1 2 static char help[] = "Newton method to solve u'' + u^{2} = f, sequentially.\n\ 3 This example employs a user-defined monitoring routine.\n\n"; 4 5 /* 6 Include "petscdraw.h" so that we can use PETSc drawing routines. 7 Include "petscsnes.h" so that we can use SNES solvers. Note that this 8 file automatically includes: 9 petscsys.h - base PETSc routines petscvec.h - vectors 10 petscmat.h - matrices 11 petscis.h - index sets petscksp.h - Krylov subspace methods 12 petscviewer.h - viewers petscpc.h - preconditioners 13 petscksp.h - linear solvers 14 */ 15 16 #include <petscsnes.h> 17 18 /* 19 User-defined routines 20 */ 21 extern PetscErrorCode FormJacobian(SNES,Vec,Mat,Mat,void*); 22 extern PetscErrorCode FormFunction(SNES,Vec,Vec,void*); 23 extern PetscErrorCode FormInitialGuess(Vec); 24 extern PetscErrorCode Monitor(SNES,PetscInt,PetscReal,void*); 25 26 /* 27 User-defined context for monitoring 28 */ 29 typedef struct { 30 PetscViewer viewer; 31 } MonitorCtx; 32 33 int main(int argc,char **argv) 34 { 35 SNES snes; /* SNES context */ 36 Vec x,r,F,U; /* vectors */ 37 Mat J; /* Jacobian matrix */ 38 MonitorCtx monP; /* monitoring context */ 39 PetscInt its,n = 5,i,maxit,maxf; 40 PetscMPIInt size; 41 PetscScalar h,xp,v,none = -1.0; 42 PetscReal abstol,rtol,stol,norm; 43 44 PetscFunctionBeginUser; 45 PetscCall(PetscInitialize(&argc,&argv,(char*)0,help)); 46 PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD,&size)); 47 PetscCheck(size == 1,PETSC_COMM_SELF,PETSC_ERR_WRONG_MPI_SIZE,"This is a uniprocessor example only!"); 48 PetscCall(PetscOptionsGetInt(NULL,NULL,"-n",&n,NULL)); 49 h = 1.0/(n-1); 50 51 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 52 Create nonlinear solver context 53 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 54 55 PetscCall(SNESCreate(PETSC_COMM_WORLD,&snes)); 56 57 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 58 Create vector data structures; set function evaluation routine 59 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 60 /* 61 Note that we form 1 vector from scratch and then duplicate as needed. 62 */ 63 PetscCall(VecCreate(PETSC_COMM_WORLD,&x)); 64 PetscCall(VecSetSizes(x,PETSC_DECIDE,n)); 65 PetscCall(VecSetFromOptions(x)); 66 PetscCall(VecDuplicate(x,&r)); 67 PetscCall(VecDuplicate(x,&F)); 68 PetscCall(VecDuplicate(x,&U)); 69 70 /* 71 Set function evaluation routine and vector 72 */ 73 PetscCall(SNESSetFunction(snes,r,FormFunction,(void*)F)); 74 75 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 76 Create matrix data structure; set Jacobian evaluation routine 77 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 78 79 PetscCall(MatCreate(PETSC_COMM_WORLD,&J)); 80 PetscCall(MatSetSizes(J,PETSC_DECIDE,PETSC_DECIDE,n,n)); 81 PetscCall(MatSetFromOptions(J)); 82 PetscCall(MatSeqAIJSetPreallocation(J,3,NULL)); 83 84 /* 85 Set Jacobian matrix data structure and default Jacobian evaluation 86 routine. User can override with: 87 -snes_fd : default finite differencing approximation of Jacobian 88 -snes_mf : matrix-free Newton-Krylov method with no preconditioning 89 (unless user explicitly sets preconditioner) 90 -snes_mf_operator : form preconditioning matrix as set by the user, 91 but use matrix-free approx for Jacobian-vector 92 products within Newton-Krylov method 93 */ 94 95 PetscCall(SNESSetJacobian(snes,J,J,FormJacobian,NULL)); 96 97 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 98 Customize nonlinear solver; set runtime options 99 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 100 101 /* 102 Set an optional user-defined monitoring routine 103 */ 104 PetscCall(PetscViewerDrawOpen(PETSC_COMM_WORLD,0,0,0,0,400,400,&monP.viewer)); 105 PetscCall(SNESMonitorSet(snes,Monitor,&monP,0)); 106 107 /* 108 Set names for some vectors to facilitate monitoring (optional) 109 */ 110 PetscCall(PetscObjectSetName((PetscObject)x,"Approximate Solution")); 111 PetscCall(PetscObjectSetName((PetscObject)U,"Exact Solution")); 112 113 /* 114 Set SNES/KSP/KSP/PC runtime options, e.g., 115 -snes_view -snes_monitor -ksp_type <ksp> -pc_type <pc> 116 */ 117 PetscCall(SNESSetFromOptions(snes)); 118 119 /* 120 Print parameters used for convergence testing (optional) ... just 121 to demonstrate this routine; this information is also printed with 122 the option -snes_view 123 */ 124 PetscCall(SNESGetTolerances(snes,&abstol,&rtol,&stol,&maxit,&maxf)); 125 PetscCall(PetscPrintf(PETSC_COMM_WORLD,"atol=%g, rtol=%g, stol=%g, maxit=%" PetscInt_FMT ", maxf=%" PetscInt_FMT "\n",(double)abstol,(double)rtol,(double)stol,maxit,maxf)); 126 127 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 128 Initialize application: 129 Store right-hand-side of PDE and exact solution 130 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 131 132 xp = 0.0; 133 for (i=0; i<n; i++) { 134 v = 6.0*xp + PetscPowScalar(xp+1.e-12,6.0); /* +1.e-12 is to prevent 0^6 */ 135 PetscCall(VecSetValues(F,1,&i,&v,INSERT_VALUES)); 136 v = xp*xp*xp; 137 PetscCall(VecSetValues(U,1,&i,&v,INSERT_VALUES)); 138 xp += h; 139 } 140 141 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 142 Evaluate initial guess; then solve nonlinear system 143 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 144 /* 145 Note: The user should initialize the vector, x, with the initial guess 146 for the nonlinear solver prior to calling SNESSolve(). In particular, 147 to employ an initial guess of zero, the user should explicitly set 148 this vector to zero by calling VecSet(). 149 */ 150 PetscCall(FormInitialGuess(x)); 151 PetscCall(SNESSolve(snes,NULL,x)); 152 PetscCall(SNESGetIterationNumber(snes,&its)); 153 PetscCall(PetscPrintf(PETSC_COMM_WORLD,"number of SNES iterations = %" PetscInt_FMT "\n\n",its)); 154 155 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 156 Check solution and clean up 157 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 158 159 /* 160 Check the error 161 */ 162 PetscCall(VecAXPY(x,none,U)); 163 PetscCall(VecNorm(x,NORM_2,&norm)); 164 PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Norm of error %g, Iterations %" PetscInt_FMT "\n",(double)norm,its)); 165 166 /* 167 Free work space. All PETSc objects should be destroyed when they 168 are no longer needed. 169 */ 170 PetscCall(VecDestroy(&x)); PetscCall(VecDestroy(&r)); 171 PetscCall(VecDestroy(&U)); PetscCall(VecDestroy(&F)); 172 PetscCall(MatDestroy(&J)); PetscCall(SNESDestroy(&snes)); 173 PetscCall(PetscViewerDestroy(&monP.viewer)); 174 PetscCall(PetscFinalize()); 175 return 0; 176 } 177 /* ------------------------------------------------------------------- */ 178 /* 179 FormInitialGuess - Computes initial guess. 180 181 Input/Output Parameter: 182 . x - the solution vector 183 */ 184 PetscErrorCode FormInitialGuess(Vec x) 185 { 186 PetscScalar pfive = .50; 187 PetscCall(VecSet(x,pfive)); 188 return 0; 189 } 190 /* ------------------------------------------------------------------- */ 191 /* 192 FormFunction - Evaluates nonlinear function, F(x). 193 194 Input Parameters: 195 . snes - the SNES context 196 . x - input vector 197 . ctx - optional user-defined context, as set by SNESSetFunction() 198 199 Output Parameter: 200 . f - function vector 201 202 Note: 203 The user-defined context can contain any application-specific data 204 needed for the function evaluation (such as various parameters, work 205 vectors, and grid information). In this program the context is just 206 a vector containing the right-hand-side of the discretized PDE. 207 */ 208 209 PetscErrorCode FormFunction(SNES snes,Vec x,Vec f,void *ctx) 210 { 211 Vec g = (Vec)ctx; 212 const PetscScalar *xx,*gg; 213 PetscScalar *ff,d; 214 PetscInt i,n; 215 216 /* 217 Get pointers to vector data. 218 - For default PETSc vectors, VecGetArray() returns a pointer to 219 the data array. Otherwise, the routine is implementation dependent. 220 - You MUST call VecRestoreArray() when you no longer need access to 221 the array. 222 */ 223 PetscCall(VecGetArrayRead(x,&xx)); 224 PetscCall(VecGetArray(f,&ff)); 225 PetscCall(VecGetArrayRead(g,&gg)); 226 227 /* 228 Compute function 229 */ 230 PetscCall(VecGetSize(x,&n)); 231 d = (PetscReal)(n - 1); d = d*d; 232 ff[0] = xx[0]; 233 for (i=1; i<n-1; i++) ff[i] = d*(xx[i-1] - 2.0*xx[i] + xx[i+1]) + xx[i]*xx[i] - gg[i]; 234 ff[n-1] = xx[n-1] - 1.0; 235 236 /* 237 Restore vectors 238 */ 239 PetscCall(VecRestoreArrayRead(x,&xx)); 240 PetscCall(VecRestoreArray(f,&ff)); 241 PetscCall(VecRestoreArrayRead(g,&gg)); 242 return 0; 243 } 244 /* ------------------------------------------------------------------- */ 245 /* 246 FormJacobian - Evaluates Jacobian matrix. 247 248 Input Parameters: 249 . snes - the SNES context 250 . x - input vector 251 . dummy - optional user-defined context (not used here) 252 253 Output Parameters: 254 . jac - Jacobian matrix 255 . B - optionally different preconditioning matrix 256 257 */ 258 259 PetscErrorCode FormJacobian(SNES snes,Vec x,Mat jac,Mat B,void *dummy) 260 { 261 const PetscScalar *xx; 262 PetscScalar A[3],d; 263 PetscInt i,n,j[3]; 264 265 /* 266 Get pointer to vector data 267 */ 268 PetscCall(VecGetArrayRead(x,&xx)); 269 270 /* 271 Compute Jacobian entries and insert into matrix. 272 - Note that in this case we set all elements for a particular 273 row at once. 274 */ 275 PetscCall(VecGetSize(x,&n)); 276 d = (PetscReal)(n - 1); d = d*d; 277 278 /* 279 Interior grid points 280 */ 281 for (i=1; i<n-1; i++) { 282 j[0] = i - 1; j[1] = i; j[2] = i + 1; 283 A[0] = A[2] = d; A[1] = -2.0*d + 2.0*xx[i]; 284 PetscCall(MatSetValues(B,1,&i,3,j,A,INSERT_VALUES)); 285 } 286 287 /* 288 Boundary points 289 */ 290 i = 0; A[0] = 1.0; 291 292 PetscCall(MatSetValues(B,1,&i,1,&i,A,INSERT_VALUES)); 293 294 i = n-1; A[0] = 1.0; 295 296 PetscCall(MatSetValues(B,1,&i,1,&i,A,INSERT_VALUES)); 297 298 /* 299 Restore vector 300 */ 301 PetscCall(VecRestoreArrayRead(x,&xx)); 302 303 /* 304 Assemble matrix 305 */ 306 PetscCall(MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY)); 307 PetscCall(MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY)); 308 if (jac != B) { 309 PetscCall(MatAssemblyBegin(jac,MAT_FINAL_ASSEMBLY)); 310 PetscCall(MatAssemblyEnd(jac,MAT_FINAL_ASSEMBLY)); 311 } 312 return 0; 313 } 314 /* ------------------------------------------------------------------- */ 315 /* 316 Monitor - User-defined monitoring routine that views the 317 current iterate with an x-window plot. 318 319 Input Parameters: 320 snes - the SNES context 321 its - iteration number 322 norm - 2-norm function value (may be estimated) 323 ctx - optional user-defined context for private data for the 324 monitor routine, as set by SNESMonitorSet() 325 326 Note: 327 See the manpage for PetscViewerDrawOpen() for useful runtime options, 328 such as -nox to deactivate all x-window output. 329 */ 330 PetscErrorCode Monitor(SNES snes,PetscInt its,PetscReal fnorm,void *ctx) 331 { 332 MonitorCtx *monP = (MonitorCtx*) ctx; 333 Vec x; 334 335 PetscCall(PetscPrintf(PETSC_COMM_WORLD,"iter = %" PetscInt_FMT ", SNES Function norm %g\n",its,(double)fnorm)); 336 PetscCall(SNESGetSolution(snes,&x)); 337 PetscCall(VecView(x,monP->viewer)); 338 return 0; 339 } 340 341 /*TEST 342 343 test: 344 args: -nox -snes_monitor_cancel -snes_monitor_short -snes_view -pc_type jacobi -ksp_gmres_cgs_refinement_type refine_always 345 346 test: 347 suffix: 2 348 args: -nox -snes_monitor_cancel -snes_monitor_short -snes_type newtontr -snes_view 349 requires: !single 350 351 test: 352 suffix: 3 353 args: -nox -malloc no -options_left no -snes_monitor_cancel -snes_monitor_short -snes_view -pc_type jacobi -ksp_gmres_cgs_refinement_type refine_always 354 355 test: 356 suffix: 4 357 args: -nox -snes_monitor_cancel -snes_monitor_short -snes_type newtontrdc -snes_view 358 requires: !single 359 360 TEST*/ 361