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 INFO(1) = Autonomous CALL RODAS3(NVAR,TIN,TOUT,STEPMIN,STEPMAX,STEPMIN, + VAR,ATOL,RTOL, + Info,FUNC_CHEM,JAC_CHEM) RETURN END SUBROUTINE RODAS3(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 Stiffly accurate Rosenbrock 3(2), with C stiffly accurate embedded formula for error control. C C All the arguments aggree with the KPP syntax. C 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 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. C C Adrian Sandu, March 1996 C The Center for Global and Regional Environmental Research KPP_REAL K1(NVAR), K2(NVAR), K3(NVAR), K4(NVAR) KPP_REAL F1(NVAR), JAC(LU_NONZERO) 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 c43, tau, x1, x2, ytol, elo INTEGER n,nfcn,njac,Naccept,Nreject,i,j,ier INTEGER Info(5) LOGICAL IsReject,Autonomous EXTERNAL FUNC_CHEM, JAC_CHEM c Initialization of counters, etc. Autonomous = Info(1) .EQ. 1 uround = 1.d-15 c43 = - 8.d0/3.d0 H = DMAX1(1.d-8, Hstart) Hmin = DMAX1(Hmin,uround*(Tnext-T)) Hmax = DMIN1(Hmax,Tnext-T) Tplus = T IsReject = .false. Naccept = 0 Nreject = 0 Nfcn = 0 Njac = 0 C === 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 = -2.0d0/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(NVAR, T, y, F1) C ====== NONAUTONOMOUS CASE =============== IF (.not. Autonomous) THEN tau = DSQRT( uround*DMAX1( 1.0d-5, DABS(T) ) ) CALL FUNC_CHEM(NVAR, T+tau, y, K2) nfcn=nfcn+1 do 30 j = 1,NVAR K3(j) = ( K2(j)-F1(j) )/tau 30 continue C ----- STAGE 1 (NONAUTONOMOUS) ----- x1 = 0.5*H do 40 j = 1,NVAR K1(j) = F1(j) + x1*K3(j) 40 continue CALL KppSolve (JAC, K1) C ----- STAGE 2 (NONAUTONOMOUS) ----- x1 = 4.d0/H x2 = 1.5d0*H do 50 j = 1,NVAR K2(j) = F1(j) - x1*K1(j) + x2*K3(j) 50 continue CALL KppSolve (JAC, K2) C ====== AUTONOMOUS CASE =============== ELSE C ----- STAGE 1 (AUTONOMOUS) ----- do 60 j = 1,NVAR K1(j) = F1(j) 60 continue CALL KppSolve (JAC, K1) C ----- STAGE 2 (AUTONOMOUS) ----- x1 = 4.d0/H do 70 j = 1,NVAR K2(j) = F1(j) - x1*K1(j) 70 continue CALL KppSolve (JAC, K2) END IF C ----- STAGE 3 ----- do 80 j = 1,NVAR ynew(j) = y(j) - 2.0d0*K1(j) 80 continue CALL FUNC_CHEM(NVAR, T+H, ynew, F1) nfcn=nfcn+1 do 90 j = 1,NVAR K3(j) = F1(j) + ( -K1(j) + K2(j) )/H 90 continue CALL KppSolve (JAC, K3) C ----- STAGE 4 ----- do 100 j = 1,NVAR ynew(j) = y(j) - 2.0d0*K1(j) - K3(j) 100 continue CALL FUNC_CHEM(NVAR, T+H, ynew, F1) nfcn=nfcn+1 do 110 j = 1,NVAR K4(j) = F1(j) + ( -K1(j) + K2(j) - C43*K3(j) )/H 110 continue CALL KppSolve (JAC, K4) C ---- The Solution --- do 120 j = 1,NVAR ynew(j) = y(j) - 2.0d0*K1(j) - K3(j) - K4(j) 120 continue C ====== Error estimation ======== ERR=0.d0 do 130 i=1,NVAR ytol = AbsTol(i) + RelTol(i)*DABS(ynew(i)) ERR = ERR + ( K4(i)/ytol )**2 130 continue ERR = DMAX1( uround, DSQRT( ERR/NVAR ) ) C ======= Choose the stepsize =============================== elo = 3.0D0 ! estimator local order 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 previos step was rejected END IF IsReject = .false. Naccept = Naccept+1 END IF C ======= End of the time loop =============================== if ( T .lt. Tnext ) go to 10 C ======= Output Information ================================= Info(2) = Nfcn Info(3) = Njac Info(4) = Naccept Info(5) = Nreject Hstart = H RETURN END SUBROUTINE FUNC_CHEM(N, T, Y, P) INCLUDE 'KPP_ROOT_params.h' INCLUDE 'KPP_ROOT_global.h' 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 RETURN END SUBROUTINE JAC_CHEM(N, T, Y, J) INCLUDE 'KPP_ROOT_params.h' INCLUDE 'KPP_ROOT_global.h' 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 RETURN END