1 static char help[] = "Bratu nonlinear PDE in 2d.\n\ 2 We solve the Bratu (SFI - solid fuel ignition) problem in a 2D rectangular\n\ 3 domain, using distributed arrays (DMDAs) to partition the parallel grid.\n\ 4 The command line options include:\n\ 5 -par <parameter>, where <parameter> indicates the problem's nonlinearity\n\ 6 problem SFI: <parameter> = Bratu parameter (0 <= par <= 6.81)\n\n\ 7 -m_par/n_par <parameter>, where <parameter> indicates an integer\n \ 8 that MMS3 will be evaluated with 2^m_par, 2^n_par"; 9 10 /*T 11 Concepts: SNES^parallel Bratu example 12 Concepts: DMDA^using distributed arrays; 13 Concepts: IS coloirng types; 14 Processors: n 15 T*/ 16 17 18 19 /* ------------------------------------------------------------------------ 20 21 Solid Fuel Ignition (SFI) problem. This problem is modeled by 22 the partial differential equation 23 24 -Laplacian u - lambda*exp(u) = 0, 0 < x,y < 1, 25 26 with boundary conditions 27 28 u = 0 for x = 0, x = 1, y = 0, y = 1. 29 30 A finite difference approximation with the usual 5-point stencil 31 is used to discretize the boundary value problem to obtain a nonlinear 32 system of equations. 33 34 35 This example shows how geometric multigrid can be run transparently with a nonlinear solver so long 36 as SNESSetDM() is provided. Example usage 37 38 ./ex5 -pc_type mg -ksp_monitor -snes_view -pc_mg_levels 3 -pc_mg_galerkin pmat -da_grid_x 17 -da_grid_y 17 39 -mg_levels_ksp_monitor -snes_monitor -mg_levels_pc_type sor -pc_mg_type full 40 41 or to run with grid sequencing on the nonlinear problem (note that you do not need to provide the number of 42 multigrid levels, it will be determined automatically based on the number of refinements done) 43 44 ./ex5 -pc_type mg -ksp_monitor -snes_view -pc_mg_galerkin pmat -snes_grid_sequence 3 45 -mg_levels_ksp_monitor -snes_monitor -mg_levels_pc_type sor -pc_mg_type full 46 47 ------------------------------------------------------------------------- */ 48 49 /* 50 Include "petscdmda.h" so that we can use distributed arrays (DMDAs). 51 Include "petscsnes.h" so that we can use SNES solvers. Note that this 52 */ 53 #include <petscdm.h> 54 #include <petscdmda.h> 55 #include <petscsnes.h> 56 #include <petscmatlab.h> 57 #include <petsc/private/snesimpl.h> /* For SNES_Solve event */ 58 59 /* 60 User-defined application context - contains data needed by the 61 application-provided call-back routines, FormJacobianLocal() and 62 FormFunctionLocal(). 63 */ 64 typedef struct AppCtx AppCtx; 65 struct AppCtx { 66 PetscReal param; /* test problem parameter */ 67 PetscInt m,n; /* MMS3 parameters */ 68 PetscErrorCode (*mms_solution)(AppCtx*,const DMDACoor2d*,PetscScalar*); 69 PetscErrorCode (*mms_forcing)(AppCtx*,const DMDACoor2d*,PetscScalar*); 70 }; 71 72 /* 73 User-defined routines 74 */ 75 extern PetscErrorCode FormInitialGuess(DM,AppCtx*,Vec); 76 extern PetscErrorCode FormFunctionLocal(DMDALocalInfo*,PetscScalar**,PetscScalar**,AppCtx*); 77 extern PetscErrorCode FormExactSolution(DM,AppCtx*,Vec); 78 extern PetscErrorCode ZeroBCSolution(AppCtx*,const DMDACoor2d*,PetscScalar*); 79 extern PetscErrorCode MMSSolution1(AppCtx*,const DMDACoor2d*,PetscScalar*); 80 extern PetscErrorCode MMSForcing1(AppCtx*,const DMDACoor2d*,PetscScalar*); 81 extern PetscErrorCode MMSSolution2(AppCtx*,const DMDACoor2d*,PetscScalar*); 82 extern PetscErrorCode MMSForcing2(AppCtx*,const DMDACoor2d*,PetscScalar*); 83 extern PetscErrorCode MMSSolution3(AppCtx*,const DMDACoor2d*,PetscScalar*); 84 extern PetscErrorCode MMSForcing3(AppCtx*,const DMDACoor2d*,PetscScalar*); 85 extern PetscErrorCode MMSSolution4(AppCtx*,const DMDACoor2d*,PetscScalar*); 86 extern PetscErrorCode MMSForcing4(AppCtx*,const DMDACoor2d*,PetscScalar*); 87 extern PetscErrorCode FormJacobianLocal(DMDALocalInfo*,PetscScalar**,Mat,Mat,AppCtx*); 88 extern PetscErrorCode FormObjectiveLocal(DMDALocalInfo*,PetscScalar**,PetscReal*,AppCtx*); 89 extern PetscErrorCode FormFunctionMatlab(SNES,Vec,Vec,void*); 90 extern PetscErrorCode NonlinearGS(SNES,Vec,Vec,void*); 91 92 int main(int argc,char **argv) 93 { 94 SNES snes; /* nonlinear solver */ 95 Vec x; /* solution vector */ 96 AppCtx user; /* user-defined work context */ 97 PetscInt its; /* iterations for convergence */ 98 PetscErrorCode ierr; 99 PetscReal bratu_lambda_max = 6.81; 100 PetscReal bratu_lambda_min = 0.; 101 PetscInt MMS = 0; 102 PetscBool flg = PETSC_FALSE; 103 DM da; 104 Vec r = NULL; 105 KSP ksp; 106 PetscInt lits,slits; 107 108 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 109 Initialize program 110 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 111 112 ierr = PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr; 113 114 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 115 Initialize problem parameters 116 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 117 user.param = 6.0; 118 ierr = PetscOptionsGetReal(NULL,NULL,"-par",&user.param,NULL);CHKERRQ(ierr); 119 if (user.param > bratu_lambda_max || user.param < bratu_lambda_min) SETERRQ3(PETSC_COMM_SELF,1,"Lambda, %g, is out of range, [%g, %g]", user.param, bratu_lambda_min, bratu_lambda_max); 120 ierr = PetscOptionsGetInt(NULL,NULL,"-mms",&MMS,NULL);CHKERRQ(ierr); 121 if (MMS == 3) { 122 PetscInt mPar = 2, nPar = 1; 123 ierr = PetscOptionsGetInt(NULL,NULL,"-m_par",&mPar,NULL);CHKERRQ(ierr); 124 ierr = PetscOptionsGetInt(NULL,NULL,"-n_par",&nPar,NULL);CHKERRQ(ierr); 125 user.m = PetscPowInt(2,mPar); 126 user.n = PetscPowInt(2,nPar); 127 } 128 129 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 130 Create nonlinear solver context 131 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 132 ierr = SNESCreate(PETSC_COMM_WORLD,&snes);CHKERRQ(ierr); 133 ierr = SNESSetCountersReset(snes,PETSC_FALSE);CHKERRQ(ierr); 134 ierr = SNESSetNGS(snes, NonlinearGS, NULL);CHKERRQ(ierr); 135 136 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 137 Create distributed array (DMDA) to manage parallel grid and vectors 138 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 139 ierr = DMDACreate2d(PETSC_COMM_WORLD, DM_BOUNDARY_NONE, DM_BOUNDARY_NONE,DMDA_STENCIL_STAR,4,4,PETSC_DECIDE,PETSC_DECIDE,1,1,NULL,NULL,&da);CHKERRQ(ierr); 140 ierr = DMSetFromOptions(da);CHKERRQ(ierr); 141 ierr = DMSetUp(da);CHKERRQ(ierr); 142 ierr = DMDASetUniformCoordinates(da, 0.0, 1.0, 0.0, 1.0, 0.0, 1.0);CHKERRQ(ierr); 143 ierr = DMSetApplicationContext(da,&user);CHKERRQ(ierr); 144 ierr = SNESSetDM(snes,da);CHKERRQ(ierr); 145 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 146 Extract global vectors from DMDA; then duplicate for remaining 147 vectors that are the same types 148 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 149 ierr = DMCreateGlobalVector(da,&x);CHKERRQ(ierr); 150 151 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 152 Set local function evaluation routine 153 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 154 user.mms_solution = ZeroBCSolution; 155 switch (MMS) { 156 case 0: user.mms_solution = NULL; user.mms_forcing = NULL;CHKERRQ(ierr); 157 case 1: user.mms_solution = MMSSolution1; user.mms_forcing = MMSForcing1; break; 158 case 2: user.mms_solution = MMSSolution2; user.mms_forcing = MMSForcing2; break; 159 case 3: user.mms_solution = MMSSolution3; user.mms_forcing = MMSForcing3; break; 160 case 4: user.mms_solution = MMSSolution4; user.mms_forcing = MMSForcing4; break; 161 default: SETERRQ1(PETSC_COMM_WORLD,PETSC_ERR_USER,"Unknown MMS type %d",MMS); 162 } 163 ierr = DMDASNESSetFunctionLocal(da,INSERT_VALUES,(DMDASNESFunction)FormFunctionLocal,&user);CHKERRQ(ierr); 164 ierr = PetscOptionsGetBool(NULL,NULL,"-fd",&flg,NULL);CHKERRQ(ierr); 165 if (!flg) { 166 ierr = DMDASNESSetJacobianLocal(da,(DMDASNESJacobian)FormJacobianLocal,&user);CHKERRQ(ierr); 167 } 168 169 ierr = PetscOptionsGetBool(NULL,NULL,"-obj",&flg,NULL);CHKERRQ(ierr); 170 if (flg) { 171 ierr = DMDASNESSetObjectiveLocal(da,(DMDASNESObjective)FormObjectiveLocal,&user);CHKERRQ(ierr); 172 } 173 174 if (PetscDefined(HAVE_MATLAB_ENGINE)) { 175 PetscBool matlab_function = PETSC_FALSE; 176 ierr = PetscOptionsGetBool(NULL,NULL,"-matlab_function",&matlab_function,0);CHKERRQ(ierr); 177 if (matlab_function) { 178 ierr = VecDuplicate(x,&r);CHKERRQ(ierr); 179 ierr = SNESSetFunction(snes,r,FormFunctionMatlab,&user);CHKERRQ(ierr); 180 } 181 } 182 183 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 184 Customize nonlinear solver; set runtime options 185 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 186 ierr = SNESSetFromOptions(snes);CHKERRQ(ierr); 187 188 ierr = FormInitialGuess(da,&user,x);CHKERRQ(ierr); 189 190 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 191 Solve nonlinear system 192 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 193 ierr = SNESSolve(snes,NULL,x);CHKERRQ(ierr); 194 ierr = SNESGetIterationNumber(snes,&its);CHKERRQ(ierr); 195 196 ierr = SNESGetLinearSolveIterations(snes,&slits);CHKERRQ(ierr); 197 ierr = SNESGetKSP(snes,&ksp);CHKERRQ(ierr); 198 ierr = KSPGetTotalIterations(ksp,&lits);CHKERRQ(ierr); 199 if (lits != slits) SETERRQ2(PETSC_COMM_WORLD,PETSC_ERR_PLIB,"Number of total linear iterations reported by SNES %D does not match reported by KSP %D",slits,lits); 200 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 201 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 202 203 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 204 If using MMS, check the l_2 error 205 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 206 if (MMS) { 207 Vec e; 208 PetscReal errorl2, errorinf; 209 PetscInt N; 210 211 ierr = VecDuplicate(x, &e);CHKERRQ(ierr); 212 ierr = PetscObjectViewFromOptions((PetscObject) x, NULL, "-sol_view");CHKERRQ(ierr); 213 ierr = FormExactSolution(da, &user, e);CHKERRQ(ierr); 214 ierr = PetscObjectViewFromOptions((PetscObject) e, NULL, "-exact_view");CHKERRQ(ierr); 215 ierr = VecAXPY(e, -1.0, x);CHKERRQ(ierr); 216 ierr = PetscObjectViewFromOptions((PetscObject) e, NULL, "-error_view");CHKERRQ(ierr); 217 ierr = VecNorm(e, NORM_2, &errorl2);CHKERRQ(ierr); 218 ierr = VecNorm(e, NORM_INFINITY, &errorinf);CHKERRQ(ierr); 219 ierr = VecGetSize(e, &N);CHKERRQ(ierr); 220 ierr = PetscPrintf(PETSC_COMM_WORLD, "N: %D error L2 %g inf %g\n", N, (double) errorl2/PetscSqrtReal(N), (double) errorinf);CHKERRQ(ierr); 221 ierr = VecDestroy(&e);CHKERRQ(ierr); 222 ierr = PetscLogEventSetDof(SNES_Solve, 0, N);CHKERRQ(ierr); 223 ierr = PetscLogEventSetError(SNES_Solve, 0, errorl2/PetscSqrtReal(N));CHKERRQ(ierr); 224 } 225 226 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 227 Free work space. All PETSc objects should be destroyed when they 228 are no longer needed. 229 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 230 ierr = VecDestroy(&r);CHKERRQ(ierr); 231 ierr = VecDestroy(&x);CHKERRQ(ierr); 232 ierr = SNESDestroy(&snes);CHKERRQ(ierr); 233 ierr = DMDestroy(&da);CHKERRQ(ierr); 234 ierr = PetscFinalize(); 235 return ierr; 236 } 237 /* ------------------------------------------------------------------- */ 238 /* 239 FormInitialGuess - Forms initial approximation. 240 241 Input Parameters: 242 da - The DM 243 user - user-defined application context 244 245 Output Parameter: 246 X - vector 247 */ 248 PetscErrorCode FormInitialGuess(DM da,AppCtx *user,Vec X) 249 { 250 PetscInt i,j,Mx,My,xs,ys,xm,ym; 251 PetscErrorCode ierr; 252 PetscReal lambda,temp1,temp,hx,hy; 253 PetscScalar **x; 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); 257 258 lambda = user->param; 259 hx = 1.0/(PetscReal)(Mx-1); 260 hy = 1.0/(PetscReal)(My-1); 261 temp1 = lambda/(lambda + 1.0); 262 263 /* 264 Get a pointer to vector data. 265 - For default PETSc vectors, VecGetArray() returns a pointer to 266 the data array. Otherwise, the routine is implementation dependent. 267 - You MUST call VecRestoreArray() when you no longer need access to 268 the array. 269 */ 270 ierr = DMDAVecGetArray(da,X,&x);CHKERRQ(ierr); 271 272 /* 273 Get local grid boundaries (for 2-dimensional DMDA): 274 xs, ys - starting grid indices (no ghost points) 275 xm, ym - widths of local grid (no ghost points) 276 277 */ 278 ierr = DMDAGetCorners(da,&xs,&ys,NULL,&xm,&ym,NULL);CHKERRQ(ierr); 279 280 /* 281 Compute initial guess over the locally owned part of the grid 282 */ 283 for (j=ys; j<ys+ym; j++) { 284 temp = (PetscReal)(PetscMin(j,My-j-1))*hy; 285 for (i=xs; i<xs+xm; i++) { 286 if (i == 0 || j == 0 || i == Mx-1 || j == My-1) { 287 /* boundary conditions are all zero Dirichlet */ 288 x[j][i] = 0.0; 289 } else { 290 x[j][i] = temp1*PetscSqrtReal(PetscMin((PetscReal)(PetscMin(i,Mx-i-1))*hx,temp)); 291 } 292 } 293 } 294 295 /* 296 Restore vector 297 */ 298 ierr = DMDAVecRestoreArray(da,X,&x);CHKERRQ(ierr); 299 PetscFunctionReturn(0); 300 } 301 302 /* 303 FormExactSolution - Forms MMS solution 304 305 Input Parameters: 306 da - The DM 307 user - user-defined application context 308 309 Output Parameter: 310 X - vector 311 */ 312 PetscErrorCode FormExactSolution(DM da, AppCtx *user, Vec U) 313 { 314 DM coordDA; 315 Vec coordinates; 316 DMDACoor2d **coords; 317 PetscScalar **u; 318 PetscInt xs, ys, xm, ym, i, j; 319 PetscErrorCode ierr; 320 321 PetscFunctionBeginUser; 322 ierr = DMDAGetCorners(da, &xs, &ys, NULL, &xm, &ym, NULL);CHKERRQ(ierr); 323 ierr = DMGetCoordinateDM(da, &coordDA);CHKERRQ(ierr); 324 ierr = DMGetCoordinates(da, &coordinates);CHKERRQ(ierr); 325 ierr = DMDAVecGetArray(coordDA, coordinates, &coords);CHKERRQ(ierr); 326 ierr = DMDAVecGetArray(da, U, &u);CHKERRQ(ierr); 327 for (j = ys; j < ys+ym; ++j) { 328 for (i = xs; i < xs+xm; ++i) { 329 user->mms_solution(user,&coords[j][i],&u[j][i]); 330 } 331 } 332 ierr = DMDAVecRestoreArray(da, U, &u);CHKERRQ(ierr); 333 ierr = DMDAVecRestoreArray(coordDA, coordinates, &coords);CHKERRQ(ierr); 334 PetscFunctionReturn(0); 335 } 336 337 PetscErrorCode ZeroBCSolution(AppCtx *user,const DMDACoor2d *c,PetscScalar *u) 338 { 339 u[0] = 0.; 340 return 0; 341 } 342 343 /* The functions below evaluate the MMS solution u(x,y) and associated forcing 344 345 f(x,y) = -u_xx - u_yy - lambda exp(u) 346 347 such that u(x,y) is an exact solution with f(x,y) as the right hand side forcing term. 348 */ 349 PetscErrorCode MMSSolution1(AppCtx *user,const DMDACoor2d *c,PetscScalar *u) 350 { 351 PetscReal x = PetscRealPart(c->x), y = PetscRealPart(c->y); 352 u[0] = x*(1 - x)*y*(1 - y); 353 PetscLogFlops(5); 354 return 0; 355 } 356 PetscErrorCode MMSForcing1(AppCtx *user,const DMDACoor2d *c,PetscScalar *f) 357 { 358 PetscReal x = PetscRealPart(c->x), y = PetscRealPart(c->y); 359 f[0] = 2*x*(1 - x) + 2*y*(1 - y) - user->param*PetscExpReal(x*(1 - x)*y*(1 - y)); 360 return 0; 361 } 362 363 PetscErrorCode MMSSolution2(AppCtx *user,const DMDACoor2d *c,PetscScalar *u) 364 { 365 PetscReal x = PetscRealPart(c->x), y = PetscRealPart(c->y); 366 u[0] = PetscSinReal(PETSC_PI*x)*PetscSinReal(PETSC_PI*y); 367 PetscLogFlops(5); 368 return 0; 369 } 370 PetscErrorCode MMSForcing2(AppCtx *user,const DMDACoor2d *c,PetscScalar *f) 371 { 372 PetscReal x = PetscRealPart(c->x), y = PetscRealPart(c->y); 373 f[0] = 2*PetscSqr(PETSC_PI)*PetscSinReal(PETSC_PI*x)*PetscSinReal(PETSC_PI*y) - user->param*PetscExpReal(PetscSinReal(PETSC_PI*x)*PetscSinReal(PETSC_PI*y)); 374 return 0; 375 } 376 377 PetscErrorCode MMSSolution3(AppCtx *user,const DMDACoor2d *c,PetscScalar *u) 378 { 379 PetscReal x = PetscRealPart(c->x), y = PetscRealPart(c->y); 380 u[0] = PetscSinReal(user->m*PETSC_PI*x*(1-y))*PetscSinReal(user->n*PETSC_PI*y*(1-x)); 381 PetscLogFlops(5); 382 return 0; 383 } 384 PetscErrorCode MMSForcing3(AppCtx *user,const DMDACoor2d *c,PetscScalar *f) 385 { 386 PetscReal x = PetscRealPart(c->x), y = PetscRealPart(c->y); 387 PetscReal m = user->m, n = user->n, lambda = user->param; 388 f[0] = (-(PetscExpReal(PetscSinReal(m*PETSC_PI*x*(1 - y))*PetscSinReal(n*PETSC_PI*(1 - x)*y))*lambda) 389 + PetscSqr(PETSC_PI)*(-2*m*n*((-1 + x)*x + (-1 + y)*y)*PetscCosReal(m*PETSC_PI*x*(-1 + y))*PetscCosReal(n*PETSC_PI*(-1 + x)*y) 390 + (PetscSqr(m)*(PetscSqr(x) + PetscSqr(-1 + y)) + PetscSqr(n)*(PetscSqr(-1 + x) + PetscSqr(y))) 391 *PetscSinReal(m*PETSC_PI*x*(-1 + y))*PetscSinReal(n*PETSC_PI*(-1 + x)*y))); 392 return 0; 393 } 394 395 PetscErrorCode MMSSolution4(AppCtx *user,const DMDACoor2d *c,PetscScalar *u) 396 { 397 const PetscReal Lx = 1.,Ly = 1.; 398 PetscReal x = PetscRealPart(c->x), y = PetscRealPart(c->y); 399 u[0] = (PetscPowReal(x,4)-PetscSqr(Lx)*PetscSqr(x))*(PetscPowReal(y,4)-PetscSqr(Ly)*PetscSqr(y)); 400 PetscLogFlops(9); 401 return 0; 402 } 403 PetscErrorCode MMSForcing4(AppCtx *user,const DMDACoor2d *c,PetscScalar *f) 404 { 405 const PetscReal Lx = 1.,Ly = 1.; 406 PetscReal x = PetscRealPart(c->x), y = PetscRealPart(c->y); 407 f[0] = (2*PetscSqr(x)*(PetscSqr(x)-PetscSqr(Lx))*(PetscSqr(Ly)-6*PetscSqr(y)) 408 + 2*PetscSqr(y)*(PetscSqr(Lx)-6*PetscSqr(x))*(PetscSqr(y)-PetscSqr(Ly)) 409 - user->param*PetscExpReal((PetscPowReal(x,4)-PetscSqr(Lx)*PetscSqr(x))*(PetscPowReal(y,4)-PetscSqr(Ly)*PetscSqr(y)))); 410 return 0; 411 } 412 413 /* ------------------------------------------------------------------- */ 414 /* 415 FormFunctionLocal - Evaluates nonlinear function, F(x) on local process patch 416 417 418 */ 419 PetscErrorCode FormFunctionLocal(DMDALocalInfo *info,PetscScalar **x,PetscScalar **f,AppCtx *user) 420 { 421 PetscErrorCode ierr; 422 PetscInt i,j; 423 PetscReal lambda,hx,hy,hxdhy,hydhx; 424 PetscScalar u,ue,uw,un,us,uxx,uyy,mms_solution,mms_forcing; 425 DMDACoor2d c; 426 427 PetscFunctionBeginUser; 428 lambda = user->param; 429 hx = 1.0/(PetscReal)(info->mx-1); 430 hy = 1.0/(PetscReal)(info->my-1); 431 hxdhy = hx/hy; 432 hydhx = hy/hx; 433 /* 434 Compute function over the locally owned part of the grid 435 */ 436 for (j=info->ys; j<info->ys+info->ym; j++) { 437 for (i=info->xs; i<info->xs+info->xm; i++) { 438 if (i == 0 || j == 0 || i == info->mx-1 || j == info->my-1) { 439 c.x = i*hx; c.y = j*hy; 440 ierr = user->mms_solution(user,&c,&mms_solution);CHKERRQ(ierr); 441 f[j][i] = 2.0*(hydhx+hxdhy)*(x[j][i] - mms_solution); 442 } else { 443 u = x[j][i]; 444 uw = x[j][i-1]; 445 ue = x[j][i+1]; 446 un = x[j-1][i]; 447 us = x[j+1][i]; 448 449 /* Enforce boundary conditions at neighboring points -- setting these values causes the Jacobian to be symmetric. */ 450 if (i-1 == 0) {c.x = (i-1)*hx; c.y = j*hy; ierr = user->mms_solution(user,&c,&uw);CHKERRQ(ierr);} 451 if (i+1 == info->mx-1) {c.x = (i+1)*hx; c.y = j*hy; ierr = user->mms_solution(user,&c,&ue);CHKERRQ(ierr);} 452 if (j-1 == 0) {c.x = i*hx; c.y = (j-1)*hy; ierr = user->mms_solution(user,&c,&un);CHKERRQ(ierr);} 453 if (j+1 == info->my-1) {c.x = i*hx; c.y = (j+1)*hy; ierr = user->mms_solution(user,&c,&us);CHKERRQ(ierr);} 454 455 uxx = (2.0*u - uw - ue)*hydhx; 456 uyy = (2.0*u - un - us)*hxdhy; 457 mms_forcing = 0; 458 c.x = i*hx; c.y = j*hy; 459 if (user->mms_forcing) {ierr = user->mms_forcing(user,&c,&mms_forcing);CHKERRQ(ierr);} 460 f[j][i] = uxx + uyy - hx*hy*(lambda*PetscExpScalar(u) + mms_forcing); 461 } 462 } 463 } 464 ierr = PetscLogFlops(11.0*info->ym*info->xm);CHKERRQ(ierr); 465 PetscFunctionReturn(0); 466 } 467 468 /* FormObjectiveLocal - Evaluates nonlinear function, F(x) on local process patch */ 469 PetscErrorCode FormObjectiveLocal(DMDALocalInfo *info,PetscScalar **x,PetscReal *obj,AppCtx *user) 470 { 471 PetscErrorCode ierr; 472 PetscInt i,j; 473 PetscReal lambda,hx,hy,hxdhy,hydhx,sc,lobj=0; 474 PetscScalar u,ue,uw,un,us,uxux,uyuy; 475 MPI_Comm comm; 476 477 PetscFunctionBeginUser; 478 *obj = 0; 479 ierr = PetscObjectGetComm((PetscObject)info->da,&comm);CHKERRQ(ierr); 480 lambda = user->param; 481 hx = 1.0/(PetscReal)(info->mx-1); 482 hy = 1.0/(PetscReal)(info->my-1); 483 sc = hx*hy*lambda; 484 hxdhy = hx/hy; 485 hydhx = hy/hx; 486 /* 487 Compute function over the locally owned part of the grid 488 */ 489 for (j=info->ys; j<info->ys+info->ym; j++) { 490 for (i=info->xs; i<info->xs+info->xm; i++) { 491 if (i == 0 || j == 0 || i == info->mx-1 || j == info->my-1) { 492 lobj += PetscRealPart((hydhx + hxdhy)*x[j][i]*x[j][i]); 493 } else { 494 u = x[j][i]; 495 uw = x[j][i-1]; 496 ue = x[j][i+1]; 497 un = x[j-1][i]; 498 us = x[j+1][i]; 499 500 if (i-1 == 0) uw = 0.; 501 if (i+1 == info->mx-1) ue = 0.; 502 if (j-1 == 0) un = 0.; 503 if (j+1 == info->my-1) us = 0.; 504 505 /* F[u] = 1/2\int_{\omega}\nabla^2u(x)*u(x)*dx */ 506 507 uxux = u*(2.*u - ue - uw)*hydhx; 508 uyuy = u*(2.*u - un - us)*hxdhy; 509 510 lobj += PetscRealPart(0.5*(uxux + uyuy) - sc*PetscExpScalar(u)); 511 } 512 } 513 } 514 ierr = PetscLogFlops(12.0*info->ym*info->xm);CHKERRQ(ierr); 515 ierr = MPI_Allreduce(&lobj,obj,1,MPIU_REAL,MPIU_SUM,comm);CHKERRMPI(ierr); 516 PetscFunctionReturn(0); 517 } 518 519 /* 520 FormJacobianLocal - Evaluates Jacobian matrix on local process patch 521 */ 522 PetscErrorCode FormJacobianLocal(DMDALocalInfo *info,PetscScalar **x,Mat jac,Mat jacpre,AppCtx *user) 523 { 524 PetscErrorCode ierr; 525 PetscInt i,j,k; 526 MatStencil col[5],row; 527 PetscScalar lambda,v[5],hx,hy,hxdhy,hydhx,sc; 528 DM coordDA; 529 Vec coordinates; 530 DMDACoor2d **coords; 531 532 PetscFunctionBeginUser; 533 lambda = user->param; 534 /* Extract coordinates */ 535 ierr = DMGetCoordinateDM(info->da, &coordDA);CHKERRQ(ierr); 536 ierr = DMGetCoordinates(info->da, &coordinates);CHKERRQ(ierr); 537 ierr = DMDAVecGetArray(coordDA, coordinates, &coords);CHKERRQ(ierr); 538 hx = info->xm > 1 ? PetscRealPart(coords[info->ys][info->xs+1].x) - PetscRealPart(coords[info->ys][info->xs].x) : 1.0; 539 hy = info->ym > 1 ? PetscRealPart(coords[info->ys+1][info->xs].y) - PetscRealPart(coords[info->ys][info->xs].y) : 1.0; 540 ierr = DMDAVecRestoreArray(coordDA, coordinates, &coords);CHKERRQ(ierr); 541 hxdhy = hx/hy; 542 hydhx = hy/hx; 543 sc = hx*hy*lambda; 544 545 546 /* 547 Compute entries for the locally owned part of the Jacobian. 548 - Currently, all PETSc parallel matrix formats are partitioned by 549 contiguous chunks of rows across the processors. 550 - Each processor needs to insert only elements that it owns 551 locally (but any non-local elements will be sent to the 552 appropriate processor during matrix assembly). 553 - Here, we set all entries for a particular row at once. 554 - We can set matrix entries either using either 555 MatSetValuesLocal() or MatSetValues(), as discussed above. 556 */ 557 for (j=info->ys; j<info->ys+info->ym; j++) { 558 for (i=info->xs; i<info->xs+info->xm; i++) { 559 row.j = j; row.i = i; 560 /* boundary points */ 561 if (i == 0 || j == 0 || i == info->mx-1 || j == info->my-1) { 562 v[0] = 2.0*(hydhx + hxdhy); 563 ierr = MatSetValuesStencil(jacpre,1,&row,1,&row,v,INSERT_VALUES);CHKERRQ(ierr); 564 } else { 565 k = 0; 566 /* interior grid points */ 567 if (j-1 != 0) { 568 v[k] = -hxdhy; 569 col[k].j = j - 1; col[k].i = i; 570 k++; 571 } 572 if (i-1 != 0) { 573 v[k] = -hydhx; 574 col[k].j = j; col[k].i = i-1; 575 k++; 576 } 577 578 v[k] = 2.0*(hydhx + hxdhy) - sc*PetscExpScalar(x[j][i]); col[k].j = row.j; col[k].i = row.i; k++; 579 580 if (i+1 != info->mx-1) { 581 v[k] = -hydhx; 582 col[k].j = j; col[k].i = i+1; 583 k++; 584 } 585 if (j+1 != info->mx-1) { 586 v[k] = -hxdhy; 587 col[k].j = j + 1; col[k].i = i; 588 k++; 589 } 590 ierr = MatSetValuesStencil(jacpre,1,&row,k,col,v,INSERT_VALUES);CHKERRQ(ierr); 591 } 592 } 593 } 594 595 /* 596 Assemble matrix, using the 2-step process: 597 MatAssemblyBegin(), MatAssemblyEnd(). 598 */ 599 ierr = MatAssemblyBegin(jacpre,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 600 ierr = MatAssemblyEnd(jacpre,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 601 /* 602 Tell the matrix we will never add a new nonzero location to the 603 matrix. If we do, it will generate an error. 604 */ 605 ierr = MatSetOption(jac,MAT_NEW_NONZERO_LOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr); 606 PetscFunctionReturn(0); 607 } 608 609 PetscErrorCode FormFunctionMatlab(SNES snes,Vec X,Vec F,void *ptr) 610 { 611 #if PetscDefined(HAVE_MATLAB_ENGINE) 612 AppCtx *user = (AppCtx*)ptr; 613 PetscErrorCode ierr; 614 PetscInt Mx,My; 615 PetscReal lambda,hx,hy; 616 Vec localX,localF; 617 MPI_Comm comm; 618 DM da; 619 620 PetscFunctionBeginUser; 621 ierr = SNESGetDM(snes,&da);CHKERRQ(ierr); 622 ierr = DMGetLocalVector(da,&localX);CHKERRQ(ierr); 623 ierr = DMGetLocalVector(da,&localF);CHKERRQ(ierr); 624 ierr = PetscObjectSetName((PetscObject)localX,"localX");CHKERRQ(ierr); 625 ierr = PetscObjectSetName((PetscObject)localF,"localF");CHKERRQ(ierr); 626 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); 627 628 lambda = user->param; 629 hx = 1.0/(PetscReal)(Mx-1); 630 hy = 1.0/(PetscReal)(My-1); 631 632 ierr = PetscObjectGetComm((PetscObject)snes,&comm);CHKERRQ(ierr); 633 /* 634 Scatter ghost points to local vector,using the 2-step process 635 DMGlobalToLocalBegin(),DMGlobalToLocalEnd(). 636 By placing code between these two statements, computations can be 637 done while messages are in transition. 638 */ 639 ierr = DMGlobalToLocalBegin(da,X,INSERT_VALUES,localX);CHKERRQ(ierr); 640 ierr = DMGlobalToLocalEnd(da,X,INSERT_VALUES,localX);CHKERRQ(ierr); 641 ierr = PetscMatlabEnginePut(PETSC_MATLAB_ENGINE_(comm),(PetscObject)localX);CHKERRQ(ierr); 642 ierr = PetscMatlabEngineEvaluate(PETSC_MATLAB_ENGINE_(comm),"localF=ex5m(localX,%18.16e,%18.16e,%18.16e)",hx,hy,lambda);CHKERRQ(ierr); 643 ierr = PetscMatlabEngineGet(PETSC_MATLAB_ENGINE_(comm),(PetscObject)localF);CHKERRQ(ierr); 644 645 /* 646 Insert values into global vector 647 */ 648 ierr = DMLocalToGlobalBegin(da,localF,INSERT_VALUES,F);CHKERRQ(ierr); 649 ierr = DMLocalToGlobalEnd(da,localF,INSERT_VALUES,F);CHKERRQ(ierr); 650 ierr = DMRestoreLocalVector(da,&localX);CHKERRQ(ierr); 651 ierr = DMRestoreLocalVector(da,&localF);CHKERRQ(ierr); 652 PetscFunctionReturn(0); 653 #else 654 return 0; /* Never called */ 655 #endif 656 } 657 658 /* ------------------------------------------------------------------- */ 659 /* 660 Applies some sweeps on nonlinear Gauss-Seidel on each process 661 662 */ 663 PetscErrorCode NonlinearGS(SNES snes,Vec X, Vec B, void *ctx) 664 { 665 PetscInt i,j,k,Mx,My,xs,ys,xm,ym,its,tot_its,sweeps,l; 666 PetscErrorCode ierr; 667 PetscReal lambda,hx,hy,hxdhy,hydhx,sc; 668 PetscScalar **x,**b,bij,F,F0=0,J,u,un,us,ue,eu,uw,uxx,uyy,y; 669 PetscReal atol,rtol,stol; 670 DM da; 671 AppCtx *user; 672 Vec localX,localB; 673 674 PetscFunctionBeginUser; 675 tot_its = 0; 676 ierr = SNESNGSGetSweeps(snes,&sweeps);CHKERRQ(ierr); 677 ierr = SNESNGSGetTolerances(snes,&atol,&rtol,&stol,&its);CHKERRQ(ierr); 678 ierr = SNESGetDM(snes,&da);CHKERRQ(ierr); 679 ierr = DMGetApplicationContext(da,(void**)&user);CHKERRQ(ierr); 680 681 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); 682 683 lambda = user->param; 684 hx = 1.0/(PetscReal)(Mx-1); 685 hy = 1.0/(PetscReal)(My-1); 686 sc = hx*hy*lambda; 687 hxdhy = hx/hy; 688 hydhx = hy/hx; 689 690 691 ierr = DMGetLocalVector(da,&localX);CHKERRQ(ierr); 692 if (B) { 693 ierr = DMGetLocalVector(da,&localB);CHKERRQ(ierr); 694 } 695 for (l=0; l<sweeps; l++) { 696 697 ierr = DMGlobalToLocalBegin(da,X,INSERT_VALUES,localX);CHKERRQ(ierr); 698 ierr = DMGlobalToLocalEnd(da,X,INSERT_VALUES,localX);CHKERRQ(ierr); 699 if (B) { 700 ierr = DMGlobalToLocalBegin(da,B,INSERT_VALUES,localB);CHKERRQ(ierr); 701 ierr = DMGlobalToLocalEnd(da,B,INSERT_VALUES,localB);CHKERRQ(ierr); 702 } 703 /* 704 Get a pointer to vector data. 705 - For default PETSc vectors, VecGetArray() returns a pointer to 706 the data array. Otherwise, the routine is implementation dependent. 707 - You MUST call VecRestoreArray() when you no longer need access to 708 the array. 709 */ 710 ierr = DMDAVecGetArray(da,localX,&x);CHKERRQ(ierr); 711 if (B) ierr = DMDAVecGetArray(da,localB,&b);CHKERRQ(ierr); 712 /* 713 Get local grid boundaries (for 2-dimensional DMDA): 714 xs, ys - starting grid indices (no ghost points) 715 xm, ym - widths of local grid (no ghost points) 716 */ 717 ierr = DMDAGetCorners(da,&xs,&ys,NULL,&xm,&ym,NULL);CHKERRQ(ierr); 718 719 for (j=ys; j<ys+ym; j++) { 720 for (i=xs; i<xs+xm; i++) { 721 if (i == 0 || j == 0 || i == Mx-1 || j == My-1) { 722 /* boundary conditions are all zero Dirichlet */ 723 x[j][i] = 0.0; 724 } else { 725 if (B) bij = b[j][i]; 726 else bij = 0.; 727 728 u = x[j][i]; 729 un = x[j-1][i]; 730 us = x[j+1][i]; 731 ue = x[j][i-1]; 732 uw = x[j][i+1]; 733 734 for (k=0; k<its; k++) { 735 eu = PetscExpScalar(u); 736 uxx = (2.0*u - ue - uw)*hydhx; 737 uyy = (2.0*u - un - us)*hxdhy; 738 F = uxx + uyy - sc*eu - bij; 739 if (k == 0) F0 = F; 740 J = 2.0*(hydhx + hxdhy) - sc*eu; 741 y = F/J; 742 u -= y; 743 tot_its++; 744 745 if (atol > PetscAbsReal(PetscRealPart(F)) || 746 rtol*PetscAbsReal(PetscRealPart(F0)) > PetscAbsReal(PetscRealPart(F)) || 747 stol*PetscAbsReal(PetscRealPart(u)) > PetscAbsReal(PetscRealPart(y))) { 748 break; 749 } 750 } 751 x[j][i] = u; 752 } 753 } 754 } 755 /* 756 Restore vector 757 */ 758 ierr = DMDAVecRestoreArray(da,localX,&x);CHKERRQ(ierr); 759 ierr = DMLocalToGlobalBegin(da,localX,INSERT_VALUES,X);CHKERRQ(ierr); 760 ierr = DMLocalToGlobalEnd(da,localX,INSERT_VALUES,X);CHKERRQ(ierr); 761 } 762 ierr = PetscLogFlops(tot_its*(21.0));CHKERRQ(ierr); 763 ierr = DMRestoreLocalVector(da,&localX);CHKERRQ(ierr); 764 if (B) { 765 ierr = DMDAVecRestoreArray(da,localB,&b);CHKERRQ(ierr); 766 ierr = DMRestoreLocalVector(da,&localB);CHKERRQ(ierr); 767 } 768 PetscFunctionReturn(0); 769 } 770 771 /*TEST 772 773 test: 774 suffix: asm_0 775 requires: !single 776 args: -mms 1 -par 0.0 -snes_monitor_short -snes_converged_reason -snes_view -ksp_rtol 1.0e-9 -ksp_monitor_short -ksp_type richardson -pc_type asm -pc_asm_blocks 2 -pc_asm_overlap 0 -pc_asm_local_type additive -sub_pc_type lu 777 778 test: 779 suffix: msm_0 780 requires: !single 781 args: -mms 1 -par 0.0 -snes_monitor_short -snes_converged_reason -snes_view -ksp_rtol 1.0e-9 -ksp_monitor_short -ksp_type richardson -pc_type asm -pc_asm_blocks 2 -pc_asm_overlap 0 -pc_asm_local_type multiplicative -sub_pc_type lu 782 783 test: 784 suffix: asm_1 785 requires: !single 786 args: -mms 1 -par 0.0 -snes_monitor_short -snes_converged_reason -snes_view -ksp_rtol 1.0e-9 -ksp_monitor_short -ksp_type richardson -pc_type asm -pc_asm_blocks 2 -pc_asm_overlap 0 -pc_asm_local_type additive -sub_pc_type lu -da_grid_x 8 787 788 test: 789 suffix: msm_1 790 requires: !single 791 args: -mms 1 -par 0.0 -snes_monitor_short -snes_converged_reason -snes_view -ksp_rtol 1.0e-9 -ksp_monitor_short -ksp_type richardson -pc_type asm -pc_asm_blocks 2 -pc_asm_overlap 0 -pc_asm_local_type multiplicative -sub_pc_type lu -da_grid_x 8 792 793 test: 794 suffix: asm_2 795 requires: !single 796 args: -mms 1 -par 0.0 -snes_monitor_short -snes_converged_reason -snes_view -ksp_rtol 1.0e-9 -ksp_monitor_short -ksp_type richardson -pc_type asm -pc_asm_blocks 3 -pc_asm_overlap 0 -pc_asm_local_type additive -sub_pc_type lu -da_grid_x 8 797 798 test: 799 suffix: msm_2 800 requires: !single 801 args: -mms 1 -par 0.0 -snes_monitor_short -snes_converged_reason -snes_view -ksp_rtol 1.0e-9 -ksp_monitor_short -ksp_type richardson -pc_type asm -pc_asm_blocks 3 -pc_asm_overlap 0 -pc_asm_local_type multiplicative -sub_pc_type lu -da_grid_x 8 802 803 test: 804 suffix: asm_3 805 requires: !single 806 args: -mms 1 -par 0.0 -snes_monitor_short -snes_converged_reason -snes_view -ksp_rtol 1.0e-9 -ksp_monitor_short -ksp_type richardson -pc_type asm -pc_asm_blocks 4 -pc_asm_overlap 0 -pc_asm_local_type additive -sub_pc_type lu -da_grid_x 8 807 808 test: 809 suffix: msm_3 810 requires: !single 811 args: -mms 1 -par 0.0 -snes_monitor_short -snes_converged_reason -snes_view -ksp_rtol 1.0e-9 -ksp_monitor_short -ksp_type richardson -pc_type asm -pc_asm_blocks 4 -pc_asm_overlap 0 -pc_asm_local_type multiplicative -sub_pc_type lu -da_grid_x 8 812 813 test: 814 suffix: asm_4 815 requires: !single 816 nsize: 2 817 args: -mms 1 -par 0.0 -snes_monitor_short -snes_converged_reason -snes_view -ksp_rtol 1.0e-9 -ksp_monitor_short -ksp_type richardson -pc_type asm -pc_asm_blocks 2 -pc_asm_overlap 0 -pc_asm_local_type additive -sub_pc_type lu -da_grid_x 8 818 819 test: 820 suffix: msm_4 821 requires: !single 822 nsize: 2 823 args: -mms 1 -par 0.0 -snes_monitor_short -snes_converged_reason -snes_view -ksp_rtol 1.0e-9 -ksp_monitor_short -ksp_type richardson -pc_type asm -pc_asm_blocks 2 -pc_asm_overlap 0 -pc_asm_local_type multiplicative -sub_pc_type lu -da_grid_x 8 824 825 test: 826 suffix: asm_5 827 requires: !single 828 nsize: 2 829 args: -mms 1 -par 0.0 -snes_monitor_short -snes_converged_reason -snes_view -ksp_rtol 1.0e-9 -ksp_monitor_short -ksp_type richardson -pc_type asm -pc_asm_blocks 4 -pc_asm_overlap 0 -pc_asm_local_type additive -sub_pc_type lu -da_grid_x 8 830 831 test: 832 suffix: msm_5 833 requires: !single 834 nsize: 2 835 args: -mms 1 -par 0.0 -snes_monitor_short -snes_converged_reason -snes_view -ksp_rtol 1.0e-9 -ksp_monitor_short -ksp_type richardson -pc_type asm -pc_asm_blocks 4 -pc_asm_overlap 0 -pc_asm_local_type multiplicative -sub_pc_type lu -da_grid_x 8 836 837 test: 838 args: -snes_rtol 1.e-5 -pc_type mg -ksp_monitor_short -snes_view -pc_mg_levels 3 -pc_mg_galerkin pmat -da_grid_x 17 -da_grid_y 17 -mg_levels_ksp_monitor_short -mg_levels_ksp_norm_type unpreconditioned -snes_monitor_short -mg_levels_ksp_chebyshev_esteig 0.5,1.1 -mg_levels_pc_type sor -pc_mg_type full 839 requires: !single 840 841 test: 842 suffix: 2 843 args: -pc_type mg -ksp_converged_reason -snes_view -pc_mg_galerkin pmat -snes_grid_sequence 3 -mg_levels_ksp_norm_type unpreconditioned -snes_monitor_short -mg_levels_ksp_chebyshev_esteig 0.5,1.1 -mg_levels_pc_type sor -pc_mg_type full -ksp_atol -1. 844 845 test: 846 suffix: 3 847 nsize: 2 848 args: -snes_grid_sequence 2 -snes_mf_operator -snes_converged_reason -snes_view -pc_type mg -snes_atol -1 -snes_rtol 1.e-2 849 filter: grep -v "otal number of function evaluations" 850 851 test: 852 suffix: 4 853 nsize: 2 854 args: -snes_grid_sequence 2 -snes_monitor_short -ksp_converged_reason -snes_converged_reason -snes_view -pc_type mg -snes_atol -1 -ksp_atol -1 855 856 test: 857 suffix: 5_anderson 858 args: -da_grid_x 81 -da_grid_y 81 -snes_monitor_short -snes_max_it 50 -par 6.0 -snes_type anderson 859 860 test: 861 suffix: 5_aspin 862 nsize: 4 863 args: -snes_monitor_short -ksp_monitor_short -snes_converged_reason -da_refine 4 -da_overlap 3 -snes_type aspin -snes_view 864 865 test: 866 suffix: 5_broyden 867 args: -da_grid_x 81 -da_grid_y 81 -snes_monitor_short -snes_max_it 50 -par 6.0 -snes_type qn -snes_qn_type broyden -snes_qn_m 10 868 869 test: 870 suffix: 5_fas 871 args: -fas_coarse_snes_max_it 1 -fas_coarse_pc_type lu -fas_coarse_ksp_type preonly -snes_monitor_short -snes_type fas -fas_coarse_ksp_type richardson -da_refine 6 872 requires: !single 873 874 test: 875 suffix: 5_fas_additive 876 args: -fas_coarse_snes_max_it 1 -fas_coarse_pc_type lu -fas_coarse_ksp_type preonly -snes_monitor_short -snes_type fas -fas_coarse_ksp_type richardson -da_refine 6 -snes_fas_type additive -snes_max_it 50 877 878 test: 879 suffix: 5_fas_monitor 880 args: -da_refine 1 -snes_type fas -snes_fas_monitor 881 requires: !single 882 883 test: 884 suffix: 5_ls 885 args: -da_grid_x 81 -da_grid_y 81 -snes_monitor_short -snes_max_it 50 -par 6.0 -snes_type newtonls 886 887 test: 888 suffix: 5_ls_sell_sor 889 args: -da_grid_x 81 -da_grid_y 81 -snes_monitor_short -snes_max_it 50 -par 6.0 -snes_type newtonls -dm_mat_type sell -pc_type sor 890 output_file: output/ex5_5_ls.out 891 892 test: 893 suffix: 5_nasm 894 nsize: 4 895 args: -snes_monitor_short -snes_converged_reason -da_refine 4 -da_overlap 3 -snes_type nasm -snes_nasm_type restrict -snes_max_it 10 896 897 test: 898 suffix: 5_ncg 899 args: -da_grid_x 81 -da_grid_y 81 -snes_monitor_short -snes_max_it 50 -par 6.0 -snes_type ncg -snes_ncg_type fr 900 901 test: 902 suffix: 5_newton_asm_dmda 903 nsize: 4 904 args: -snes_monitor_short -ksp_monitor_short -snes_converged_reason -da_refine 4 -da_overlap 3 -snes_type newtonls -pc_type asm -pc_asm_dm_subdomains -malloc_dump 905 requires: !single 906 907 test: 908 suffix: 5_newton_gasm_dmda 909 nsize: 4 910 args: -snes_monitor_short -ksp_monitor_short -snes_converged_reason -da_refine 4 -da_overlap 3 -snes_type newtonls -pc_type gasm -malloc_dump 911 requires: !single 912 913 test: 914 suffix: 5_ngmres 915 args: -da_grid_x 81 -da_grid_y 81 -snes_monitor_short -snes_max_it 50 -par 6.0 -snes_type ngmres -snes_ngmres_m 10 916 917 test: 918 suffix: 5_ngmres_fas 919 args: -snes_rtol 1.e-4 -snes_type ngmres -npc_fas_coarse_snes_max_it 1 -npc_fas_coarse_snes_type newtonls -npc_fas_coarse_pc_type lu -npc_fas_coarse_ksp_type preonly -snes_ngmres_m 10 -snes_monitor_short -npc_snes_max_it 1 -npc_snes_type fas -npc_fas_coarse_ksp_type richardson -da_refine 6 920 921 test: 922 suffix: 5_ngmres_ngs 923 args: -da_grid_x 81 -da_grid_y 81 -snes_monitor_short -snes_max_it 50 -par 6.0 -snes_type ngmres -npc_snes_type ngs -npc_snes_max_it 1 924 925 test: 926 suffix: 5_ngmres_nrichardson 927 args: -da_grid_x 81 -da_grid_y 81 -snes_monitor_short -snes_max_it 50 -par 6.0 -snes_type ngmres -snes_ngmres_m 10 -npc_snes_type nrichardson -npc_snes_max_it 3 928 output_file: output/ex5_5_ngmres_richardson.out 929 930 test: 931 suffix: 5_nrichardson 932 args: -da_grid_x 81 -da_grid_y 81 -snes_monitor_short -snes_max_it 50 -par 6.0 -snes_type nrichardson 933 934 test: 935 suffix: 5_qn 936 args: -da_grid_x 81 -da_grid_y 81 -snes_monitor_short -snes_max_it 50 -par 6.0 -snes_type qn -snes_linesearch_type cp -snes_qn_m 10 937 938 test: 939 suffix: 6 940 nsize: 4 941 args: -snes_converged_reason -ksp_converged_reason -da_grid_x 129 -da_grid_y 129 -pc_type mg -pc_mg_levels 8 -mg_levels_ksp_type chebyshev -mg_levels_ksp_chebyshev_esteig 0,0.5,0,1.1 -mg_levels_ksp_max_it 2 942 943 test: 944 requires: complex !single 945 suffix: complex 946 args: -snes_mf_operator -mat_mffd_complex -snes_monitor 947 948 TEST*/ 949