SUBROUTINE INTEGRATE( TIN, TOUT ) USE KPP_ROOT_global ! TIN - Start Time KPP_REAL TIN ! TOUT - End Time KPP_REAL TOUT INTEGER INFO(5) EXTERNAL FUNC_CHEM, JAC_CHEM INFO(1) = Autonomous call ROS2(NVAR,TIN,TOUT,STEPMIN,STEPMAX, & STEPMIN,VAR,ATOL,RTOL, & Info,FUNC_CHEM,JAC_CHEM) END SUBROUTINE INTEGRATE SUBROUTINE ROS2(N,T,Tnext,Hmin,Hmax,Hstart, & y,AbsTol,RelTol, & Info,FUNC_CHEM,JAC_CHEM) USE KPP_ROOT_params USE KPP_ROOT_Jacobian_sparsity IMPLICIT NONE ! INPUT ARGUMENTS: ! y = Vector of (NVAR) concentrations, contains the ! initial values on input ! [T, Tnext] = the integration interval ! Hmin, Hmax = lower and upper bounds for the selected step-size. ! Note that for Step = Hmin the current computed ! solution is unconditionally accepted by the error ! control mechanism. ! AbsTol, RelTol = (NVAR) dimensional vectors of ! componentwise absolute and relative tolerances. ! FUNC_CHEM = name of routine of derivatives. KPP syntax. ! See the header below. ! JAC_CHEM = name of routine that computes the Jacobian, in ! sparse format. KPP syntax. See the header below. ! Info(1) = 1 for autonomous system ! = 0 for nonautonomous system ! Info(2) = 1 for third order embedded formula ! = 0 for first order embedded formula ! ! Note: Stage 3 used to build strongly A-stable order 3 formula for error control ! Embed3 = (Info(2).EQ.1) ! if Embed3 = .true. then the third order embedded formula is used ! .false. then a first order embedded formula is used ! ! ! OUTPUT ARGUMENTS: ! y = the values of concentrations at Tend. ! T = equals Tend on output. ! Info(2) = # of FUNC_CHEM calls. ! Info(3) = # of JAC_CHEM calls. ! Info(4) = # of accepted steps. ! 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, 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 ! 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 ! 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) 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) ! === Starting the time loop === 10 CONTINUE Tplus = T + H if ( Tplus .gt. Tnext ) then H = Tnext - T Tplus = Tnext end if call JAC_CHEM(NVAR, T, y, JAC) Njac = Njac+1 ghinv = -1.0d0/(gamma*H) DO j=1,NVAR JAC(LU_DIAG(j)) = JAC(LU_DIAG(j)) + ghinv END DO 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(NVAR, T, y, F1) ! ====== NONAUTONOMOUS CASE =============== IF (.not. Autonomous) THEN tau = dsign(dround*dmax1( 1.0d-6, dabs(T) ), T) call FUNC_CHEM(NVAR, T+tau, y, K2) nfcn=nfcn+1 DO j = 1,NVAR DFDT(j) = ( K2(j)-F1(j) )/tau END DO END IF ! .NOT.Autonomous ! ----- STAGE 1 ----- DO j = 1,NVAR K1(j) = F1(j) END DO IF (.NOT.Autonomous) THEN delta = gamma*H DO j = 1,NVAR K1(j) = K1(j) + delta*DFDT(j) END DO END IF ! .NOT.Autonomous call KppSolve (JAC, K1) ! ----- STAGE 2 ----- DO j = 1,NVAR ynew(j) = y(j) + a21*K1(j) END DO call FUNC_CHEM(NVAR, T+H, ynew, F1) nfcn=nfcn+1 beta = 2.d0/(gamma*H) DO j = 1,NVAR K2(j) = F1(j) + beta*K1(j) END DO IF (.NOT. Autonomous) THEN delta = -gamma*H DO j = 1,NVAR K2(j) = K2(j) + delta*DFDT(j) END DO END IF ! .NOT.Autonomous call KppSolve (JAC, K2) ! ----- STAGE 3 ----- IF (Embed3) THEN beta1 = -c31/H beta2 = -c32/H delta = gamma3*H DO j = 1,NVAR K3(j) = F1(j) + beta1*K1(j) + beta2*K2(j) END DO IF (.NOT.Autonomous) THEN DO j = 1,NVAR K3(j) = K3(j) + delta*DFDT(j) END DO END IF ! .NOT.Autonomous CALL KppSolve (JAC, K3) END IF ! Embed3 ! ---- The Solution --- DO j = 1,NVAR ynew(j) = y(j) + m1*K1(j) + m2*K2(j) END DO ! ====== Error estimation ======== ERR=0.d0 DO 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 END DO ERR = DMAX1( uround, DSQRT( ERR/NVAR ) ) ! ======= 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)) ! ======= Rejected/Accepted Step ============================ IF ( (ERR.gt.1).and.(H.gt.Hmin) ) THEN IsReject = .true. H = DMIN1(H/10,Hnew) Nreject = Nreject+1 ELSE DO i=1,NVAR y(i) = ynew(i) END DO 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 ! ======= End of the time loop =============================== IF ( T .lt. Tnext ) GO TO 10 ! ======= Output Information ================================= Info(2) = Nfcn Info(3) = Njac Info(4) = Naccept Info(5) = Nreject END SUBROUTINE Ros2 SUBROUTINE FUNC_CHEM(N, T, Y, P) USE KPP_ROOT_global INTEGER N 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 END SUBROUTINE FUNC_CHEM SUBROUTINE JAC_CHEM(N, T, Y, J) USE KPP_ROOT_global INTEGER N 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 END SUBROUTINE JAC_CHEM