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