1 2 static char help[] = "Basic equation for generator stability analysis.\n"; 3 4 /*F 5 6 \begin{eqnarray} 7 \frac{2 H}{\omega_s}\frac{d \omega}{dt} & = & P_m - \frac{EV}{X} \sin(\theta) \\ 8 \frac{d \theta}{dt} = \omega - \omega_s 9 \end{eqnarray} 10 11 F*/ 12 13 /* 14 Include "petscts.h" so that we can use TS solvers. Note that this 15 file automatically includes: 16 petscsys.h - base PETSc routines petscvec.h - vectors 17 petscmat.h - matrices 18 petscis.h - index sets petscksp.h - Krylov subspace methods 19 petscviewer.h - viewers petscpc.h - preconditioners 20 petscksp.h - linear solvers 21 */ 22 23 #include <petscts.h> 24 25 typedef struct { 26 PetscScalar H, omega_s, E, V, X; 27 PetscRandom rand; 28 } AppCtx; 29 30 /* 31 Defines the ODE passed to the ODE solver 32 */ 33 static PetscErrorCode IFunction(TS ts, PetscReal t, Vec U, Vec Udot, Vec F, AppCtx *ctx) 34 { 35 PetscScalar *f, r; 36 const PetscScalar *u, *udot; 37 static PetscScalar R = .4; 38 39 PetscFunctionBegin; 40 PetscCall(PetscRandomGetValue(ctx->rand, &r)); 41 if (r > .9) R = .5; 42 if (r < .1) R = .4; 43 R = .4; 44 /* The next three lines allow us to access the entries of the vectors directly */ 45 PetscCall(VecGetArrayRead(U, &u)); 46 PetscCall(VecGetArrayRead(Udot, &udot)); 47 PetscCall(VecGetArray(F, &f)); 48 f[0] = 2.0 * ctx->H * udot[0] / ctx->omega_s + ctx->E * ctx->V * PetscSinScalar(u[1]) / ctx->X - R; 49 f[1] = udot[1] - u[0] + ctx->omega_s; 50 51 PetscCall(VecRestoreArrayRead(U, &u)); 52 PetscCall(VecRestoreArrayRead(Udot, &udot)); 53 PetscCall(VecRestoreArray(F, &f)); 54 PetscFunctionReturn(0); 55 } 56 57 /* 58 Defines the Jacobian of the ODE passed to the ODE solver. See TSSetIJacobian() for the meaning of a and the Jacobian. 59 */ 60 static PetscErrorCode IJacobian(TS ts, PetscReal t, Vec U, Vec Udot, PetscReal a, Mat A, Mat B, AppCtx *ctx) 61 { 62 PetscInt rowcol[] = {0, 1}; 63 PetscScalar J[2][2]; 64 const PetscScalar *u, *udot; 65 66 PetscFunctionBegin; 67 PetscCall(VecGetArrayRead(U, &u)); 68 PetscCall(VecGetArrayRead(Udot, &udot)); 69 J[0][0] = 2.0 * ctx->H * a / ctx->omega_s; 70 J[0][1] = -ctx->E * ctx->V * PetscCosScalar(u[1]) / ctx->X; 71 J[1][0] = -1.0; 72 J[1][1] = a; 73 PetscCall(MatSetValues(B, 2, rowcol, 2, rowcol, &J[0][0], INSERT_VALUES)); 74 PetscCall(VecRestoreArrayRead(U, &u)); 75 PetscCall(VecRestoreArrayRead(Udot, &udot)); 76 77 PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY)); 78 PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY)); 79 if (A != B) { 80 PetscCall(MatAssemblyBegin(B, MAT_FINAL_ASSEMBLY)); 81 PetscCall(MatAssemblyEnd(B, MAT_FINAL_ASSEMBLY)); 82 } 83 PetscFunctionReturn(0); 84 } 85 86 int main(int argc, char **argv) 87 { 88 TS ts; /* ODE integrator */ 89 Vec U; /* solution will be stored here */ 90 Mat A; /* Jacobian matrix */ 91 PetscMPIInt size; 92 PetscInt n = 2; 93 AppCtx ctx; 94 PetscScalar *u; 95 96 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 97 Initialize program 98 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 99 PetscFunctionBeginUser; 100 PetscCall(PetscInitialize(&argc, &argv, (char *)0, help)); 101 PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD, &size)); 102 PetscCheck(size == 1, PETSC_COMM_WORLD, PETSC_ERR_WRONG_MPI_SIZE, "Only for sequential runs"); 103 104 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 105 Create necessary matrix and vectors 106 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 107 PetscCall(MatCreate(PETSC_COMM_WORLD, &A)); 108 PetscCall(MatSetSizes(A, n, n, PETSC_DETERMINE, PETSC_DETERMINE)); 109 PetscCall(MatSetFromOptions(A)); 110 PetscCall(MatSetUp(A)); 111 112 PetscCall(MatCreateVecs(A, &U, NULL)); 113 114 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 115 Set runtime options 116 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 117 PetscOptionsBegin(PETSC_COMM_WORLD, NULL, "Reaction options", ""); 118 { 119 ctx.omega_s = 1.0; 120 PetscCall(PetscOptionsScalar("-omega_s", "", "", ctx.omega_s, &ctx.omega_s, NULL)); 121 ctx.H = 1.0; 122 PetscCall(PetscOptionsScalar("-H", "", "", ctx.H, &ctx.H, NULL)); 123 ctx.E = 1.0; 124 PetscCall(PetscOptionsScalar("-E", "", "", ctx.E, &ctx.E, NULL)); 125 ctx.V = 1.0; 126 PetscCall(PetscOptionsScalar("-V", "", "", ctx.V, &ctx.V, NULL)); 127 ctx.X = 1.0; 128 PetscCall(PetscOptionsScalar("-X", "", "", ctx.X, &ctx.X, NULL)); 129 130 PetscCall(VecGetArray(U, &u)); 131 u[0] = 1; 132 u[1] = .7; 133 PetscCall(VecRestoreArray(U, &u)); 134 PetscCall(PetscOptionsGetVec(NULL, NULL, "-initial", U, NULL)); 135 } 136 PetscOptionsEnd(); 137 138 PetscCall(PetscRandomCreate(PETSC_COMM_WORLD, &ctx.rand)); 139 PetscCall(PetscRandomSetFromOptions(ctx.rand)); 140 141 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 142 Create timestepping solver context 143 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 144 PetscCall(TSCreate(PETSC_COMM_WORLD, &ts)); 145 PetscCall(TSSetProblemType(ts, TS_NONLINEAR)); 146 PetscCall(TSSetType(ts, TSROSW)); 147 PetscCall(TSSetIFunction(ts, NULL, (TSIFunction)IFunction, &ctx)); 148 PetscCall(TSSetIJacobian(ts, A, A, (TSIJacobian)IJacobian, &ctx)); 149 150 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 151 Set initial conditions 152 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 153 PetscCall(TSSetSolution(ts, U)); 154 155 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 156 Set solver options 157 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 158 PetscCall(TSSetMaxTime(ts, 2000.0)); 159 PetscCall(TSSetExactFinalTime(ts, TS_EXACTFINALTIME_MATCHSTEP)); 160 PetscCall(TSSetTimeStep(ts, .001)); 161 PetscCall(TSSetFromOptions(ts)); 162 163 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 164 Solve nonlinear system 165 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 166 PetscCall(TSSolve(ts, U)); 167 168 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 169 Free work space. All PETSc objects should be destroyed when they are no longer needed. 170 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 171 PetscCall(MatDestroy(&A)); 172 PetscCall(VecDestroy(&U)); 173 PetscCall(TSDestroy(&ts)); 174 PetscCall(PetscRandomDestroy(&ctx.rand)); 175 PetscCall(PetscFinalize()); 176 return 0; 177 } 178 179 /*TEST 180 181 build: 182 requires: !complex !single 183 184 test: 185 args: -ksp_gmres_cgs_refinement_type refine_always -snes_type newtonls -ts_max_steps 10 186 187 test: 188 suffix: 2 189 args: -ts_max_steps 10 190 191 TEST*/ 192