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 PetscErrorCode ierr; 51 const PetscScalar *y,*ydot; 52 PetscScalar *f; 53 54 PetscFunctionBegin; 55 /* The next three lines allow us to access the entries of the vectors directly */ 56 ierr = VecGetArrayRead(Y,&y);CHKERRQ(ierr); 57 ierr = VecGetArrayRead(Ydot,&ydot);CHKERRQ(ierr); 58 ierr = VecGetArrayWrite(F,&f);CHKERRQ(ierr); 59 60 f[0] = ydot[0]/1.e6 - ydot[1]/1.e6 - PetscSinReal(200*PETSC_PI*t)/2500. + y[0]/1000.; 61 f[1] = -ydot[0]/1.e6 + ydot[1]/1.e6 - 0.0006666766666666667 + PetscExpReal((500*(y[1] - y[2]))/13.)/1.e8 + y[1]/4500.; 62 f[2] = ydot[2]/500000. + 1.e-6 - PetscExpReal((500*(y[1] - y[2]))/13.)/1.e6 + y[2]/9000.; 63 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.; 64 f[4] = (3*ydot[4])/1.e6 - (3*ydot[3])/1.e6 + y[4]/9000.; 65 66 ierr = VecRestoreArrayRead(Y,&y);CHKERRQ(ierr); 67 ierr = VecRestoreArrayRead(Ydot,&ydot);CHKERRQ(ierr); 68 ierr = VecRestoreArrayWrite(F,&f);CHKERRQ(ierr); 69 PetscFunctionReturn(0); 70 } 71 72 /* 73 Defines the Jacobian of the ODE passed to the ODE solver. See TSSetIJacobian() for the meaning of a and the Jacobian. 74 */ 75 static PetscErrorCode IJacobianImplicit(TS ts,PetscReal t,Vec Y,Vec Ydot,PetscReal a,Mat A,Mat B,void *ctx) 76 { 77 PetscErrorCode ierr; 78 PetscInt rowcol[] = {0,1,2,3,4}; 79 const PetscScalar *y,*ydot; 80 PetscScalar J[5][5]; 81 82 PetscFunctionBegin; 83 ierr = VecGetArrayRead(Y,&y);CHKERRQ(ierr); 84 ierr = VecGetArrayRead(Ydot,&ydot);CHKERRQ(ierr); 85 86 ierr = PetscMemzero(J,sizeof(J));CHKERRQ(ierr); 87 88 J[0][0]= a/1.e6 + 0.001; 89 J[0][1]= -a/1.e6; 90 J[1][0]= -a/1.e6; 91 J[1][1]= a/1.e6 + 0.00022222222222222223 + PetscExpReal((500*(y[1] - y[2]))/13.)/2.6e6; 92 J[1][2]= -PetscExpReal((500*(y[1] - y[2]))/13.)/2.6e6; 93 J[2][1]= -PetscExpReal((500*(y[1] - y[2]))/13.)/26000.; 94 J[2][2]= a/500000 + 0.00011111111111111112 + PetscExpReal((500*(y[1] - y[2]))/13.)/26000.; 95 J[3][1]= (99*PetscExpReal((500*(y[1] - y[2]))/13.))/2.6e6; 96 J[3][2]= (-99*PetscExpReal((500*(y[1] - y[2]))/13.))/2.6e6; 97 J[3][3]= (3*a)/1.e6 + 0.00011111111111111112; 98 J[3][4]= -(3*a)/1.e6; 99 J[4][3]= -(3*a)/1.e6; 100 J[4][4]= (3*a)/1.e6 + 0.00011111111111111112 ; 101 102 ierr = MatSetValues(B,5,rowcol,5,rowcol,&J[0][0],INSERT_VALUES);CHKERRQ(ierr); 103 104 ierr = VecRestoreArrayRead(Y,&y);CHKERRQ(ierr); 105 ierr = VecRestoreArrayRead(Ydot,&ydot);CHKERRQ(ierr); 106 107 ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 108 ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 109 if (A != B) { 110 ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 111 ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 112 } 113 PetscFunctionReturn(0); 114 } 115 116 int main(int argc,char **argv) 117 { 118 TS ts; /* ODE integrator */ 119 Vec Y; /* solution will be stored here */ 120 Mat A; /* Jacobian matrix */ 121 PetscErrorCode ierr; 122 PetscMPIInt size; 123 PetscInt n = 5; 124 PetscScalar *y; 125 126 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 127 Initialize program 128 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 129 ierr = PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr; 130 ierr = MPI_Comm_size(PETSC_COMM_WORLD,&size);CHKERRMPI(ierr); 131 if (size > 1) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP,"Only for sequential runs"); 132 133 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 134 Create necessary matrix and vectors 135 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 136 ierr = MatCreate(PETSC_COMM_WORLD,&A);CHKERRQ(ierr); 137 ierr = MatSetSizes(A,n,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr); 138 ierr = MatSetFromOptions(A);CHKERRQ(ierr); 139 ierr = MatSetUp(A);CHKERRQ(ierr); 140 141 ierr = MatCreateVecs(A,&Y,NULL);CHKERRQ(ierr); 142 143 ierr = VecGetArray(Y,&y);CHKERRQ(ierr); 144 y[0] = 0.0; 145 y[1] = 3.0; 146 y[2] = y[1]; 147 y[3] = 6.0; 148 y[4] = 0.0; 149 ierr = VecRestoreArray(Y,&y);CHKERRQ(ierr); 150 151 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 152 Create timestepping solver context 153 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 154 ierr = TSCreate(PETSC_COMM_WORLD,&ts);CHKERRQ(ierr); 155 ierr = TSSetProblemType(ts,TS_NONLINEAR);CHKERRQ(ierr); 156 ierr = TSSetType(ts,TSARKIMEX);CHKERRQ(ierr); 157 /* Must use ARKIMEX with fully implicit stages since mass matrix is not the indentity */ 158 ierr = TSARKIMEXSetType(ts,TSARKIMEXPRSSP2);CHKERRQ(ierr); 159 ierr = TSSetEquationType(ts,TS_EQ_DAE_IMPLICIT_INDEX1);CHKERRQ(ierr); 160 /*ierr = TSSetType(ts,TSROSW);CHKERRQ(ierr);*/ 161 ierr = TSSetIFunction(ts,NULL,IFunctionImplicit,NULL);CHKERRQ(ierr); 162 ierr = TSSetIJacobian(ts,A,A,IJacobianImplicit,NULL);CHKERRQ(ierr); 163 164 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 165 Set initial conditions 166 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 167 ierr = TSSetSolution(ts,Y);CHKERRQ(ierr); 168 169 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 170 Set solver options 171 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 172 ierr = TSSetMaxTime(ts,0.15);CHKERRQ(ierr); 173 ierr = TSSetExactFinalTime(ts,TS_EXACTFINALTIME_STEPOVER);CHKERRQ(ierr); 174 ierr = TSSetTimeStep(ts,.001);CHKERRQ(ierr); 175 ierr = TSSetFromOptions(ts);CHKERRQ(ierr); 176 177 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 178 Do time stepping 179 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 180 ierr = TSSolve(ts,Y);CHKERRQ(ierr); 181 182 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 183 Free work space. All PETSc objects should be destroyed when they are no longer needed. 184 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 185 ierr = MatDestroy(&A);CHKERRQ(ierr); 186 ierr = VecDestroy(&Y);CHKERRQ(ierr); 187 ierr = TSDestroy(&ts);CHKERRQ(ierr); 188 ierr = PetscFinalize(); 189 return ierr; 190 } 191 192 /*TEST 193 build: 194 requires: !single !complex 195 test: 196 args: -ts_monitor 197 198 TEST*/ 199