1 static char help[] = "Time-dependent PDE in 2d for calculating joint PDF. \n"; 2 /* 3 p_t = -x_t*p_x -y_t*p_y + f(t)*p_yy 4 xmin < x < xmax, ymin < y < ymax; 5 6 Boundary conditions: 7 Zero dirichlet in y using ghosted values 8 Periodic in x 9 10 Note that x_t and y_t in the above are given functions of x and y; they are not derivatives of x and y. 11 x_t = (y - ws) 12 y_t = (ws/2H)*(Pm - Pmax*sin(x) - D*(w - ws)) 13 14 In this example, we can see the effect of a fault, that zeroes the electrical power output 15 Pmax*sin(x), on the PDF. The fault on/off times can be controlled by options -tf and -tcl respectively. 16 17 */ 18 19 #include <petscdm.h> 20 #include <petscdmda.h> 21 #include <petscts.h> 22 23 /* 24 User-defined data structures and routines 25 */ 26 typedef struct { 27 PetscScalar ws; /* Synchronous speed */ 28 PetscScalar H; /* Inertia constant */ 29 PetscScalar D; /* Damping constant */ 30 PetscScalar Pmax, Pmax_s; /* Maximum power output of generator */ 31 PetscScalar PM_min; /* Mean mechanical power input */ 32 PetscScalar lambda; /* correlation time */ 33 PetscScalar q; /* noise strength */ 34 PetscScalar mux; /* Initial average angle */ 35 PetscScalar sigmax; /* Standard deviation of initial angle */ 36 PetscScalar muy; /* Average speed */ 37 PetscScalar sigmay; /* standard deviation of initial speed */ 38 PetscScalar rho; /* Cross-correlation coefficient */ 39 PetscScalar xmin; /* left boundary of angle */ 40 PetscScalar xmax; /* right boundary of angle */ 41 PetscScalar ymin; /* bottom boundary of speed */ 42 PetscScalar ymax; /* top boundary of speed */ 43 PetscScalar dx; /* x step size */ 44 PetscScalar dy; /* y step size */ 45 PetscScalar disper_coe; /* Dispersion coefficient */ 46 DM da; 47 PetscInt st_width; /* Stencil width */ 48 DMBoundaryType bx; /* x boundary type */ 49 DMBoundaryType by; /* y boundary type */ 50 PetscReal tf, tcl; /* Fault incidence and clearing times */ 51 } AppCtx; 52 53 PetscErrorCode Parameter_settings(AppCtx *); 54 PetscErrorCode ini_bou(Vec, AppCtx *); 55 PetscErrorCode IFunction(TS, PetscReal, Vec, Vec, Vec, void *); 56 PetscErrorCode IJacobian(TS, PetscReal, Vec, Vec, PetscReal, Mat, Mat, void *); 57 PetscErrorCode PostStep(TS); 58 59 int main(int argc, char **argv) 60 { 61 Vec x; /* Solution vector */ 62 TS ts; /* Time-stepping context */ 63 AppCtx user; /* Application context */ 64 PetscViewer viewer; 65 66 PetscFunctionBeginUser; 67 PetscCall(PetscInitialize(&argc, &argv, "petscopt_ex8", help)); 68 69 /* Get physics and time parameters */ 70 PetscCall(Parameter_settings(&user)); 71 /* Create a 2D DA with dof = 1 */ 72 PetscCall(DMDACreate2d(PETSC_COMM_WORLD, user.bx, user.by, DMDA_STENCIL_STAR, 4, 4, PETSC_DECIDE, PETSC_DECIDE, 1, user.st_width, NULL, NULL, &user.da)); 73 PetscCall(DMSetFromOptions(user.da)); 74 PetscCall(DMSetUp(user.da)); 75 /* Set x and y coordinates */ 76 PetscCall(DMDASetUniformCoordinates(user.da, user.xmin, user.xmax, user.ymin, user.ymax, 0, 0)); 77 PetscCall(DMDASetCoordinateName(user.da, 0, "X - the angle")); 78 PetscCall(DMDASetCoordinateName(user.da, 1, "Y - the speed")); 79 80 /* Get global vector x from DM */ 81 PetscCall(DMCreateGlobalVector(user.da, &x)); 82 83 PetscCall(ini_bou(x, &user)); 84 PetscCall(PetscViewerBinaryOpen(PETSC_COMM_WORLD, "ini_x", FILE_MODE_WRITE, &viewer)); 85 PetscCall(VecView(x, viewer)); 86 PetscCall(PetscViewerDestroy(&viewer)); 87 88 PetscCall(TSCreate(PETSC_COMM_WORLD, &ts)); 89 PetscCall(TSSetDM(ts, user.da)); 90 PetscCall(TSSetProblemType(ts, TS_NONLINEAR)); 91 PetscCall(TSSetType(ts, TSARKIMEX)); 92 PetscCall(TSSetIFunction(ts, NULL, IFunction, &user)); 93 /* PetscCall(TSSetIJacobian(ts,NULL,NULL,IJacobian,&user)); */ 94 PetscCall(TSSetApplicationContext(ts, &user)); 95 PetscCall(TSSetTimeStep(ts, .005)); 96 PetscCall(TSSetFromOptions(ts)); 97 PetscCall(TSSetPostStep(ts, PostStep)); 98 PetscCall(TSSolve(ts, x)); 99 100 PetscCall(PetscViewerBinaryOpen(PETSC_COMM_WORLD, "fin_x", FILE_MODE_WRITE, &viewer)); 101 PetscCall(VecView(x, viewer)); 102 PetscCall(PetscViewerDestroy(&viewer)); 103 104 PetscCall(VecDestroy(&x)); 105 PetscCall(DMDestroy(&user.da)); 106 PetscCall(TSDestroy(&ts)); 107 PetscCall(PetscFinalize()); 108 return 0; 109 } 110 111 PetscErrorCode PostStep(TS ts) 112 { 113 Vec X; 114 AppCtx *user; 115 PetscReal t; 116 PetscScalar asum; 117 118 PetscFunctionBegin; 119 PetscCall(TSGetApplicationContext(ts, &user)); 120 PetscCall(TSGetTime(ts, &t)); 121 PetscCall(TSGetSolution(ts, &X)); 122 /* 123 if (t >= .2) { 124 PetscCall(TSGetSolution(ts,&X)); 125 PetscCall(VecView(X,PETSC_VIEWER_BINARY_WORLD)); 126 exit(0); 127 results in initial conditions after fault in binaryoutput 128 }*/ 129 130 if ((t > user->tf) && (t < user->tcl)) user->Pmax = 0.0; /* A short-circuit that drives the electrical power output (Pmax*sin(delta)) to zero */ 131 else user->Pmax = user->Pmax_s; 132 133 PetscCall(VecSum(X, &asum)); 134 PetscCall(PetscPrintf(PETSC_COMM_WORLD, "sum(p) at t = %f = %f\n", (double)t, (double)asum)); 135 PetscFunctionReturn(PETSC_SUCCESS); 136 } 137 138 PetscErrorCode ini_bou(Vec X, AppCtx *user) 139 { 140 DM cda; 141 DMDACoor2d **coors; 142 PetscScalar **p; 143 Vec gc; 144 PetscInt M, N, Ir, J; 145 PetscMPIInt rank; 146 147 PetscFunctionBeginUser; 148 PetscCallMPI(MPI_Comm_rank(PETSC_COMM_WORLD, &rank)); 149 PetscCall(DMDAGetInfo(user->da, NULL, &M, &N, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL)); 150 user->dx = (user->xmax - user->xmin) / (M - 1); 151 user->dy = (user->ymax - user->ymin) / (N - 1); 152 PetscCall(DMGetCoordinateDM(user->da, &cda)); 153 PetscCall(DMGetCoordinates(user->da, &gc)); 154 PetscCall(DMDAVecGetArrayRead(cda, gc, &coors)); 155 PetscCall(DMDAVecGetArray(user->da, X, &p)); 156 157 /* Point mass at (mux,muy) */ 158 PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Original user->mux = %f, user->muy = %f\n", (double)PetscRealPart(user->mux), (double)PetscRealPart(user->muy))); 159 PetscCall(DMDAGetLogicalCoordinate(user->da, user->mux, user->muy, 0.0, &Ir, &J, NULL, &user->mux, &user->muy, NULL)); 160 user->PM_min = user->Pmax * PetscSinScalar(user->mux); 161 PetscCall( 162 PetscPrintf(PETSC_COMM_WORLD, "Corrected user->mux = %f, user->muy = %f user->PM_min = %f,user->dx = %f\n", (double)PetscRealPart(user->mux), (double)PetscRealPart(user->muy), (double)PetscRealPart(user->PM_min), (double)PetscRealPart(user->dx))); 163 if (Ir > -1 && J > -1) p[J][Ir] = 1.0; 164 165 PetscCall(DMDAVecRestoreArrayRead(cda, gc, &coors)); 166 PetscCall(DMDAVecRestoreArray(user->da, X, &p)); 167 PetscFunctionReturn(PETSC_SUCCESS); 168 } 169 170 /* First advection term */ 171 PetscErrorCode adv1(PetscScalar **p, PetscScalar y, PetscInt i, PetscInt j, PetscInt M, PetscScalar *p1, AppCtx *user) 172 { 173 PetscScalar f = (y - user->ws), fpos = PetscMax(f, 0), fneg = PetscMin(f, 0); 174 175 PetscFunctionBegin; 176 if (user->st_width == 1) { 177 *p1 = fpos * (p[j][i] - p[j][i - 1]) / user->dx + fneg * (p[j][i + 1] - p[j][i]) / user->dx; 178 } else if (user->st_width == 2) { 179 *p1 = fpos * (3 * p[j][i] - 4 * p[j][i - 1] + p[j][i - 2]) / (2 * user->dx) + fneg * (-p[j][i + 2] + 4 * p[j][i + 1] - 3 * p[j][i]) / (2 * user->dx); 180 } else if (user->st_width == 3) { 181 *p1 = fpos * (2 * p[j][i + 1] + 3 * p[j][i] - 6 * p[j][i - 1] + p[j][i - 2]) / (6 * user->dx) + fneg * (-p[j][i + 2] + 6 * p[j][i + 1] - 3 * p[j][i] - 2 * p[j][i - 1]) / (6 * user->dx); 182 } 183 /* *p1 = f*(p[j][i+1] - p[j][i-1])/user->dx;*/ 184 PetscFunctionReturn(PETSC_SUCCESS); 185 } 186 187 /* Second advection term */ 188 PetscErrorCode adv2(PetscScalar **p, PetscScalar x, PetscScalar y, PetscInt i, PetscInt j, PetscInt N, PetscScalar *p2, AppCtx *user) 189 { 190 PetscScalar f, fpos, fneg; 191 192 PetscFunctionBegin; 193 f = (user->ws / (2 * user->H)) * (user->PM_min - user->Pmax * PetscSinScalar(x) - user->D * (y - user->ws)); 194 fpos = PetscMax(f, 0); 195 fneg = PetscMin(f, 0); 196 if (user->st_width == 1) { 197 *p2 = fpos * (p[j][i] - p[j - 1][i]) / user->dy + fneg * (p[j + 1][i] - p[j][i]) / user->dy; 198 } else if (user->st_width == 2) { 199 *p2 = fpos * (3 * p[j][i] - 4 * p[j - 1][i] + p[j - 2][i]) / (2 * user->dy) + fneg * (-p[j + 2][i] + 4 * p[j + 1][i] - 3 * p[j][i]) / (2 * user->dy); 200 } else if (user->st_width == 3) { 201 *p2 = fpos * (2 * p[j + 1][i] + 3 * p[j][i] - 6 * p[j - 1][i] + p[j - 2][i]) / (6 * user->dy) + fneg * (-p[j + 2][i] + 6 * p[j + 1][i] - 3 * p[j][i] - 2 * p[j - 1][i]) / (6 * user->dy); 202 } 203 204 /* *p2 = f*(p[j+1][i] - p[j-1][i])/user->dy;*/ 205 PetscFunctionReturn(PETSC_SUCCESS); 206 } 207 208 /* Diffusion term */ 209 PetscErrorCode diffuse(PetscScalar **p, PetscInt i, PetscInt j, PetscReal t, PetscScalar *p_diff, AppCtx *user) 210 { 211 PetscFunctionBeginUser; 212 if (user->st_width == 1) { 213 *p_diff = user->disper_coe * ((p[j - 1][i] - 2 * p[j][i] + p[j + 1][i]) / (user->dy * user->dy)); 214 } else if (user->st_width == 2) { 215 *p_diff = user->disper_coe * ((-p[j - 2][i] + 16 * p[j - 1][i] - 30 * p[j][i] + 16 * p[j + 1][i] - p[j + 2][i]) / (12.0 * user->dy * user->dy)); 216 } else if (user->st_width == 3) { 217 *p_diff = user->disper_coe * ((2 * p[j - 3][i] - 27 * p[j - 2][i] + 270 * p[j - 1][i] - 490 * p[j][i] + 270 * p[j + 1][i] - 27 * p[j + 2][i] + 2 * p[j + 3][i]) / (180.0 * user->dy * user->dy)); 218 } 219 PetscFunctionReturn(PETSC_SUCCESS); 220 } 221 222 PetscErrorCode IFunction(TS ts, PetscReal t, Vec X, Vec Xdot, Vec F, PetscCtx ctx) 223 { 224 AppCtx *user = (AppCtx *)ctx; 225 DM cda; 226 DMDACoor2d **coors; 227 PetscScalar **p, **f, **pdot; 228 PetscInt i, j; 229 PetscInt xs, ys, xm, ym, M, N; 230 Vec localX, gc, localXdot; 231 PetscScalar p_adv1 = 0.0, p_adv2 = 0.0, p_diff = 0; 232 PetscScalar diffuse1, gamma; 233 234 PetscFunctionBeginUser; 235 PetscCall(DMDAGetInfo(user->da, NULL, &M, &N, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL)); 236 PetscCall(DMGetCoordinateDM(user->da, &cda)); 237 PetscCall(DMDAGetCorners(cda, &xs, &ys, 0, &xm, &ym, 0)); 238 239 PetscCall(DMGetLocalVector(user->da, &localX)); 240 PetscCall(DMGetLocalVector(user->da, &localXdot)); 241 242 PetscCall(DMGlobalToLocalBegin(user->da, X, INSERT_VALUES, localX)); 243 PetscCall(DMGlobalToLocalEnd(user->da, X, INSERT_VALUES, localX)); 244 PetscCall(DMGlobalToLocalBegin(user->da, Xdot, INSERT_VALUES, localXdot)); 245 PetscCall(DMGlobalToLocalEnd(user->da, Xdot, INSERT_VALUES, localXdot)); 246 247 PetscCall(DMGetCoordinatesLocal(user->da, &gc)); 248 249 PetscCall(DMDAVecGetArrayRead(cda, gc, &coors)); 250 PetscCall(DMDAVecGetArrayRead(user->da, localX, &p)); 251 PetscCall(DMDAVecGetArrayRead(user->da, localXdot, &pdot)); 252 PetscCall(DMDAVecGetArray(user->da, F, &f)); 253 254 gamma = user->D * user->ws / (2 * user->H); 255 diffuse1 = user->lambda * user->lambda * user->q / (user->lambda * gamma + 1) * (1.0 - PetscExpScalar(-t * (gamma + 1.0) / user->lambda)); 256 user->disper_coe = user->ws * user->ws / (4 * user->H * user->H) * diffuse1; 257 258 for (i = xs; i < xs + xm; i++) { 259 for (j = ys; j < ys + ym; j++) { 260 PetscCall(adv1(p, coors[j][i].y, i, j, M, &p_adv1, user)); 261 PetscCall(adv2(p, coors[j][i].x, coors[j][i].y, i, j, N, &p_adv2, user)); 262 PetscCall(diffuse(p, i, j, t, &p_diff, user)); 263 f[j][i] = -p_adv1 - p_adv2 + p_diff - pdot[j][i]; 264 } 265 } 266 PetscCall(DMDAVecRestoreArrayRead(user->da, localX, &p)); 267 PetscCall(DMDAVecRestoreArrayRead(user->da, localX, &pdot)); 268 PetscCall(DMRestoreLocalVector(user->da, &localX)); 269 PetscCall(DMRestoreLocalVector(user->da, &localXdot)); 270 PetscCall(DMDAVecRestoreArray(user->da, F, &f)); 271 PetscCall(DMDAVecRestoreArrayRead(cda, gc, &coors)); 272 PetscFunctionReturn(PETSC_SUCCESS); 273 } 274 275 PetscErrorCode IJacobian(TS ts, PetscReal t, Vec X, Vec Xdot, PetscReal a, Mat J, Mat Jpre, PetscCtx ctx) 276 { 277 AppCtx *user = (AppCtx *)ctx; 278 DM cda; 279 DMDACoor2d **coors; 280 PetscInt i, j; 281 PetscInt xs, ys, xm, ym, M, N; 282 Vec gc; 283 PetscScalar val[5], xi, yi; 284 MatStencil row, col[5]; 285 PetscScalar c1, c3, c5, c1pos, c1neg, c3pos, c3neg; 286 287 PetscFunctionBeginUser; 288 PetscCall(DMDAGetInfo(user->da, NULL, &M, &N, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL)); 289 PetscCall(DMGetCoordinateDM(user->da, &cda)); 290 PetscCall(DMDAGetCorners(cda, &xs, &ys, 0, &xm, &ym, 0)); 291 292 PetscCall(DMGetCoordinatesLocal(user->da, &gc)); 293 PetscCall(DMDAVecGetArrayRead(cda, gc, &coors)); 294 for (i = xs; i < xs + xm; i++) { 295 for (j = ys; j < ys + ym; j++) { 296 PetscInt nc = 0; 297 xi = coors[j][i].x; 298 yi = coors[j][i].y; 299 row.i = i; 300 row.j = j; 301 c1 = (yi - user->ws) / user->dx; 302 c1pos = PetscMax(c1, 0); 303 c1neg = PetscMin(c1, 0); 304 c3 = (user->ws / (2.0 * user->H)) * (user->PM_min - user->Pmax * PetscSinScalar(xi) - user->D * (yi - user->ws)) / user->dy; 305 c3pos = PetscMax(c3, 0); 306 c3neg = PetscMin(c3, 0); 307 c5 = (PetscPowScalar((user->lambda * user->ws) / (2 * user->H), 2) * user->q * (1.0 - PetscExpScalar(-t / user->lambda))) / (user->dy * user->dy); 308 col[nc].i = i - 1; 309 col[nc].j = j; 310 val[nc++] = c1pos; 311 col[nc].i = i + 1; 312 col[nc].j = j; 313 val[nc++] = -c1neg; 314 col[nc].i = i; 315 col[nc].j = j - 1; 316 val[nc++] = c3pos + c5; 317 col[nc].i = i; 318 col[nc].j = j + 1; 319 val[nc++] = -c3neg + c5; 320 col[nc].i = i; 321 col[nc].j = j; 322 val[nc++] = -c1pos + c1neg - c3pos + c3neg - 2 * c5 - a; 323 PetscCall(MatSetValuesStencil(Jpre, 1, &row, nc, col, val, INSERT_VALUES)); 324 } 325 } 326 PetscCall(DMDAVecRestoreArrayRead(cda, gc, &coors)); 327 328 PetscCall(MatAssemblyBegin(Jpre, MAT_FINAL_ASSEMBLY)); 329 PetscCall(MatAssemblyEnd(Jpre, MAT_FINAL_ASSEMBLY)); 330 if (J != Jpre) { 331 PetscCall(MatAssemblyBegin(J, MAT_FINAL_ASSEMBLY)); 332 PetscCall(MatAssemblyEnd(J, MAT_FINAL_ASSEMBLY)); 333 } 334 PetscFunctionReturn(PETSC_SUCCESS); 335 } 336 337 PetscErrorCode Parameter_settings(AppCtx *user) 338 { 339 PetscBool flg; 340 341 PetscFunctionBeginUser; 342 /* Set default parameters */ 343 user->ws = 1.0; 344 user->H = 5.0; 345 user->D = 0.0; 346 user->Pmax = user->Pmax_s = 2.1; 347 user->PM_min = 1.0; 348 user->lambda = 0.1; 349 user->q = 1.0; 350 user->mux = PetscAsinScalar(user->PM_min / user->Pmax); 351 user->sigmax = 0.1; 352 user->sigmay = 0.1; 353 user->rho = 0.0; 354 user->xmin = -PETSC_PI; 355 user->xmax = PETSC_PI; 356 user->bx = DM_BOUNDARY_PERIODIC; 357 user->by = DM_BOUNDARY_GHOSTED; 358 user->tf = user->tcl = -1; 359 user->ymin = -2.0; 360 user->ymax = 2.0; 361 user->st_width = 1; 362 363 PetscCall(PetscOptionsGetScalar(NULL, NULL, "-ws", &user->ws, &flg)); 364 PetscCall(PetscOptionsGetScalar(NULL, NULL, "-Inertia", &user->H, &flg)); 365 PetscCall(PetscOptionsGetScalar(NULL, NULL, "-D", &user->D, &flg)); 366 PetscCall(PetscOptionsGetScalar(NULL, NULL, "-Pmax", &user->Pmax, &flg)); 367 PetscCall(PetscOptionsGetScalar(NULL, NULL, "-PM_min", &user->PM_min, &flg)); 368 PetscCall(PetscOptionsGetScalar(NULL, NULL, "-lambda", &user->lambda, &flg)); 369 PetscCall(PetscOptionsGetScalar(NULL, NULL, "-q", &user->q, &flg)); 370 PetscCall(PetscOptionsGetScalar(NULL, NULL, "-mux", &user->mux, &flg)); 371 PetscCall(PetscOptionsGetScalar(NULL, NULL, "-muy", &user->muy, &flg)); 372 if (flg == 0) user->muy = user->ws; 373 PetscCall(PetscOptionsGetScalar(NULL, NULL, "-xmin", &user->xmin, &flg)); 374 PetscCall(PetscOptionsGetScalar(NULL, NULL, "-xmax", &user->xmax, &flg)); 375 PetscCall(PetscOptionsGetScalar(NULL, NULL, "-ymin", &user->ymin, &flg)); 376 PetscCall(PetscOptionsGetScalar(NULL, NULL, "-ymax", &user->ymax, &flg)); 377 PetscCall(PetscOptionsGetInt(NULL, NULL, "-stencil_width", &user->st_width, &flg)); 378 PetscCall(PetscOptionsGetEnum(NULL, NULL, "-bx", DMBoundaryTypes, (PetscEnum *)&user->bx, &flg)); 379 PetscCall(PetscOptionsGetEnum(NULL, NULL, "-by", DMBoundaryTypes, (PetscEnum *)&user->by, &flg)); 380 PetscCall(PetscOptionsGetReal(NULL, NULL, "-tf", &user->tf, &flg)); 381 PetscCall(PetscOptionsGetReal(NULL, NULL, "-tcl", &user->tcl, &flg)); 382 PetscFunctionReturn(PETSC_SUCCESS); 383 } 384 385 /*TEST 386 387 build: 388 requires: !complex x 389 390 test: 391 args: -ts_max_steps 1 392 localrunfiles: petscopt_ex8 393 timeoutfactor: 3 394 395 TEST*/ 396