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 PetscErrorCode ierr; 36 PetscScalar *f,r; 37 const PetscScalar *u,*udot; 38 static PetscScalar R = .4; 39 40 PetscFunctionBegin; 41 ierr = PetscRandomGetValue(ctx->rand,&r);CHKERRQ(ierr); 42 if (r > .9) R = .5; 43 if (r < .1) R = .4; 44 R = .4; 45 /* The next three lines allow us to access the entries of the vectors directly */ 46 ierr = VecGetArrayRead(U,&u);CHKERRQ(ierr); 47 ierr = VecGetArrayRead(Udot,&udot);CHKERRQ(ierr); 48 ierr = VecGetArray(F,&f);CHKERRQ(ierr); 49 f[0] = 2.0*ctx->H*udot[0]/ctx->omega_s + ctx->E*ctx->V*PetscSinScalar(u[1])/ctx->X - R; 50 f[1] = udot[1] - u[0] + ctx->omega_s; 51 52 ierr = VecRestoreArrayRead(U,&u);CHKERRQ(ierr); 53 ierr = VecRestoreArrayRead(Udot,&udot);CHKERRQ(ierr); 54 ierr = VecRestoreArray(F,&f);CHKERRQ(ierr); 55 PetscFunctionReturn(0); 56 } 57 58 /* 59 Defines the Jacobian of the ODE passed to the ODE solver. See TSSetIJacobian() for the meaning of a and the Jacobian. 60 */ 61 static PetscErrorCode IJacobian(TS ts,PetscReal t,Vec U,Vec Udot,PetscReal a,Mat A,Mat B,AppCtx *ctx) 62 { 63 PetscErrorCode ierr; 64 PetscInt rowcol[] = {0,1}; 65 PetscScalar J[2][2]; 66 const PetscScalar *u,*udot; 67 68 PetscFunctionBegin; 69 ierr = VecGetArrayRead(U,&u);CHKERRQ(ierr); 70 ierr = VecGetArrayRead(Udot,&udot);CHKERRQ(ierr); 71 J[0][0] = 2.0*ctx->H*a/ctx->omega_s; J[0][1] = -ctx->E*ctx->V*PetscCosScalar(u[1])/ctx->X; 72 J[1][0] = -1.0; J[1][1] = a; 73 ierr = MatSetValues(B,2,rowcol,2,rowcol,&J[0][0],INSERT_VALUES);CHKERRQ(ierr); 74 ierr = VecRestoreArrayRead(U,&u);CHKERRQ(ierr); 75 ierr = VecRestoreArrayRead(Udot,&udot);CHKERRQ(ierr); 76 77 ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 78 ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 79 if (A != B) { 80 ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 81 ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 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 PetscErrorCode ierr; 92 PetscMPIInt size; 93 PetscInt n = 2; 94 AppCtx ctx; 95 PetscScalar *u; 96 97 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 98 Initialize program 99 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 100 ierr = PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr; 101 ierr = MPI_Comm_size(PETSC_COMM_WORLD,&size);CHKERRQ(ierr); 102 if (size > 1) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP,"Only for sequential runs"); 103 104 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 105 Create necessary matrix and vectors 106 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 107 ierr = MatCreate(PETSC_COMM_WORLD,&A);CHKERRQ(ierr); 108 ierr = MatSetSizes(A,n,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr); 109 ierr = MatSetFromOptions(A);CHKERRQ(ierr); 110 ierr = MatSetUp(A);CHKERRQ(ierr); 111 112 ierr = MatCreateVecs(A,&U,NULL);CHKERRQ(ierr); 113 114 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 115 Set runtime options 116 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 117 ierr = PetscOptionsBegin(PETSC_COMM_WORLD,NULL,"Reaction options","");CHKERRQ(ierr); 118 { 119 ctx.omega_s = 1.0; 120 ierr = PetscOptionsScalar("-omega_s","","",ctx.omega_s,&ctx.omega_s,NULL);CHKERRQ(ierr); 121 ctx.H = 1.0; 122 ierr = PetscOptionsScalar("-H","","",ctx.H,&ctx.H,NULL);CHKERRQ(ierr); 123 ctx.E = 1.0; 124 ierr = PetscOptionsScalar("-E","","",ctx.E,&ctx.E,NULL);CHKERRQ(ierr); 125 ctx.V = 1.0; 126 ierr = PetscOptionsScalar("-V","","",ctx.V,&ctx.V,NULL);CHKERRQ(ierr); 127 ctx.X = 1.0; 128 ierr = PetscOptionsScalar("-X","","",ctx.X,&ctx.X,NULL);CHKERRQ(ierr); 129 130 ierr = VecGetArray(U,&u);CHKERRQ(ierr); 131 u[0] = 1; 132 u[1] = .7; 133 ierr = VecRestoreArray(U,&u);CHKERRQ(ierr); 134 ierr = PetscOptionsGetVec(NULL,NULL,"-initial",U,NULL);CHKERRQ(ierr); 135 } 136 ierr = PetscOptionsEnd();CHKERRQ(ierr); 137 138 ierr = PetscRandomCreate(PETSC_COMM_WORLD,&ctx.rand);CHKERRQ(ierr); 139 ierr = PetscRandomSetFromOptions(ctx.rand);CHKERRQ(ierr); 140 141 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 142 Create timestepping solver context 143 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 144 ierr = TSCreate(PETSC_COMM_WORLD,&ts);CHKERRQ(ierr); 145 ierr = TSSetProblemType(ts,TS_NONLINEAR);CHKERRQ(ierr); 146 ierr = TSSetType(ts,TSROSW);CHKERRQ(ierr); 147 ierr = TSSetIFunction(ts,NULL,(TSIFunction) IFunction,&ctx);CHKERRQ(ierr); 148 ierr = TSSetIJacobian(ts,A,A,(TSIJacobian)IJacobian,&ctx);CHKERRQ(ierr); 149 150 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 151 Set initial conditions 152 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 153 ierr = TSSetSolution(ts,U);CHKERRQ(ierr); 154 155 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 156 Set solver options 157 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 158 ierr = TSSetMaxTime(ts,2000.0);CHKERRQ(ierr); 159 ierr = TSSetExactFinalTime(ts,TS_EXACTFINALTIME_MATCHSTEP);CHKERRQ(ierr); 160 ierr = TSSetTimeStep(ts,.001);CHKERRQ(ierr); 161 ierr = TSSetFromOptions(ts);CHKERRQ(ierr); 162 163 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 164 Solve nonlinear system 165 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 166 ierr = TSSolve(ts,U);CHKERRQ(ierr); 167 168 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 169 Free work space. All PETSc objects should be destroyed when they are no longer needed. 170 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 171 ierr = MatDestroy(&A);CHKERRQ(ierr); 172 ierr = VecDestroy(&U);CHKERRQ(ierr); 173 ierr = TSDestroy(&ts);CHKERRQ(ierr); 174 ierr = PetscRandomDestroy(&ctx.rand);CHKERRQ(ierr); 175 ierr = PetscFinalize(); 176 return ierr; 177 } 178 179 180 /*TEST 181 182 build: 183 requires: !complex !single 184 185 test: 186 args: -ksp_gmres_cgs_refinement_type refine_always -snes_type newtonls -ts_max_steps 10 187 188 test: 189 suffix: 2 190 args: -ts_max_steps 10 191 192 TEST*/ 193