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 PetscFunctionBegin; 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 PetscFunctionBegin; 54 /* The next three lines allow us to access the entries of the vectors directly */ 55 CHKERRQ(VecGetArrayRead(Y,&y)); 56 CHKERRQ(VecGetArrayRead(Ydot,&ydot)); 57 CHKERRQ(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 CHKERRQ(VecRestoreArrayRead(Y,&y)); 66 CHKERRQ(VecRestoreArrayRead(Ydot,&ydot)); 67 CHKERRQ(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 PetscFunctionBegin; 81 CHKERRQ(VecGetArrayRead(Y,&y)); 82 CHKERRQ(VecGetArrayRead(Ydot,&ydot)); 83 84 CHKERRQ(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 CHKERRQ(MatSetValues(B,5,rowcol,5,rowcol,&J[0][0],INSERT_VALUES)); 101 102 CHKERRQ(VecRestoreArrayRead(Y,&y)); 103 CHKERRQ(VecRestoreArrayRead(Ydot,&ydot)); 104 105 CHKERRQ(MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY)); 106 CHKERRQ(MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY)); 107 if (A != B) { 108 CHKERRQ(MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY)); 109 CHKERRQ(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 PetscErrorCode ierr; 120 PetscMPIInt size; 121 PetscInt n = 5; 122 PetscScalar *y; 123 124 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 125 Initialize program 126 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 127 ierr = PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr; 128 CHKERRMPI(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 CHKERRQ(MatCreate(PETSC_COMM_WORLD,&A)); 135 CHKERRQ(MatSetSizes(A,n,n,PETSC_DETERMINE,PETSC_DETERMINE)); 136 CHKERRQ(MatSetFromOptions(A)); 137 CHKERRQ(MatSetUp(A)); 138 139 CHKERRQ(MatCreateVecs(A,&Y,NULL)); 140 141 CHKERRQ(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 CHKERRQ(VecRestoreArray(Y,&y)); 148 149 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 150 Create timestepping solver context 151 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 152 CHKERRQ(TSCreate(PETSC_COMM_WORLD,&ts)); 153 CHKERRQ(TSSetProblemType(ts,TS_NONLINEAR)); 154 CHKERRQ(TSSetType(ts,TSARKIMEX)); 155 /* Must use ARKIMEX with fully implicit stages since mass matrix is not the indentity */ 156 CHKERRQ(TSARKIMEXSetType(ts,TSARKIMEXPRSSP2)); 157 CHKERRQ(TSSetEquationType(ts,TS_EQ_DAE_IMPLICIT_INDEX1)); 158 /*CHKERRQ(TSSetType(ts,TSROSW));*/ 159 CHKERRQ(TSSetIFunction(ts,NULL,IFunctionImplicit,NULL)); 160 CHKERRQ(TSSetIJacobian(ts,A,A,IJacobianImplicit,NULL)); 161 162 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 163 Set initial conditions 164 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 165 CHKERRQ(TSSetSolution(ts,Y)); 166 167 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 168 Set solver options 169 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 170 CHKERRQ(TSSetMaxTime(ts,0.15)); 171 CHKERRQ(TSSetExactFinalTime(ts,TS_EXACTFINALTIME_STEPOVER)); 172 CHKERRQ(TSSetTimeStep(ts,.001)); 173 CHKERRQ(TSSetFromOptions(ts)); 174 175 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 176 Do time stepping 177 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 178 CHKERRQ(TSSolve(ts,Y)); 179 180 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 181 Free work space. All PETSc objects should be destroyed when they are no longer needed. 182 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 183 CHKERRQ(MatDestroy(&A)); 184 CHKERRQ(VecDestroy(&Y)); 185 CHKERRQ(TSDestroy(&ts)); 186 ierr = PetscFinalize(); 187 return ierr; 188 } 189 190 /*TEST 191 build: 192 requires: !single !complex 193 test: 194 args: -ts_monitor 195 196 TEST*/ 197