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C *******************************************************************
C ** THIS FORTRAN CODE IS INTENDED TO ILLUSTRATE POINTS MADE IN **
C ** THE TEXT. TO OUR KNOWLEDGE IT WORKS CORRECTLY. HOWEVER IT IS **
C ** THE RESPONSIBILITY OF THE USER TO TEST IT, IF IT IS USED IN A **
C ** RESEARCH APPLICATION. **
C *******************************************************************
C *******************************************************************
c ** FICHE F.2 **
C ** GEAR 5-VALUE PREDICTOR-CORRECTOR ALGORITHM FOR TRANSLATION. **
C ** **
C ** REFERENCE: **
C ** **
C ** GEAR, NUMERICAL INITIAL VALUE PROBLEMS IN ORDINARY **
C ** DIFFERENTIAL EQUATIONS (PRENTICE-HALL,1971). **
C ** **
C ** SUPPLIED ROUTINES: **
C ** **
C ** SUBROUTINE PREDIC ( DT ) **
C ** PREDICTS THE NEW POSITIONS, VELOCITIES, ETC. **
C ** SUBROUTINE CORREC ( DT, M, K ) **
C ** CORRECTS THE POSITIONS, VELOCITIES ETC. USING GEAR METHOD **
C ** **
C ** PRINCIPAL VARIABLES: **
C ** **
C ** INTEGER N NUMBER OF MOLECULES **
C ** REAL DT TIMESTEP **
C ** REAL RX(N),RY(N),RZ(N) POSITIONS **
C ** REAL VX(N),VY(N),VZ(N) VELOCITIES **
C ** REAL AX(N),AY(N),AZ(N) ACCELERATIONS **
C ** REAL BX(N),BY(N),BZ(N) THIRD DERIVATIVES **
C ** REAL CX(N),CY(N),CZ(N) FOURTH DERIVATIVES **
C ** REAL FX(N),FY(N),FZ(N) FORCES **
C ** **
C ** USAGE: **
C ** **
C ** AT EACH TIMESTEP, CALL PREDIC, FORCE, CORREC IN ORDER **
C ** FOLLOWED BY ACCUMULATION OF THERMODYNAMIC QUANTITIES. **
C ** THE FORCE ROUTINE (NOT SUPPLIED HERE: SEE F.17) CALCULATES **
C ** POTENTIAL ENERGY AND FORCES ON ALL ATOMS. **
C *******************************************************************
SUBROUTINE PREDIC ( DT )
COMMON / BLOCK1 / RX, RY, RZ, VX, VY, VZ, AX, AY, AZ,
: BX, BY, BZ, CX, CY, CZ, FX, FY, FZ
C *******************************************************************
C ** PREDICTOR ROUTINE **
C ** **
C ** IN TIMESTEP-SCALED VARIABLES THE PREDICTOR IS THE PASCAL **
C ** TRIANGLE MATRIX. IN UNSCALED VARIABLES IT IS A TAYLOR SERIES **
C ** **
C ** USAGE: **
C ** **
C ** PREDIC IS CALLED TO ADVANCE THE COORDINATES, VELOCITIES ETC. **
C ** BY ONE TIMESTEP DT, PRIOR TO FORCE EVALUATION. **
C *******************************************************************
INTEGER N
PARAMETER ( N = 108 )
REAL DT
REAL RX(N), RY(N), RZ(N)
REAL VX(N), VY(N), VZ(N)
REAL AX(N), AY(N), AZ(N)
REAL BX(N), BY(N), BZ(N)
REAL CX(N), CY(N), CZ(N)
REAL FX(N), FY(N), FZ(N)
INTEGER I
REAL C1, C2, C3, C4
C *******************************************************************
C1 = DT
C2 = C1 * DT / 2.0
C3 = C2 * DT / 3.0
C4 = C3 * DT / 4.0
DO 100 I = 1, N
RX(I) = RX(I) + C1*VX(I) + C2*AX(I) + C3*BX(I) + C4*CX(I)
RY(I) = RY(I) + C1*VY(I) + C2*AY(I) + C3*BY(I) + C4*CY(I)
RZ(I) = RZ(I) + C1*VZ(I) + C2*AZ(I) + C3*BZ(I) + C4*CZ(I)
VX(I) = VX(I) + C1*AX(I) + C2*BX(I) + C3*CX(I)
VY(I) = VY(I) + C1*AY(I) + C2*BY(I) + C3*CY(I)
VZ(I) = VZ(I) + C1*AZ(I) + C2*BZ(I) + C3*CZ(I)
AX(I) = AX(I) + C1*BX(I) + C2*CX(I)
AY(I) = AY(I) + C1*BY(I) + C2*CY(I)
AZ(I) = AZ(I) + C1*BZ(I) + C2*CZ(I)
BX(I) = BX(I) + C1*CX(I)
BY(I) = BY(I) + C1*CY(I)
BZ(I) = BZ(I) + C1*CZ(I)
100 CONTINUE
RETURN
END
SUBROUTINE CORREC ( DT, M, K )
COMMON / BLOCK1 / RX, RY, RZ, VX, VY, VZ, AX, AY, AZ,
: BX, BY, BZ, CX, CY, CZ, FX, FY, FZ
C *******************************************************************
C ** CORRECTOR ROUTINE **
C ** **
C ** CORRECTS POSITIONS, VELOCITIES ETC. AFTER FORCE EVALUATION. **
C ** IN TIMESTEP-SCALED VARIABLES THE NUMERICAL COEFFICIENTS ARE **
C ** GIVEN BY GEAR (REF ABOVE): 19/120, 3/4, 1, 1/2, 1/12. **
C ** IN UNSCALED FORM THESE MUST BE MULTIPLIED BY FACTORS **
C ** INVOLVING THE TIMESTEP AS SHOWN HERE. **
C ** **
C ** PRINCIPAL VARIABLES: **
C ** **
C ** REAL M ATOMIC MASS **
C ** REAL K KINETIC ENERGY PER ATOM **
C ** REAL GEAR0,GEAR1,GEAR2,GEAR3 GEAR COEFFICIENTS **
C ** **
C ** USAGE: **
C ** **
C ** IT IS ASSUMED THAT INTERMOLECULAR FORCES HAVE BEEN CALCULATED **
C ** AND STORED IN FX,FY,FZ. CORREC SIMPLY APPLIES THE CORRECTOR **
C ** EQUATIONS BASED ON THE DIFFERENCES BETWEEN PREDICTED AND **
C ** EVALUATED ACCELERATIONS. IT ALSO CALCULATES KINETIC ENERGY. **
C *******************************************************************
INTEGER N
PARAMETER ( N = 108)
REAL DT
REAL RX(N), RY(N), RZ(N)
REAL VX(N), VY(N), VZ(N)
REAL AX(N), AY(N), AZ(N)
REAL BX(N), BY(N), BZ(N)
REAL CX(N), CY(N), CZ(N)
REAL FX(N), FY(N), FZ(N)
REAL M, K
INTEGER I
REAL AXI, AYI, AZI
REAL CORRX, CORRY, CORRZ
REAL C1, C2, C3, C4
REAL CR, CV, CB, CC
REAL GEAR0, GEAR1, GEAR3, GEAR4
PARAMETER ( GEAR0 = 19.0 / 120.0, GEAR1 = 3.0 / 4.0,
: GEAR3 = 1.0 / 2.0, GEAR4 = 1.0 / 12.0 )
C *******************************************************************
C1 = DT
C2 = C1 * DT / 2.0
C3 = C2 * DT / 3.0
C4 = C3 * DT / 4.0
CR = GEAR0 * C2
CV = GEAR1 * C2 / C1
CB = GEAR3 * C2 / C3
CC = GEAR4 * C2 / C4
K = 0.0
DO 100 I = 1, N
AXI = FX(I) / M
AYI = FY(I) / M
AZI = FZ(I) / M
CORRX = AXI - AX(I)
CORRY = AYI - AY(I)
CORRZ = AZI - AZ(I)
RX(I) = RX(I) + CR * CORRX
RY(I) = RY(I) + CR * CORRY
RZ(I) = RZ(I) + CR * CORRZ
VX(I) = VX(I) + CV * CORRX
VY(I) = VY(I) + CV * CORRY
VZ(I) = VZ(I) + CV * CORRZ
AX(I) = AXI
AY(I) = AYI
AZ(I) = AZI
BX(I) = BX(I) + CB * CORRX
BY(I) = BY(I) + CB * CORRY
BZ(I) = BZ(I) + CB * CORRZ
CX(I) = CX(I) + CC * CORRX
CY(I) = CY(I) + CC * CORRY
CZ(I) = CZ(I) + CC * CORRZ
K = K + VX(I) ** 2 + VY(I) ** 2 + VZ(I) ** 2
100 CONTINUE
K = 0.5 * M * K
RETURN
END
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