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(0); 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); user->dy = (user->ymax - user->ymin)/(N-1); 151 PetscCall(DMGetCoordinateDM(user->da,&cda)); 152 PetscCall(DMGetCoordinates(user->da,&gc)); 153 PetscCall(DMDAVecGetArrayRead(cda,gc,&coors)); 154 PetscCall(DMDAVecGetArray(user->da,X,&p)); 155 156 /* Point mass at (mux,muy) */ 157 PetscCall(PetscPrintf(PETSC_COMM_WORLD,"Original user->mux = %f, user->muy = %f\n",(double)PetscRealPart(user->mux),(double)PetscRealPart(user->muy))); 158 PetscCall(DMDAGetLogicalCoordinate(user->da,user->mux,user->muy,0.0,&Ir,&J,NULL,&user->mux,&user->muy,NULL)); 159 user->PM_min = user->Pmax*PetscSinScalar(user->mux); 160 PetscCall(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))); 161 if (Ir > -1 && J > -1) { 162 p[J][Ir] = 1.0; 163 } 164 165 PetscCall(DMDAVecRestoreArrayRead(cda,gc,&coors)); 166 PetscCall(DMDAVecRestoreArray(user->da,X,&p)); 167 PetscFunctionReturn(0); 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,fpos,fneg; 174 PetscFunctionBegin; 175 f = (y - user->ws); 176 fpos = PetscMax(f,0); 177 fneg = PetscMin(f,0); 178 if (user->st_width == 1) { 179 *p1 = fpos*(p[j][i] - p[j][i-1])/user->dx + fneg*(p[j][i+1] - p[j][i])/user->dx; 180 } else if (user->st_width == 2) { 181 *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); 182 } else if (user->st_width == 3) { 183 *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); 184 } 185 /* *p1 = f*(p[j][i+1] - p[j][i-1])/user->dx;*/ 186 PetscFunctionReturn(0); 187 } 188 189 /* Second advection term */ 190 PetscErrorCode adv2(PetscScalar **p,PetscScalar x,PetscScalar y,PetscInt i,PetscInt j,PetscInt N,PetscScalar *p2,AppCtx *user) 191 { 192 PetscScalar f,fpos,fneg; 193 PetscFunctionBegin; 194 f = (user->ws/(2*user->H))*(user->PM_min - user->Pmax*PetscSinScalar(x) - user->D*(y - user->ws)); 195 fpos = PetscMax(f,0); 196 fneg = PetscMin(f,0); 197 if (user->st_width == 1) { 198 *p2 = fpos*(p[j][i] - p[j-1][i])/user->dy + fneg*(p[j+1][i] - p[j][i])/user->dy; 199 } else if (user->st_width ==2) { 200 *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); 201 } else if (user->st_width == 3) { 202 *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); 203 } 204 205 /* *p2 = f*(p[j+1][i] - p[j-1][i])/user->dy;*/ 206 PetscFunctionReturn(0); 207 } 208 209 /* Diffusion term */ 210 PetscErrorCode diffuse(PetscScalar **p,PetscInt i,PetscInt j,PetscReal t,PetscScalar *p_diff,AppCtx * user) 211 { 212 PetscFunctionBeginUser; 213 if (user->st_width == 1) { 214 *p_diff = user->disper_coe*((p[j-1][i] - 2*p[j][i] + p[j+1][i])/(user->dy*user->dy)); 215 } else if (user->st_width == 2) { 216 *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)); 217 } else if (user->st_width == 3) { 218 *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)); 219 } 220 PetscFunctionReturn(0); 221 } 222 223 PetscErrorCode IFunction(TS ts,PetscReal t,Vec X,Vec Xdot,Vec F,void *ctx) 224 { 225 AppCtx *user = (AppCtx*)ctx; 226 DM cda; 227 DMDACoor2d **coors; 228 PetscScalar **p,**f,**pdot; 229 PetscInt i,j; 230 PetscInt xs,ys,xm,ym,M,N; 231 Vec localX,gc,localXdot; 232 PetscScalar p_adv1 = 0.0,p_adv2 = 0.0,p_diff = 0; 233 PetscScalar diffuse1,gamma; 234 235 PetscFunctionBeginUser; 236 PetscCall(DMDAGetInfo(user->da,NULL,&M,&N,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL)); 237 PetscCall(DMGetCoordinateDM(user->da,&cda)); 238 PetscCall(DMDAGetCorners(cda,&xs,&ys,0,&xm,&ym,0)); 239 240 PetscCall(DMGetLocalVector(user->da,&localX)); 241 PetscCall(DMGetLocalVector(user->da,&localXdot)); 242 243 PetscCall(DMGlobalToLocalBegin(user->da,X,INSERT_VALUES,localX)); 244 PetscCall(DMGlobalToLocalEnd(user->da,X,INSERT_VALUES,localX)); 245 PetscCall(DMGlobalToLocalBegin(user->da,Xdot,INSERT_VALUES,localXdot)); 246 PetscCall(DMGlobalToLocalEnd(user->da,Xdot,INSERT_VALUES,localXdot)); 247 248 PetscCall(DMGetCoordinatesLocal(user->da,&gc)); 249 250 PetscCall(DMDAVecGetArrayRead(cda,gc,&coors)); 251 PetscCall(DMDAVecGetArrayRead(user->da,localX,&p)); 252 PetscCall(DMDAVecGetArrayRead(user->da,localXdot,&pdot)); 253 PetscCall(DMDAVecGetArray(user->da,F,&f)); 254 255 gamma = user->D*user->ws/(2*user->H); 256 diffuse1 = user->lambda*user->lambda*user->q/(user->lambda*gamma+1)*(1.0 - PetscExpScalar(-t*(gamma+1.0)/user->lambda)); 257 user->disper_coe = user->ws*user->ws/(4*user->H*user->H)*diffuse1; 258 259 for (i=xs; i < xs+xm; i++) { 260 for (j=ys; j < ys+ym; j++) { 261 PetscCall(adv1(p,coors[j][i].y,i,j,M,&p_adv1,user)); 262 PetscCall(adv2(p,coors[j][i].x,coors[j][i].y,i,j,N,&p_adv2,user)); 263 PetscCall(diffuse(p,i,j,t,&p_diff,user)); 264 f[j][i] = -p_adv1 - p_adv2 + p_diff - pdot[j][i]; 265 } 266 } 267 PetscCall(DMDAVecRestoreArrayRead(user->da,localX,&p)); 268 PetscCall(DMDAVecRestoreArrayRead(user->da,localX,&pdot)); 269 PetscCall(DMRestoreLocalVector(user->da,&localX)); 270 PetscCall(DMRestoreLocalVector(user->da,&localXdot)); 271 PetscCall(DMDAVecRestoreArray(user->da,F,&f)); 272 PetscCall(DMDAVecRestoreArrayRead(cda,gc,&coors)); 273 274 PetscFunctionReturn(0); 275 } 276 277 PetscErrorCode IJacobian(TS ts,PetscReal t,Vec X,Vec Xdot,PetscReal a,Mat J,Mat Jpre,void *ctx) 278 { 279 AppCtx *user=(AppCtx*)ctx; 280 DM cda; 281 DMDACoor2d **coors; 282 PetscInt i,j; 283 PetscInt xs,ys,xm,ym,M,N; 284 Vec gc; 285 PetscScalar val[5],xi,yi; 286 MatStencil row,col[5]; 287 PetscScalar c1,c3,c5,c1pos,c1neg,c3pos,c3neg; 288 289 PetscFunctionBeginUser; 290 PetscCall(DMDAGetInfo(user->da,NULL,&M,&N,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL,NULL)); 291 PetscCall(DMGetCoordinateDM(user->da,&cda)); 292 PetscCall(DMDAGetCorners(cda,&xs,&ys,0,&xm,&ym,0)); 293 294 PetscCall(DMGetCoordinatesLocal(user->da,&gc)); 295 PetscCall(DMDAVecGetArrayRead(cda,gc,&coors)); 296 for (i=xs; i < xs+xm; i++) { 297 for (j=ys; j < ys+ym; j++) { 298 PetscInt nc = 0; 299 xi = coors[j][i].x; yi = coors[j][i].y; 300 row.i = i; 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; col[nc].j = j; val[nc++] = c1pos; 309 col[nc].i = i+1; col[nc].j = j; val[nc++] = -c1neg; 310 col[nc].i = i; col[nc].j = j-1; val[nc++] = c3pos + c5; 311 col[nc].i = i; col[nc].j = j+1; val[nc++] = -c3neg + c5; 312 col[nc].i = i; col[nc].j = j; val[nc++] = -c1pos + c1neg -c3pos + c3neg -2*c5 -a; 313 PetscCall(MatSetValuesStencil(Jpre,1,&row,nc,col,val,INSERT_VALUES)); 314 } 315 } 316 PetscCall(DMDAVecRestoreArrayRead(cda,gc,&coors)); 317 318 PetscCall(MatAssemblyBegin(Jpre,MAT_FINAL_ASSEMBLY)); 319 PetscCall(MatAssemblyEnd(Jpre,MAT_FINAL_ASSEMBLY)); 320 if (J != Jpre) { 321 PetscCall(MatAssemblyBegin(J,MAT_FINAL_ASSEMBLY)); 322 PetscCall(MatAssemblyEnd(J,MAT_FINAL_ASSEMBLY)); 323 } 324 PetscFunctionReturn(0); 325 } 326 327 PetscErrorCode Parameter_settings(AppCtx *user) 328 { 329 PetscBool flg; 330 331 PetscFunctionBeginUser; 332 /* Set default parameters */ 333 user->ws = 1.0; 334 user->H = 5.0; 335 user->D = 0.0; 336 user->Pmax = user->Pmax_s = 2.1; 337 user->PM_min = 1.0; 338 user->lambda = 0.1; 339 user->q = 1.0; 340 user->mux = PetscAsinScalar(user->PM_min/user->Pmax); 341 user->sigmax = 0.1; 342 user->sigmay = 0.1; 343 user->rho = 0.0; 344 user->xmin = -PETSC_PI; 345 user->xmax = PETSC_PI; 346 user->bx = DM_BOUNDARY_PERIODIC; 347 user->by = DM_BOUNDARY_GHOSTED; 348 user->tf = user->tcl = -1; 349 user->ymin = -2.0; 350 user->ymax = 2.0; 351 user->st_width = 1; 352 353 PetscCall(PetscOptionsGetScalar(NULL,NULL,"-ws",&user->ws,&flg)); 354 PetscCall(PetscOptionsGetScalar(NULL,NULL,"-Inertia",&user->H,&flg)); 355 PetscCall(PetscOptionsGetScalar(NULL,NULL,"-D",&user->D,&flg)); 356 PetscCall(PetscOptionsGetScalar(NULL,NULL,"-Pmax",&user->Pmax,&flg)); 357 PetscCall(PetscOptionsGetScalar(NULL,NULL,"-PM_min",&user->PM_min,&flg)); 358 PetscCall(PetscOptionsGetScalar(NULL,NULL,"-lambda",&user->lambda,&flg)); 359 PetscCall(PetscOptionsGetScalar(NULL,NULL,"-q",&user->q,&flg)); 360 PetscCall(PetscOptionsGetScalar(NULL,NULL,"-mux",&user->mux,&flg)); 361 PetscCall(PetscOptionsGetScalar(NULL,NULL,"-muy",&user->muy,&flg)); 362 if (flg == 0) user->muy = user->ws; 363 PetscCall(PetscOptionsGetScalar(NULL,NULL,"-xmin",&user->xmin,&flg)); 364 PetscCall(PetscOptionsGetScalar(NULL,NULL,"-xmax",&user->xmax,&flg)); 365 PetscCall(PetscOptionsGetScalar(NULL,NULL,"-ymin",&user->ymin,&flg)); 366 PetscCall(PetscOptionsGetScalar(NULL,NULL,"-ymax",&user->ymax,&flg)); 367 PetscCall(PetscOptionsGetInt(NULL,NULL,"-stencil_width",&user->st_width,&flg)); 368 PetscCall(PetscOptionsGetEnum(NULL,NULL,"-bx",DMBoundaryTypes,(PetscEnum*)&user->bx,&flg)); 369 PetscCall(PetscOptionsGetEnum(NULL,NULL,"-by",DMBoundaryTypes,(PetscEnum*)&user->by,&flg)); 370 PetscCall(PetscOptionsGetReal(NULL,NULL,"-tf",&user->tf,&flg)); 371 PetscCall(PetscOptionsGetReal(NULL,NULL,"-tcl",&user->tcl,&flg)); 372 PetscFunctionReturn(0); 373 } 374 375 /*TEST 376 377 build: 378 requires: !complex x 379 380 test: 381 args: -ts_max_steps 1 382 localrunfiles: petscopt_ex8 383 timeoutfactor: 3 384 385 TEST*/ 386