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