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; J[0][1] = -ctx->E*ctx->V*PetscCosScalar(u[1])/ctx->X; 70 J[1][0] = -1.0; J[1][1] = a; 71 PetscCall(MatSetValues(B,2,rowcol,2,rowcol,&J[0][0],INSERT_VALUES)); 72 PetscCall(VecRestoreArrayRead(U,&u)); 73 PetscCall(VecRestoreArrayRead(Udot,&udot)); 74 75 PetscCall(MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY)); 76 PetscCall(MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY)); 77 if (A != B) { 78 PetscCall(MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY)); 79 PetscCall(MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY)); 80 } 81 PetscFunctionReturn(0); 82 } 83 84 int main(int argc,char **argv) 85 { 86 TS ts; /* ODE integrator */ 87 Vec U; /* solution will be stored here */ 88 Mat A; /* Jacobian matrix */ 89 PetscMPIInt size; 90 PetscInt n = 2; 91 AppCtx ctx; 92 PetscScalar *u; 93 94 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 95 Initialize program 96 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 97 PetscFunctionBeginUser; 98 PetscCall(PetscInitialize(&argc,&argv,(char*)0,help)); 99 PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD,&size)); 100 PetscCheck(size == 1,PETSC_COMM_WORLD,PETSC_ERR_WRONG_MPI_SIZE,"Only for sequential runs"); 101 102 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 103 Create necessary matrix and vectors 104 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 105 PetscCall(MatCreate(PETSC_COMM_WORLD,&A)); 106 PetscCall(MatSetSizes(A,n,n,PETSC_DETERMINE,PETSC_DETERMINE)); 107 PetscCall(MatSetFromOptions(A)); 108 PetscCall(MatSetUp(A)); 109 110 PetscCall(MatCreateVecs(A,&U,NULL)); 111 112 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 113 Set runtime options 114 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 115 PetscOptionsBegin(PETSC_COMM_WORLD,NULL,"Reaction options",""); 116 { 117 ctx.omega_s = 1.0; 118 PetscCall(PetscOptionsScalar("-omega_s","","",ctx.omega_s,&ctx.omega_s,NULL)); 119 ctx.H = 1.0; 120 PetscCall(PetscOptionsScalar("-H","","",ctx.H,&ctx.H,NULL)); 121 ctx.E = 1.0; 122 PetscCall(PetscOptionsScalar("-E","","",ctx.E,&ctx.E,NULL)); 123 ctx.V = 1.0; 124 PetscCall(PetscOptionsScalar("-V","","",ctx.V,&ctx.V,NULL)); 125 ctx.X = 1.0; 126 PetscCall(PetscOptionsScalar("-X","","",ctx.X,&ctx.X,NULL)); 127 128 PetscCall(VecGetArray(U,&u)); 129 u[0] = 1; 130 u[1] = .7; 131 PetscCall(VecRestoreArray(U,&u)); 132 PetscCall(PetscOptionsGetVec(NULL,NULL,"-initial",U,NULL)); 133 } 134 PetscOptionsEnd(); 135 136 PetscCall(PetscRandomCreate(PETSC_COMM_WORLD,&ctx.rand)); 137 PetscCall(PetscRandomSetFromOptions(ctx.rand)); 138 139 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 140 Create timestepping solver context 141 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 142 PetscCall(TSCreate(PETSC_COMM_WORLD,&ts)); 143 PetscCall(TSSetProblemType(ts,TS_NONLINEAR)); 144 PetscCall(TSSetType(ts,TSROSW)); 145 PetscCall(TSSetIFunction(ts,NULL,(TSIFunction) IFunction,&ctx)); 146 PetscCall(TSSetIJacobian(ts,A,A,(TSIJacobian)IJacobian,&ctx)); 147 148 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 149 Set initial conditions 150 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 151 PetscCall(TSSetSolution(ts,U)); 152 153 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 154 Set solver options 155 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 156 PetscCall(TSSetMaxTime(ts,2000.0)); 157 PetscCall(TSSetExactFinalTime(ts,TS_EXACTFINALTIME_MATCHSTEP)); 158 PetscCall(TSSetTimeStep(ts,.001)); 159 PetscCall(TSSetFromOptions(ts)); 160 161 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 162 Solve nonlinear system 163 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 164 PetscCall(TSSolve(ts,U)); 165 166 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 167 Free work space. All PETSc objects should be destroyed when they are no longer needed. 168 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 169 PetscCall(MatDestroy(&A)); 170 PetscCall(VecDestroy(&U)); 171 PetscCall(TSDestroy(&ts)); 172 PetscCall(PetscRandomDestroy(&ctx.rand)); 173 PetscCall(PetscFinalize()); 174 return 0; 175 } 176 177 /*TEST 178 179 build: 180 requires: !complex !single 181 182 test: 183 args: -ksp_gmres_cgs_refinement_type refine_always -snes_type newtonls -ts_max_steps 10 184 185 test: 186 suffix: 2 187 args: -ts_max_steps 10 188 189 TEST*/ 190