1 2 static char help[] = "Transistor amplifier.\n"; 3 4 /*F 5 ` This example illustrates the implementation of an implicit DAE index-1 of form M y'=f(t,y) with singular mass matrix, where 6 7 [ -C1 C1 ] 8 [ C1 -C1 ] 9 M =[ -C2 ]; Ck = k * 1e-06 10 [ -C3 C3] 11 [ C3 -C3] 12 13 [ -(U(t) - y[0])/1000 ] 14 [ -6/R + y[1]/4500 + 0.01 * h(y[1]-y[2]) ] 15 f(t,y)= [ y[2]/R - h(y[1]-y[2]) ] 16 [ (y[3]-6)/9000 + 0.99 * h([y1]-y[2]) ] 17 [ y[4]/9000 ] 18 19 U(t) = 0.4 * Sin(200 Pi t); h[V] = 1e-06 * Exp(V/0.026 - 1) ` 20 21 Useful options: -ts_monitor_lg_solution -ts_monitor_lg_timestep -lg_indicate_data_points 0 22 F*/ 23 24 /* 25 Include "petscts.h" so that we can use TS solvers. Note that this 26 file automatically includes: 27 petscsys.h - base PETSc routines petscvec.h - vectors 28 petscmat.h - matrices 29 petscis.h - index sets petscksp.h - Krylov subspace methods 30 petscviewer.h - viewers petscpc.h - preconditioners 31 petscksp.h - linear solvers 32 */ 33 #include <petscts.h> 34 35 FILE *gfilepointer_data, *gfilepointer_info; 36 37 /* Defines the source */ 38 PetscErrorCode Ue(PetscScalar t, PetscScalar *U) 39 { 40 PetscFunctionBeginUser; 41 *U = 0.4 * PetscSinReal(200 * PETSC_PI * t); 42 PetscFunctionReturn(0); 43 } 44 45 /* 46 Defines the DAE passed to the time solver 47 */ 48 static PetscErrorCode IFunctionImplicit(TS ts, PetscReal t, Vec Y, Vec Ydot, Vec F, void *ctx) 49 { 50 const PetscScalar *y, *ydot; 51 PetscScalar *f; 52 53 PetscFunctionBeginUser; 54 /* The next three lines allow us to access the entries of the vectors directly */ 55 PetscCall(VecGetArrayRead(Y, &y)); 56 PetscCall(VecGetArrayRead(Ydot, &ydot)); 57 PetscCall(VecGetArrayWrite(F, &f)); 58 59 f[0] = ydot[0] / 1.e6 - ydot[1] / 1.e6 - PetscSinReal(200 * PETSC_PI * t) / 2500. + y[0] / 1000.; 60 f[1] = -ydot[0] / 1.e6 + ydot[1] / 1.e6 - 0.0006666766666666667 + PetscExpReal((500 * (y[1] - y[2])) / 13.) / 1.e8 + y[1] / 4500.; 61 f[2] = ydot[2] / 500000. + 1.e-6 - PetscExpReal((500 * (y[1] - y[2])) / 13.) / 1.e6 + y[2] / 9000.; 62 f[3] = (3 * ydot[3]) / 1.e6 - (3 * ydot[4]) / 1.e6 - 0.0006676566666666666 + (99 * PetscExpReal((500 * (y[1] - y[2])) / 13.)) / 1.e8 + y[3] / 9000.; 63 f[4] = (3 * ydot[4]) / 1.e6 - (3 * ydot[3]) / 1.e6 + y[4] / 9000.; 64 65 PetscCall(VecRestoreArrayRead(Y, &y)); 66 PetscCall(VecRestoreArrayRead(Ydot, &ydot)); 67 PetscCall(VecRestoreArrayWrite(F, &f)); 68 PetscFunctionReturn(0); 69 } 70 71 /* 72 Defines the Jacobian of the ODE passed to the ODE solver. See TSSetIJacobian() for the meaning of a and the Jacobian. 73 */ 74 static PetscErrorCode IJacobianImplicit(TS ts, PetscReal t, Vec Y, Vec Ydot, PetscReal a, Mat A, Mat B, void *ctx) 75 { 76 PetscInt rowcol[] = {0, 1, 2, 3, 4}; 77 const PetscScalar *y, *ydot; 78 PetscScalar J[5][5]; 79 80 PetscFunctionBeginUser; 81 PetscCall(VecGetArrayRead(Y, &y)); 82 PetscCall(VecGetArrayRead(Ydot, &ydot)); 83 84 PetscCall(PetscMemzero(J, sizeof(J))); 85 86 J[0][0] = a / 1.e6 + 0.001; 87 J[0][1] = -a / 1.e6; 88 J[1][0] = -a / 1.e6; 89 J[1][1] = a / 1.e6 + 0.00022222222222222223 + PetscExpReal((500 * (y[1] - y[2])) / 13.) / 2.6e6; 90 J[1][2] = -PetscExpReal((500 * (y[1] - y[2])) / 13.) / 2.6e6; 91 J[2][1] = -PetscExpReal((500 * (y[1] - y[2])) / 13.) / 26000.; 92 J[2][2] = a / 500000 + 0.00011111111111111112 + PetscExpReal((500 * (y[1] - y[2])) / 13.) / 26000.; 93 J[3][1] = (99 * PetscExpReal((500 * (y[1] - y[2])) / 13.)) / 2.6e6; 94 J[3][2] = (-99 * PetscExpReal((500 * (y[1] - y[2])) / 13.)) / 2.6e6; 95 J[3][3] = (3 * a) / 1.e6 + 0.00011111111111111112; 96 J[3][4] = -(3 * a) / 1.e6; 97 J[4][3] = -(3 * a) / 1.e6; 98 J[4][4] = (3 * a) / 1.e6 + 0.00011111111111111112; 99 100 PetscCall(MatSetValues(B, 5, rowcol, 5, rowcol, &J[0][0], INSERT_VALUES)); 101 102 PetscCall(VecRestoreArrayRead(Y, &y)); 103 PetscCall(VecRestoreArrayRead(Ydot, &ydot)); 104 105 PetscCall(MatAssemblyBegin(A, MAT_FINAL_ASSEMBLY)); 106 PetscCall(MatAssemblyEnd(A, MAT_FINAL_ASSEMBLY)); 107 if (A != B) { 108 PetscCall(MatAssemblyBegin(B, MAT_FINAL_ASSEMBLY)); 109 PetscCall(MatAssemblyEnd(B, MAT_FINAL_ASSEMBLY)); 110 } 111 PetscFunctionReturn(0); 112 } 113 114 int main(int argc, char **argv) 115 { 116 TS ts; /* ODE integrator */ 117 Vec Y; /* solution will be stored here */ 118 Mat A; /* Jacobian matrix */ 119 PetscMPIInt size; 120 PetscInt n = 5; 121 PetscScalar *y; 122 123 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 124 Initialize program 125 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 126 PetscFunctionBeginUser; 127 PetscCall(PetscInitialize(&argc, &argv, (char *)0, help)); 128 PetscCallMPI(MPI_Comm_size(PETSC_COMM_WORLD, &size)); 129 PetscCheck(size == 1, PETSC_COMM_WORLD, PETSC_ERR_WRONG_MPI_SIZE, "Only for sequential runs"); 130 131 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 132 Create necessary matrix and vectors 133 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 134 PetscCall(MatCreate(PETSC_COMM_WORLD, &A)); 135 PetscCall(MatSetSizes(A, n, n, PETSC_DETERMINE, PETSC_DETERMINE)); 136 PetscCall(MatSetFromOptions(A)); 137 PetscCall(MatSetUp(A)); 138 139 PetscCall(MatCreateVecs(A, &Y, NULL)); 140 141 PetscCall(VecGetArray(Y, &y)); 142 y[0] = 0.0; 143 y[1] = 3.0; 144 y[2] = y[1]; 145 y[3] = 6.0; 146 y[4] = 0.0; 147 PetscCall(VecRestoreArray(Y, &y)); 148 149 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 150 Create timestepping solver context 151 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 152 PetscCall(TSCreate(PETSC_COMM_WORLD, &ts)); 153 PetscCall(TSSetProblemType(ts, TS_NONLINEAR)); 154 PetscCall(TSSetType(ts, TSARKIMEX)); 155 /* Must use ARKIMEX with fully implicit stages since mass matrix is not the indentity */ 156 PetscCall(TSARKIMEXSetType(ts, TSARKIMEXPRSSP2)); 157 PetscCall(TSSetEquationType(ts, TS_EQ_DAE_IMPLICIT_INDEX1)); 158 /*PetscCall(TSSetType(ts,TSROSW));*/ 159 PetscCall(TSSetIFunction(ts, NULL, IFunctionImplicit, NULL)); 160 PetscCall(TSSetIJacobian(ts, A, A, IJacobianImplicit, NULL)); 161 162 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 163 Set initial conditions 164 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 165 PetscCall(TSSetSolution(ts, Y)); 166 167 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 168 Set solver options 169 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 170 PetscCall(TSSetMaxTime(ts, 0.15)); 171 PetscCall(TSSetExactFinalTime(ts, TS_EXACTFINALTIME_STEPOVER)); 172 PetscCall(TSSetTimeStep(ts, .001)); 173 PetscCall(TSSetFromOptions(ts)); 174 175 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 176 Do time stepping 177 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 178 PetscCall(TSSolve(ts, Y)); 179 180 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 181 Free work space. All PETSc objects should be destroyed when they are no longer needed. 182 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 183 PetscCall(MatDestroy(&A)); 184 PetscCall(VecDestroy(&Y)); 185 PetscCall(TSDestroy(&ts)); 186 PetscCall(PetscFinalize()); 187 return 0; 188 } 189 190 /*TEST 191 build: 192 requires: !single !complex 193 test: 194 args: -ts_monitor 195 196 TEST*/ 197