsize: 1 368 args: -da_grid_x 20 -da_grid_y 20 -boundary 0 -ts_max_steps 10 -Jtype 1 -ts_monitor 369 370 371 TEST*/ 372