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