1 static char help[] = "Basic equation for generator stability analysis.\n"; 2 3 /*F 4 5 \begin{eqnarray} 6 \frac{2 H}{\omega_s}\frac{d \omega}{dt} & = & P_m - \frac{EV}{X} \sin(\theta) \\ 7 \frac{d \theta}{dt} = \omega - \omega_s 8 \end{eqnarray} 9 10 F*/ 11 12 /* 13 Include "petscts.h" so that we can use TS solvers. Note that this 14 file automatically includes: 15 petscsys.h - base PETSc routines petscvec.h - vectors 16 petscmat.h - matrices 17 petscis.h - index sets petscksp.h - Krylov subspace methods 18 petscviewer.h - viewers petscpc.h - preconditioners 19 petscksp.h - linear solvers 20 */ 21 22 #include <petscts.h> 23 24 typedef struct { 25 PetscScalar H, omega_s, E, V, X; 26 PetscRandom rand; 27 } AppCtx; 28 29 /* 30 Defines the ODE passed to the ODE solver 31 */ 32 static PetscErrorCode IFunction(TS ts, PetscReal t, Vec U, Vec Udot, Vec F, AppCtx *ctx) 33 { 34 PetscScalar *f, r; 35 const PetscScalar *u, *udot; 36 static PetscScalar R = .4; 37 38 PetscFunctionBegin; 39 PetscCall(PetscRandomGetValue(ctx->rand, &r)); 40 if (r > .9) R = .5; 41 if (r < .1) R = .4; 42 R = .4; 43 /* The next three lines allow us to access the entries of the vectors directly */ 44 PetscCall(VecGetArrayRead(U, &u)); 45 PetscCall(VecGetArrayRead(Udot, &udot)); 46 PetscCall(VecGetArray(F, &f)); 47 f[0] = 2.0 * ctx->H * udot[0] / ctx->omega_s + ctx->E * ctx->V * PetscSinScalar(u[1]) / ctx->X - R; 48 f[1] = udot[1] - u[0] + ctx->omega_s; 49 50 PetscCall(VecRestoreArrayRead(U, &u)); 51 PetscCall(VecRestoreArrayRead(Udot, &udot)); 52 PetscCall(VecRestoreArray(F, &f)); 53 PetscFunctionReturn(PETSC_SUCCESS); 54 } 55 56 /* 57 Defines the Jacobian of the ODE passed to the ODE solver. See TSSetIJacobian() for the meaning of a and the Jacobian. 58 */ 59 static PetscErrorCode IJacobian(TS ts, PetscReal t, Vec U, Vec Udot, PetscReal a, Mat A, Mat B, AppCtx *ctx) 60 { 61 PetscInt rowcol[] = {0, 1}; 62 PetscScalar J[2][2]; 63 const PetscScalar *u, *udot; 64 65 PetscFunctionBegin; 66 PetscCall(VecGetArrayRead(U, &u)); 67 PetscCall(VecGetArrayRead(Udot, &udot)); 68 J[0][0] = 2.0 * ctx->H * a / ctx->omega_s; 69 J[0][1] = -ctx->E * ctx->V * PetscCosScalar(u[1]) / ctx->X; 70 J[1][0] = -1.0; 71 J[1][1] = a; 72 PetscCall(MatSetValues(B, 2, rowcol, 2, rowcol, &J[0][0], INSERT_VALUES)); 73 PetscCall(VecRestoreArrayRead(U, &u)); 74 PetscCall(VecRestoreArrayRead(Udot, &udot)); 75 76 PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY)); 77 PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY)); 78 if (A != B) { 79 PetscCall(MatAssemblyBegin(B, MAT_FINAL_ASSEMBLY)); 80 PetscCall(MatAssemblyEnd(B, MAT_FINAL_ASSEMBLY)); 81 } 82 PetscFunctionReturn(PETSC_SUCCESS); 83 } 84 85 int main(int argc, char **argv) 86 { 87 TS ts; /* ODE integrator */ 88 Vec U; /* solution will be stored here */ 89 Mat A; /* Jacobian matrix */ 90 PetscMPIInt size; 91 PetscInt n = 2; 92 AppCtx ctx; 93 PetscScalar *u; 94 95 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 96 Initialize program 97 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 98 PetscFunctionBeginUser; 99 PetscCall(PetscInitialize(&argc, &argv, (char *)0, help)); 100 PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD, &size)); 101 PetscCheck(size == 1, PETSC_COMM_WORLD, PETSC_ERR_WRONG_MPI_SIZE, "Only for sequential runs"); 102 103 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 104 Create necessary matrix and vectors 105 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 106 PetscCall(MatCreate(PETSC_COMM_WORLD, &A)); 107 PetscCall(MatSetSizes(A, n, n, PETSC_DETERMINE, PETSC_DETERMINE)); 108 PetscCall(MatSetFromOptions(A)); 109 PetscCall(MatSetUp(A)); 110 111 PetscCall(MatCreateVecs(A, &U, NULL)); 112 113 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 114 Set runtime options 115 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 116 PetscOptionsBegin(PETSC_COMM_WORLD, NULL, "Reaction options", ""); 117 { 118 ctx.omega_s = 1.0; 119 PetscCall(PetscOptionsScalar("-omega_s", "", "", ctx.omega_s, &ctx.omega_s, NULL)); 120 ctx.H = 1.0; 121 PetscCall(PetscOptionsScalar("-H", "", "", ctx.H, &ctx.H, NULL)); 122 ctx.E = 1.0; 123 PetscCall(PetscOptionsScalar("-E", "", "", ctx.E, &ctx.E, NULL)); 124 ctx.V = 1.0; 125 PetscCall(PetscOptionsScalar("-V", "", "", ctx.V, &ctx.V, NULL)); 126 ctx.X = 1.0; 127 PetscCall(PetscOptionsScalar("-X", "", "", ctx.X, &ctx.X, NULL)); 128 129 PetscCall(VecGetArray(U, &u)); 130 u[0] = 1; 131 u[1] = .7; 132 PetscCall(VecRestoreArray(U, &u)); 133 PetscCall(PetscOptionsGetVec(NULL, NULL, "-initial", U, NULL)); 134 } 135 PetscOptionsEnd(); 136 137 PetscCall(PetscRandomCreate(PETSC_COMM_WORLD, &ctx.rand)); 138 PetscCall(PetscRandomSetFromOptions(ctx.rand)); 139 140 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 141 Create timestepping solver context 142 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 143 PetscCall(TSCreate(PETSC_COMM_WORLD, &ts)); 144 PetscCall(TSSetProblemType(ts, TS_NONLINEAR)); 145 PetscCall(TSSetType(ts, TSROSW)); 146 PetscCall(TSSetIFunction(ts, NULL, (TSIFunction)IFunction, &ctx)); 147 PetscCall(TSSetIJacobian(ts, A, A, (TSIJacobian)IJacobian, &ctx)); 148 149 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 150 Set initial conditions 151 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 152 PetscCall(TSSetSolution(ts, U)); 153 154 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 155 Set solver options 156 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 157 PetscCall(TSSetMaxTime(ts, 2000.0)); 158 PetscCall(TSSetExactFinalTime(ts, TS_EXACTFINALTIME_MATCHSTEP)); 159 PetscCall(TSSetTimeStep(ts, .001)); 160 PetscCall(TSSetFromOptions(ts)); 161 162 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 163 Solve nonlinear system 164 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 165 PetscCall(TSSolve(ts, U)); 166 167 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 168 Free work space. All PETSc objects should be destroyed when they are no longer needed. 169 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 170 PetscCall(MatDestroy(&A)); 171 PetscCall(VecDestroy(&U)); 172 PetscCall(TSDestroy(&ts)); 173 PetscCall(PetscRandomDestroy(&ctx.rand)); 174 PetscCall(PetscFinalize()); 175 return 0; 176 } 177 178 /*TEST 179 180 build: 181 requires: !complex !single 182 183 test: 184 args: -ksp_gmres_cgs_refinement_type refine_always -snes_type newtonls -ts_max_steps 10 185 186 test: 187 suffix: 2 188 args: -ts_max_steps 10 189 190 TEST*/ 191