1 static char help[] = "Meinhard't activator-inhibitor model to test TS domain error feature.\n"; 2 3 /* 4 The activator-inhibitor on a line is described by the PDE: 5 6 da/dt = \alpha a^2 / (1 + \beta h) + \rho_a - \mu_a a + D_a d^2 a/ dx^2 7 dh/dt = \alpha a^2 + \rho_h - \mu_h h + D_h d^2 h/ dx^2 8 9 The PDE part will be solve by finite-difference on the line of cells. 10 */ 11 12 #include <petscts.h> 13 14 typedef struct { 15 PetscInt nb_cells; 16 PetscReal alpha; 17 PetscReal beta; 18 PetscReal rho_a; 19 PetscReal rho_h; 20 PetscReal mu_a; 21 PetscReal mu_h; 22 PetscReal D_a; 23 PetscReal D_h; 24 } AppCtx; 25 26 PetscErrorCode RHSFunction(TS ts, PetscReal t, Vec X, Vec DXDT, void* ptr) 27 { 28 AppCtx* user = (AppCtx*)ptr; 29 PetscInt nb_cells, i; 30 PetscReal alpha, beta; 31 PetscReal rho_a, mu_a, D_a; 32 PetscReal rho_h, mu_h, D_h; 33 PetscReal a, h, da, dh, d2a, d2h; 34 PetscScalar *dxdt; 35 const PetscScalar *x; 36 37 PetscFunctionBeginUser; 38 nb_cells = user->nb_cells; 39 alpha = user->alpha; 40 beta = user->beta; 41 rho_a = user->rho_a; 42 mu_a = user->mu_a; 43 D_a = user->D_a; 44 rho_h = user->rho_h; 45 mu_h = user->mu_h; 46 D_h = user->D_h; 47 48 PetscCall(VecGetArrayRead(X, &x)); 49 PetscCall(VecGetArray(DXDT, &dxdt)); 50 51 for (i = 0 ; i < nb_cells ; i++) { 52 a = x[2*i]; 53 h = x[2*i+1]; 54 // Reaction: 55 da = alpha * a*a / (1. + beta * h) + rho_a - mu_a * a; 56 dh = alpha * a*a + rho_h - mu_h*h; 57 // Diffusion: 58 d2a = d2h = 0.; 59 if (i > 0) { 60 d2a += (x[2*(i-1)] - a); 61 d2h += (x[2*(i-1)+1] - h); 62 } 63 if (i < nb_cells-1) { 64 d2a += (x[2*(i+1)] - a); 65 d2h += (x[2*(i+1)+1] - h); 66 } 67 dxdt[2*i] = da + D_a*d2a; 68 dxdt[2*i+1] = dh + D_h*d2h; 69 } 70 PetscCall(VecRestoreArray(DXDT, &dxdt)); 71 PetscCall(VecRestoreArrayRead(X, &x)); 72 PetscFunctionReturn(0); 73 } 74 75 PetscErrorCode RHSJacobian(TS ts, PetscReal t, Vec X, Mat J, Mat B, void *ptr) 76 { 77 AppCtx *user = (AppCtx*)ptr; 78 PetscInt nb_cells, i, idx; 79 PetscReal alpha, beta; 80 PetscReal mu_a, D_a; 81 PetscReal mu_h, D_h; 82 PetscReal a, h; 83 const PetscScalar *x; 84 PetscScalar va[4], vh[4]; 85 PetscInt ca[4], ch[4], rowa, rowh; 86 87 PetscFunctionBeginUser; 88 nb_cells = user->nb_cells; 89 alpha = user->alpha; 90 beta = user->beta; 91 mu_a = user->mu_a; 92 D_a = user->D_a; 93 mu_h = user->mu_h; 94 D_h = user->D_h; 95 96 PetscCall(VecGetArrayRead(X, &x)); 97 for (i = 0; i < nb_cells ; ++i) { 98 rowa = 2*i; 99 rowh = 2*i+1; 100 a = x[2*i]; 101 h = x[2*i+1]; 102 ca[0] = ch[1] = 2*i; 103 va[0] = 2*alpha*a / (1.+beta*h) - mu_a; 104 vh[1] = 2*alpha*a; 105 ca[1] = ch[0] = 2*i+1; 106 va[1] = -beta*alpha*a*a / ((1.+beta*h)*(1.+beta*h)); 107 vh[0] = -mu_h; 108 idx = 2; 109 if (i > 0) { 110 ca[idx] = 2*(i-1); 111 ch[idx] = 2*(i-1)+1; 112 va[idx] = D_a; 113 vh[idx] = D_h; 114 va[0] -= D_a; 115 vh[0] -= D_h; 116 idx++; 117 } 118 if (i < nb_cells-1) { 119 ca[idx] = 2*(i+1); 120 ch[idx] = 2*(i+1)+1; 121 va[idx] = D_a; 122 vh[idx] = D_h; 123 va[0] -= D_a; 124 vh[0] -= D_h; 125 idx++; 126 } 127 PetscCall(MatSetValues(B, 1, &rowa, idx, ca, va, INSERT_VALUES)); 128 PetscCall(MatSetValues(B, 1, &rowh, idx, ch, vh, INSERT_VALUES)); 129 } 130 PetscCall(VecRestoreArrayRead(X, &x)); 131 PetscCall(MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY)); 132 PetscCall(MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY)); 133 if (J != B) { 134 PetscCall(MatAssemblyBegin(J,MAT_FINAL_ASSEMBLY)); 135 PetscCall(MatAssemblyEnd(J,MAT_FINAL_ASSEMBLY)); 136 } 137 PetscFunctionReturn(0); 138 } 139 140 PetscErrorCode DomainErrorFunction(TS ts, PetscReal t, Vec Y, PetscBool *accept) 141 { 142 AppCtx *user; 143 PetscReal dt; 144 const PetscScalar *x; 145 PetscInt nb_cells, i; 146 147 PetscFunctionBeginUser; 148 PetscCall(TSGetApplicationContext(ts, &user)); 149 nb_cells = user->nb_cells; 150 PetscCall(VecGetArrayRead(Y, &x)); 151 for (i = 0 ; i < 2*nb_cells ; ++i) { 152 if (PetscRealPart(x[i]) < 0) { 153 PetscCall(TSGetTimeStep(ts, &dt)); 154 PetscCall(PetscPrintf(PETSC_COMM_WORLD, " ** Domain Error at time %g\n", (double)t)); 155 *accept = PETSC_FALSE; 156 break; 157 } 158 } 159 PetscCall(VecRestoreArrayRead(Y, &x)); 160 PetscFunctionReturn(0); 161 } 162 163 PetscErrorCode FormInitialState(Vec X, AppCtx* user) 164 { 165 PetscRandom R; 166 167 PetscFunctionBeginUser; 168 PetscCall(PetscRandomCreate(PETSC_COMM_WORLD, &R)); 169 PetscCall(PetscRandomSetFromOptions(R)); 170 PetscCall(PetscRandomSetInterval(R, 0., 10.)); 171 172 /* 173 * Initialize the state vector 174 */ 175 PetscCall(VecSetRandom(X, R)); 176 PetscCall(PetscRandomDestroy(&R)); 177 PetscFunctionReturn(0); 178 } 179 180 PetscErrorCode PrintSolution(Vec X, AppCtx *user) 181 { 182 const PetscScalar *x; 183 PetscInt i; 184 PetscInt nb_cells = user->nb_cells; 185 186 PetscFunctionBeginUser; 187 PetscCall(VecGetArrayRead(X, &x)); 188 PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Activator,Inhibitor\n")); 189 for (i = 0 ; i < nb_cells ; i++) { 190 PetscCall(PetscPrintf(PETSC_COMM_WORLD, "%5.6e,%5.6e\n", (double)x[2*i], (double)x[2*i+1])); 191 } 192 PetscCall(VecRestoreArrayRead(X, &x)); 193 PetscFunctionReturn(0); 194 } 195 196 int main(int argc, char **argv) 197 { 198 TS ts; /* time-stepping context */ 199 Vec x; /* State vector */ 200 Mat J; /* Jacobian matrix */ 201 AppCtx user; /* user-defined context */ 202 PetscReal ftime; 203 PetscInt its; 204 PetscMPIInt size; 205 206 PetscFunctionBeginUser; 207 PetscCall(PetscInitialize(&argc, &argv, NULL, help)); 208 PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD, &size)); 209 PetscCheck(size == 1,PETSC_COMM_WORLD, PETSC_ERR_WRONG_MPI_SIZE, "This is a uniprocessor example only"); 210 211 /* 212 * Allow user to set the grid dimensions and the equations parameters 213 */ 214 215 user.nb_cells = 50; 216 user.alpha = 10.; 217 user.beta = 1.; 218 user.rho_a = 1.; 219 user.rho_h = 2.; 220 user.mu_a = 2.; 221 user.mu_h = 3.; 222 user.D_a = 0.; 223 user.D_h = 30.; 224 225 PetscOptionsBegin(PETSC_COMM_WORLD, "", "Problem settings", "PROBLEM"); 226 PetscCall(PetscOptionsInt("-nb_cells", "Number of cells", "ex42.c",user.nb_cells, &user.nb_cells,NULL)); 227 PetscCall(PetscOptionsReal("-alpha", "Autocatalysis factor", "ex42.c",user.alpha, &user.alpha,NULL)); 228 PetscCall(PetscOptionsReal("-beta", "Inhibition factor", "ex42.c",user.beta, &user.beta,NULL)); 229 PetscCall(PetscOptionsReal("-rho_a", "Default production of the activator", "ex42.c",user.rho_a, &user.rho_a,NULL)); 230 PetscCall(PetscOptionsReal("-mu_a", "Degradation rate of the activator", "ex42.c",user.mu_a, &user.mu_a,NULL)); 231 PetscCall(PetscOptionsReal("-D_a", "Diffusion rate of the activator", "ex42.c",user.D_a, &user.D_a,NULL)); 232 PetscCall(PetscOptionsReal("-rho_h", "Default production of the inhibitor", "ex42.c",user.rho_h, &user.rho_h,NULL)); 233 PetscCall(PetscOptionsReal("-mu_h", "Degradation rate of the inhibitor", "ex42.c",user.mu_h, &user.mu_h,NULL)); 234 PetscCall(PetscOptionsReal("-D_h", "Diffusion rate of the inhibitor", "ex42.c",user.D_h, &user.D_h,NULL)); 235 PetscOptionsEnd(); 236 237 PetscCall(PetscPrintf(PETSC_COMM_WORLD, "nb_cells: %" PetscInt_FMT "\n", user.nb_cells)); 238 PetscCall(PetscPrintf(PETSC_COMM_WORLD, "alpha: %5.5g\n", (double)user.alpha)); 239 PetscCall(PetscPrintf(PETSC_COMM_WORLD, "beta: %5.5g\n", (double)user.beta)); 240 PetscCall(PetscPrintf(PETSC_COMM_WORLD, "rho_a: %5.5g\n", (double)user.rho_a)); 241 PetscCall(PetscPrintf(PETSC_COMM_WORLD, "mu_a: %5.5g\n", (double)user.mu_a)); 242 PetscCall(PetscPrintf(PETSC_COMM_WORLD, "D_a: %5.5g\n", (double)user.D_a)); 243 PetscCall(PetscPrintf(PETSC_COMM_WORLD, "rho_h: %5.5g\n", (double)user.rho_h)); 244 PetscCall(PetscPrintf(PETSC_COMM_WORLD, "mu_h: %5.5g\n", (double)user.mu_h)); 245 PetscCall(PetscPrintf(PETSC_COMM_WORLD, "D_h: %5.5g\n", (double)user.D_h)); 246 247 /* 248 * Create vector to hold the solution 249 */ 250 PetscCall(VecCreateSeq(PETSC_COMM_WORLD, 2*user.nb_cells, &x)); 251 252 /* 253 * Create time-stepper context 254 */ 255 PetscCall(TSCreate(PETSC_COMM_WORLD, &ts)); 256 PetscCall(TSSetProblemType(ts, TS_NONLINEAR)); 257 258 /* 259 * Tell the time-stepper context where to compute the solution 260 */ 261 PetscCall(TSSetSolution(ts, x)); 262 263 /* 264 * Allocate the jacobian matrix 265 */ 266 PetscCall(MatCreateSeqAIJ(PETSC_COMM_WORLD, 2*user.nb_cells, 2*user.nb_cells, 4, 0, &J)); 267 268 /* 269 * Provide the call-back for the non-linear function we are evaluating. 270 */ 271 PetscCall(TSSetRHSFunction(ts, NULL, RHSFunction, &user)); 272 273 /* 274 * Set the Jacobian matrix and the function user to compute Jacobians 275 */ 276 PetscCall(TSSetRHSJacobian(ts, J, J, RHSJacobian, &user)); 277 278 /* 279 * Set the function checking the domain 280 */ 281 PetscCall(TSSetFunctionDomainError(ts, &DomainErrorFunction)); 282 283 /* 284 * Initialize the problem with random values 285 */ 286 PetscCall(FormInitialState(x, &user)); 287 288 /* 289 * Read the solver type from options 290 */ 291 PetscCall(TSSetType(ts, TSPSEUDO)); 292 293 /* 294 * Set a large number of timesteps and final duration time to insure 295 * convergenge to steady state 296 */ 297 PetscCall(TSSetMaxSteps(ts, 2147483647)); 298 PetscCall(TSSetMaxTime(ts, 1.e12)); 299 PetscCall(TSSetExactFinalTime(ts,TS_EXACTFINALTIME_STEPOVER)); 300 301 /* 302 * Set a larger number of potential errors 303 */ 304 PetscCall(TSSetMaxStepRejections(ts, 50)); 305 306 /* 307 * Also start with a very small dt 308 */ 309 PetscCall(TSSetTimeStep(ts, 0.05)); 310 311 /* 312 * Set a larger time step increment 313 */ 314 PetscCall(TSPseudoSetTimeStepIncrement(ts, 1.5)); 315 316 /* 317 * Let the user personalise TS 318 */ 319 PetscCall(TSSetFromOptions(ts)); 320 321 /* 322 * Set the context for the time stepper 323 */ 324 PetscCall(TSSetApplicationContext(ts, &user)); 325 326 /* 327 * Setup the time stepper, ready for evaluation 328 */ 329 PetscCall(TSSetUp(ts)); 330 331 /* 332 * Perform the solve. 333 */ 334 PetscCall(TSSolve(ts, x)); 335 PetscCall(TSGetSolveTime(ts, &ftime)); 336 PetscCall(TSGetStepNumber(ts,&its)); 337 PetscCall(PetscPrintf(PETSC_COMM_WORLD, "Number of time steps = %" PetscInt_FMT ", final time: %4.2e\nResult:\n\n", its, (double)ftime)); 338 PetscCall(PrintSolution(x, &user)); 339 340 /* 341 * Free the data structures 342 */ 343 PetscCall(VecDestroy(&x)); 344 PetscCall(MatDestroy(&J)); 345 PetscCall(TSDestroy(&ts)); 346 PetscCall(PetscFinalize()); 347 return 0; 348 } 349 350 /*TEST 351 build: 352 requires: !single !complex 353 354 test: 355 args: -ts_max_steps 8 356 output_file: output/ex42.out 357 358 TEST*/ 359