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 14 [ -(U(t) - y[0])/1000 ] 15 [ -6/R + y[1]/4500 + 0.01 * h(y[1]-y[2]) ] 16 f(t,y)= [ y[2]/R - h(y[1]-y[2]) ] 17 [ (y[3]-6)/9000 + 0.99 * h([y1]-y[2]) ] 18 [ y[4]/9000 ] 19 20 U(t) = 0.4 * Sin(200 Pi t); h[V] = 1e-06 * Exp(V/0.026 - 1) ` 21 22 Useful options: -ts_monitor_lg_solution -ts_monitor_lg_timestep -lg_indicate_data_points 0 23 F*/ 24 25 /* 26 Include "petscts.h" so that we can use TS solvers. Note that this 27 file automatically includes: 28 petscsys.h - base PETSc routines petscvec.h - vectors 29 petscmat.h - matrices 30 petscis.h - index sets petscksp.h - Krylov subspace methods 31 petscviewer.h - viewers petscpc.h - preconditioners 32 petscksp.h - linear solvers 33 */ 34 #include <petscts.h> 35 36 FILE *gfilepointer_data,*gfilepointer_info; 37 38 /* Defines the source */ 39 PetscErrorCode Ue(PetscScalar t,PetscScalar *U) 40 { 41 PetscFunctionBegin; 42 * U = 0.4*PetscSinReal(200*PETSC_PI*t); 43 PetscFunctionReturn(0); 44 } 45 46 /* 47 Defines the DAE passed to the time solver 48 */ 49 static PetscErrorCode IFunctionImplicit(TS ts,PetscReal t,Vec Y,Vec Ydot,Vec F,void *ctx) 50 { 51 PetscErrorCode ierr; 52 const PetscScalar *y,*ydot; 53 PetscScalar *f; 54 55 PetscFunctionBegin; 56 /* The next three lines allow us to access the entries of the vectors directly */ 57 ierr = VecGetArrayRead(Y,&y);CHKERRQ(ierr); 58 ierr = VecGetArrayRead(Ydot,&ydot);CHKERRQ(ierr); 59 ierr = VecGetArrayWrite(F,&f);CHKERRQ(ierr); 60 61 f[0] = ydot[0]/1.e6 - ydot[1]/1.e6 - PetscSinReal(200*PETSC_PI*t)/2500. + y[0]/1000.; 62 f[1] = -ydot[0]/1.e6 + ydot[1]/1.e6 - 0.0006666766666666667 + PetscExpReal((500*(y[1] - y[2]))/13.)/1.e8 + y[1]/4500.; 63 f[2] = ydot[2]/500000. + 1.e-6 - PetscExpReal((500*(y[1] - y[2]))/13.)/1.e6 + y[2]/9000.; 64 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.; 65 f[4] = (3*ydot[4])/1.e6 - (3*ydot[3])/1.e6 + y[4]/9000.; 66 67 ierr = VecRestoreArrayRead(Y,&y);CHKERRQ(ierr); 68 ierr = VecRestoreArrayRead(Ydot,&ydot);CHKERRQ(ierr); 69 ierr = VecRestoreArrayWrite(F,&f);CHKERRQ(ierr); 70 PetscFunctionReturn(0); 71 } 72 73 /* 74 Defines the Jacobian of the ODE passed to the ODE solver. See TSSetIJacobian() for the meaning of a and the Jacobian. 75 */ 76 static PetscErrorCode IJacobianImplicit(TS ts,PetscReal t,Vec Y,Vec Ydot,PetscReal a,Mat A,Mat B,void *ctx) 77 { 78 PetscErrorCode ierr; 79 PetscInt rowcol[] = {0,1,2,3,4}; 80 const PetscScalar *y,*ydot; 81 PetscScalar J[5][5]; 82 83 PetscFunctionBegin; 84 ierr = VecGetArrayRead(Y,&y);CHKERRQ(ierr); 85 ierr = VecGetArrayRead(Ydot,&ydot);CHKERRQ(ierr); 86 87 ierr = PetscMemzero(J,sizeof(J));CHKERRQ(ierr); 88 89 J[0][0]= a/1.e6 + 0.001; 90 J[0][1]= -a/1.e6; 91 J[1][0]= -a/1.e6; 92 J[1][1]= a/1.e6 + 0.00022222222222222223 + PetscExpReal((500*(y[1] - y[2]))/13.)/2.6e6; 93 J[1][2]= -PetscExpReal((500*(y[1] - y[2]))/13.)/2.6e6; 94 J[2][1]= -PetscExpReal((500*(y[1] - y[2]))/13.)/26000.; 95 J[2][2]= a/500000 + 0.00011111111111111112 + PetscExpReal((500*(y[1] - y[2]))/13.)/26000.; 96 J[3][1]= (99*PetscExpReal((500*(y[1] - y[2]))/13.))/2.6e6; 97 J[3][2]= (-99*PetscExpReal((500*(y[1] - y[2]))/13.))/2.6e6; 98 J[3][3]= (3*a)/1.e6 + 0.00011111111111111112; 99 J[3][4]= -(3*a)/1.e6; 100 J[4][3]= -(3*a)/1.e6; 101 J[4][4]= (3*a)/1.e6 + 0.00011111111111111112 ; 102 103 104 ierr = MatSetValues(B,5,rowcol,5,rowcol,&J[0][0],INSERT_VALUES);CHKERRQ(ierr); 105 106 ierr = VecRestoreArrayRead(Y,&y);CHKERRQ(ierr); 107 ierr = VecRestoreArrayRead(Ydot,&ydot);CHKERRQ(ierr); 108 109 ierr = MatAssemblyBegin(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 110 ierr = MatAssemblyEnd(A,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 111 if (A != B) { 112 ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 113 ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr); 114 } 115 PetscFunctionReturn(0); 116 } 117 118 int main(int argc,char **argv) 119 { 120 TS ts; /* ODE integrator */ 121 Vec Y; /* solution will be stored here */ 122 Mat A; /* Jacobian matrix */ 123 PetscErrorCode ierr; 124 PetscMPIInt size; 125 PetscInt n = 5; 126 PetscScalar *y; 127 128 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 129 Initialize program 130 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 131 ierr = PetscInitialize(&argc,&argv,(char*)0,help);if (ierr) return ierr; 132 ierr = MPI_Comm_size(PETSC_COMM_WORLD,&size);CHKERRQ(ierr); 133 if (size > 1) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP,"Only for sequential runs"); 134 135 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 136 Create necessary matrix and vectors 137 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 138 ierr = MatCreate(PETSC_COMM_WORLD,&A);CHKERRQ(ierr); 139 ierr = MatSetSizes(A,n,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr); 140 ierr = MatSetFromOptions(A);CHKERRQ(ierr); 141 ierr = MatSetUp(A);CHKERRQ(ierr); 142 143 ierr = MatCreateVecs(A,&Y,NULL);CHKERRQ(ierr); 144 145 ierr = VecGetArray(Y,&y);CHKERRQ(ierr); 146 y[0] = 0.0; 147 y[1] = 3.0; 148 y[2] = y[1]; 149 y[3] = 6.0; 150 y[4] = 0.0; 151 ierr = VecRestoreArray(Y,&y);CHKERRQ(ierr); 152 153 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 154 Create timestepping solver context 155 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 156 ierr = TSCreate(PETSC_COMM_WORLD,&ts);CHKERRQ(ierr); 157 ierr = TSSetProblemType(ts,TS_NONLINEAR);CHKERRQ(ierr); 158 ierr = TSSetType(ts,TSARKIMEX);CHKERRQ(ierr); 159 /* Must use ARKIMEX with fully implicit stages since mass matrix is not the indentity */ 160 ierr = TSARKIMEXSetType(ts,TSARKIMEXPRSSP2);CHKERRQ(ierr); 161 ierr = TSSetEquationType(ts,TS_EQ_DAE_IMPLICIT_INDEX1);CHKERRQ(ierr); 162 /*ierr = TSSetType(ts,TSROSW);CHKERRQ(ierr);*/ 163 ierr = TSSetIFunction(ts,NULL,IFunctionImplicit,NULL);CHKERRQ(ierr); 164 ierr = TSSetIJacobian(ts,A,A,IJacobianImplicit,NULL);CHKERRQ(ierr); 165 166 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 167 Set initial conditions 168 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 169 ierr = TSSetSolution(ts,Y);CHKERRQ(ierr); 170 171 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 172 Set solver options 173 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 174 ierr = TSSetMaxTime(ts,0.15);CHKERRQ(ierr); 175 ierr = TSSetExactFinalTime(ts,TS_EXACTFINALTIME_STEPOVER);CHKERRQ(ierr); 176 ierr = TSSetTimeStep(ts,.001);CHKERRQ(ierr); 177 ierr = TSSetFromOptions(ts);CHKERRQ(ierr); 178 179 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 180 Do time stepping 181 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 182 ierr = TSSolve(ts,Y);CHKERRQ(ierr); 183 184 /* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 185 Free work space. All PETSc objects should be destroyed when they are no longer needed. 186 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - */ 187 ierr = MatDestroy(&A);CHKERRQ(ierr); 188 ierr = VecDestroy(&Y);CHKERRQ(ierr); 189 ierr = TSDestroy(&ts);CHKERRQ(ierr); 190 ierr = PetscFinalize(); 191 return ierr; 192 } 193 194 /*TEST 195 build: 196 requires: !single !complex 197 test: 198 args: -ts_monitor 199 200 TEST*/ 201