SUBROUTINE INTEGRATE( TIN, TOUT ) INCLUDE 'KPP_ROOT_params.h' INCLUDE 'KPP_ROOT_global.h' C TIN - Start Time KPP_REAL TIN C TOUT - END Time KPP_REAL TOUT INTEGER INFO(5) EXTERNAL FUNC_CHEM, JAC_CHEM C-------------------------------- INTEGER N_stepss, N_accepteds, N_rejecteds, N_jacs, ITOL, IERR SAVE N_stepss, N_accepteds, N_rejecteds, N_jacs C-------------------------------- INFO(1) = 1 ! Autonomous INFO(2) = 0 CALL ROS2(NVAR,TIN,TOUT,STEPMIN,STEPMAX, + STEPMIN,VAR,ATOL,RTOL, + Info,FUNC_CHEM,JAC_CHEM) C-------------------------------- N_stepss=N_stepss+Info(4)+Info(5) N_accepteds=N_accepteds+Info(4) N_rejecteds=N_rejecteds+Info(5) N_jacs=N_jacs+Info(3) PRINT*,'Step=',N_stepss,' Acc=',N_accepteds,' Rej=',N_rejecteds, & ' Jac=',N_jacs C-------------------------------- RETURN END SUBROUTINE ROS2(N,T,Tnext,Hmin,Hmax,Hstart, + Y,AbsTol,RelTol, + Info,FUNC_CHEM,JAC_CHEM) IMPLICIT NONE INCLUDE 'KPP_ROOT_params.h' INCLUDE 'KPP_ROOT_sparse.h' C INPUT ARGUMENTS: C Y = Vector of (NVAR) concentrations, contains the C initial values on input C [T, Tnext] = the integration interval C Hmin, Hmax = lower and upper bounds for the selected step-size. C Note that for Step = Hmin the current computed C solution is unconditionally accepted by the error C control mechanism. C AbsTol, RelTol = (NVAR) dimensional vectors of C componentwise absolute and relative tolerances. C FUNC_CHEM = name of routine of derivatives. KPP syntax. C See the header below. C JAC_CHEM = name of routine that computes the Jacobian, in C sparse format. KPP syntax. See the header below. C Info(1) = 1 for autonomous system C = 0 for nonautonomous system C Info(2) = 1 for third order embedded formula C = 0 for first order embedded formula C C Note: Stage 3 used to build strongly A-stable order 3 formula for error control C Embed3 = (Info(2).EQ.1) C IF Embed3 = .true. THEN the third order embedded formula is used C .false. THEN a first order embedded formula is used C C C OUTPUT ARGUMENTS: C Y = the values of concentrations at TEND. C T = equals TEND on output. C Info(2) = # of FUNC_CHEM CALLs. C Info(3) = # of JAC_CHEM CALLs. C Info(4) = # of accepted steps. C Info(5) = # of rejected steps. KPP_REAL K1(NVAR), K2(NVAR), K3(NVAR) KPP_REAL F1(NVAR), JAC(LU_NONZERO) KPP_REAL DFDT(NVAR) KPP_REAL Hmin,Hmax,Hnew,Hstart,ghinv,uround KPP_REAL Y(NVAR), Ynew(NVAR) KPP_REAL AbsTol(NVAR), RelTol(NVAR) KPP_REAL T, Tnext, H, Hold, Tplus KPP_REAL ERR, factor, facmax KPP_REAL tau, beta, elo, dround, a21, c21, c31, c32 KPP_REAL gamma3, d1, d2, d3, gam INTEGER n,nfcn,njac,Naccept,Nreject,i,j,ier INTEGER Info(5) LOGICAL IsReject, Autonomous, Embed3 EXTERNAL FUNC_CHEM, JAC_CHEM KPP_REAL gamma, m1, m2, alpha, beta1, beta2, delta, w, e c Initialization of counters, etc. Autonomous = Info(1) .EQ. 1 Embed3 = Info(2) .EQ. 1 uround = 1.d-15 dround = dsqrt(uround) H = DMAX1(1.d-8, Hmin) Tplus = T IsReject = .false. Naccept = 0 Nreject = 0 Nfcn = 0 Njac = 0 C Method Parameters gamma = 1.d0 + 1.d0/sqrt(2.d0) a21 = - 1.d0/gamma m1 = -3.d0/(2.d0*gamma) m2 = -1.d0/(2.d0*gamma) c21 = -2.d0/gamma c31 = -1.0D0/gamma**2*(1.0D0-7.0D0*gamma+9.0D0*gamma**2) & /(-1.0D0+2.0D0*gamma) c32 = -1.0D0/gamma**2*(1.0D0-6.0D0*gamma+6.0D0*gamma**2) & /(-1.0D0+2.0D0*gamma)/2 gamma3 = 0.5D0 - 2*gamma d1 = ((-9.0D0*gamma+8.0D0*gamma**2+2.0D0)/gamma**2/ & (-1.0D0+2*gamma))/6.0D0 d2 = ((-1.0D0+3.0D0*gamma)/gamma**2/ & (-1.0D0+2.0D0*gamma))/6.0D0 d3 = -1.0D0/(3.0D0*gamma) C === Start the time loop === DO WHILE (T .LT. Tnext) 10 CONTINUE Tplus = T + H IF ( Tplus .gt. Tnext ) THEN H = Tnext - T Tplus = Tnext END IF CALL JAC_CHEM( T, Y, JAC ) Njac = Njac+1 ghinv = -1.0d0/(gamma*H) DO 20 j=1,NVAR JAC(LU_DIAG(j)) = JAC(LU_DIAG(j)) + ghinv 20 CONTINUE CALL KppDecomp (JAC, ier) IF (ier.ne.0) THEN IF ( H.gt.Hmin) THEN H = 5.0d-1*H GO TO 10 ELSE PRINT *,'IER <> 0, H=',H STOP END IF END IF CALL FUNC_CHEM( T, Y, F1 ) C ====== NONAUTONOMOUS CASE =============== IF (.NOT. Autonomous) THEN tau = DSIGN(DROUND*DMAX1( 1.0d-6, DABS(T) ), T) CALL FUNC_CHEM( T+tau, Y, K2) nfcn=nfcn+1 DO 30 j = 1,NVAR DFDT(j) = ( K2(j)-F1(j) )/tau 30 CONTINUE END IF ! .NOT.Autonomous C ----- STAGE 1 ----- delta = gamma*H DO 40 j = 1,NVAR K1(j) = F1(j) 40 CONTINUE IF (.NOT.Autonomous) THEN DO 45 j = 1,NVAR K1(j) = K1(j) + delta*DFDT(j) 45 CONTINUE END IF ! .NOT.Autonomous CALL KppSolve (JAC, K1) C ----- STAGE 2 ----- DO 50 j = 1,NVAR Ynew(j) = Y(j) + a21*K1(j) 50 CONTINUE CALL FUNC_CHEM( T+H, Ynew, F1) nfcn=nfcn+1 beta = -c21/H DO 55 j = 1,NVAR K2(j) = F1(j) + beta*K1(j) 55 CONTINUE IF (.NOT.Autonomous) THEN delta = -gamma*H DO 56 j = 1,NVAR K2(j) = K2(j) + delta*DFDT(j) 56 CONTINUE END IF ! .NOT.Autonomous CALL KppSolve (JAC, K2) C ----- STAGE 3 ----- IF (Embed3) THEN beta1 = -c31/H beta2 = -c32/H delta = gamma3*H DO 57 j = 1,NVAR K3(j) = F1(j) + beta1*K1(j) + beta2*K2(j) 57 CONTINUE IF (.NOT.Autonomous) THEN DO 58 j = 1,NVAR K3(j) = K3(j) + delta*DFDT(j) 58 CONTINUE END IF ! .NOT.Autonomous CALL KppSolve (JAC, K3) END IF ! Embed3 C ---- The Solution --- DO 120 j = 1,NVAR Ynew(j) = Y(j) + m1*K1(j) + m2*K2(j) 120 CONTINUE C ====== Error estimation ======== ERR=0.d0 DO 130 i=1,NVAR w = AbsTol(i) + RelTol(i)*DMAX1(DABS(Y(i)),DABS(Ynew(i))) IF ( Embed3 ) THEN e = d1*K1(i) + d2*K2(i) + d3*K3(i) ELSE e = 1.d0/(2.d0*gamma)*(K1(i)+K2(i)) END IF ! Embed3 ERR = ERR + ( e/w )**2 130 CONTINUE ERR = DMAX1( uround, DSQRT( ERR/NVAR ) ) C ======= Choose the stepsize =============================== IF ( Embed3 ) THEN elo = 3.0D0 ! estimator local order ELSE elo = 2.0D0 END IF factor = DMAX1(2.0D-1,DMIN1(6.0D0,ERR**(1.0D0/elo)/.9D0)) Hnew = DMIN1(Hmax,DMAX1(Hmin, H/factor)) C ======= Rejected/Accepted Step ============================ IF ( (ERR.gt.1).and.(H.gt.Hmin) ) THEN IsReject = .true. H = DMIN1(H/10,Hnew) Nreject = Nreject+1 ELSE DO 140 i=1,NVAR Y(i) = Ynew(i) 140 CONTINUE T = Tplus IF (.NOT.IsReject) THEN H = Hnew ! Do not increase stepsize IF previous step was rejected END IF IsReject = .false. Naccept = Naccept+1 END IF C ======= END of the time loop =============================== END DO C ======= Output Information ================================= Info(2) = Nfcn Info(3) = Njac Info(4) = Naccept Info(5) = Nreject RETURN END SUBROUTINE FUNC_CHEM( T, Y, P ) INCLUDE 'KPP_ROOT_params.h' INCLUDE 'KPP_ROOT_global.h' KPP_REAL T, Told KPP_REAL Y(NVAR), P(NVAR) Told = TIME TIME = T CALL Update_SUN() CALL Update_RCONST() CALL Fun( Y, FIX, RCONST, P ) TIME = Told RETURN END SUBROUTINE JAC_CHEM( T, Y, J ) INCLUDE 'KPP_ROOT_params.h' INCLUDE 'KPP_ROOT_global.h' KPP_REAL Told, T KPP_REAL Y(NVAR), J(LU_NONZERO) Told = TIME TIME = T CALL Update_SUN() CALL Update_RCONST() CALL Jac_SP( Y, FIX, RCONST, J ) TIME = Told RETURN END