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354 lines
11 KiB
Fortran
354 lines
11 KiB
Fortran
*DECK POISTG
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SUBROUTINE POISTG (NPEROD, N, MPEROD, M, A, B, C, IDIMY, Y,
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+ IERROR, W)
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C***BEGIN PROLOGUE POISTG
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C***PURPOSE Solve a block tridiagonal system of linear equations
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C that results from a staggered grid finite difference
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C approximation to 2-D elliptic PDE's.
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C***LIBRARY SLATEC (FISHPACK)
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C***CATEGORY I2B4B
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C***TYPE SINGLE PRECISION (POISTG-S)
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C***KEYWORDS ELLIPTIC, FISHPACK, HELMHOLTZ, PDE, TRIDIAGONAL
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C***AUTHOR Adams, J., (NCAR)
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C Swarztrauber, P. N., (NCAR)
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C Sweet, R., (NCAR)
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C***DESCRIPTION
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C
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C Subroutine POISTG solves the linear system of equations
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C
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C A(I)*X(I-1,J) + B(I)*X(I,J) + C(I)*X(I+1,J)
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C + X(I,J-1) - 2.*X(I,J) + X(I,J+1) = Y(I,J)
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C
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C for I=1,2,...,M and J=1,2,...,N.
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C
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C The indices I+1 and I-1 are evaluated modulo M, i.e.
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C X(0,J) = X(M,J) and X(M+1,J) = X(1,J), and X(I,0) may be equal to
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C X(I,1) or -X(I,1) and X(I,N+1) may be equal to X(I,N) or -X(I,N)
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C depending on an input parameter.
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C
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C
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C * * * * * * * * Parameter Description * * * * * * * * * *
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C
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C * * * * * * On Input * * * * * *
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C
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C NPEROD
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C Indicates the values which X(I,0) and X(I,N+1) are assumed
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C to have.
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C = 1 If X(I,0) = -X(I,1) and X(I,N+1) = -X(I,N)
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C = 2 If X(I,0) = -X(I,1) and X(I,N+1) = X(I,N)
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C = 3 If X(I,0) = X(I,1) and X(I,N+1) = X(I,N)
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C = 4 If X(I,0) = X(I,1) and X(I,N+1) = -X(I,N)
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C
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C N
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C The number of unknowns in the J-direction. N must
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C be greater than 2.
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C
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C MPEROD
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C = 0 If A(1) and C(M) are not zero
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C = 1 If A(1) = C(M) = 0
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C
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C M
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C The number of unknowns in the I-direction. M must
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C be greater than 2.
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C
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C A,B,C
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C One-dimensional arrays of length M that specify the coefficients
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C in the linear equations given above. If MPEROD = 0 the array
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C elements must not depend on the index I, but must be constant.
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C Specifically, the subroutine checks the following condition
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C
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C A(I) = C(1)
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C B(I) = B(1)
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C C(I) = C(1)
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C
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C for I = 1, 2, ..., M.
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C
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C IDIMY
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C The row (or first) dimension of the two-dimensional array Y as
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C it appears in the program calling POISTG. This parameter is
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C used to specify the variable dimension of Y. IDIMY must be at
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C least M.
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C
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C Y
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C A two-dimensional array that specifies the values of the
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C right side of the linear system of equations given above.
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C Y must be dimensioned at least M X N.
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C
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C W
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C A one-dimensional work array that must be provided by the user
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C for work space. W may require up to 9M + 4N + M(INT(log2(N)))
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C locations. The actual number of locations used is computed by
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C POISTG and returned in location W(1).
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C
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C
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C * * * * * * On Output * * * * * *
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C
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C Y
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C Contains the solution X.
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C
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C IERROR
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C An error flag that indicates invalid input parameters. Except
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C for number zero, a solution is not attempted.
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C = 0 No error
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C = 1 If M .LE. 2
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C = 2 If N .LE. 2
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C = 3 IDIMY .LT. M
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C = 4 If NPEROD .LT. 1 or NPEROD .GT. 4
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C = 5 If MPEROD .LT. 0 or MPEROD .GT. 1
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C = 6 If MPEROD = 0 and
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C A(I) .NE. C(1) or B(I) .NE. B(1) or C(I) .NE. C(1)
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C for some I = 1, 2, ..., M.
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C = 7 If MPEROD .EQ. 1 .AND. (A(1).NE.0 .OR. C(M).NE.0)
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C
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C W
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C W(1) contains the required length of W.
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C
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C *Long Description:
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C
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C * * * * * * * Program Specifications * * * * * * * * * * * *
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C
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C Dimension of A(M),B(M),C(M),Y(IDIMY,N),
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C Arguments W(see argument list)
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C
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C Latest June 1, 1977
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C Revision
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C
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C Subprograms POISTG,POSTG2,COSGEN,MERGE,TRIX,TRI3,PIMACH
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C Required
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C
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C Special NONE
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C Conditions
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C
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C Common NONE
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C Blocks
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C
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C I/O NONE
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C
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C Precision Single
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C
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C Specialist Roland Sweet
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C
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C Language FORTRAN
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C
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C History Written by Roland Sweet in 1973
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C Revised by Roland Sweet in 1977
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C
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C
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C Space 3297(decimal) = 6341(octal) locations on the
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C Required NCAR Control Data 7600
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C
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C Timing and The execution time T on the NCAR Control Data
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C Accuracy 7600 for subroutine POISTG is roughly proportional
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C to M*N*log2(N). Some typical values are listed
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C in the table below. More comprehensive timing
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C charts may be found in the reference.
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C To measure the accuracy of the algorithm a
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C uniform random number generator was used to create
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C a solution array X for the system given in the
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C 'PURPOSE ' with
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C
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C A(I) = C(I) = -0.5*B(I) = 1, I=1,2,...,M
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C
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C and, when MPEROD = 1
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C
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C A(1) = C(M) = 0
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C B(1) = B(M) =-1.
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C
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C The solution X was substituted into the given sys-
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C tem and, using double precision, a right side Y was
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C computed. Using this array Y subroutine POISTG was
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C called to produce an approximate solution Z. Then
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C the relative error, defined as
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C
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C E = MAX(ABS(Z(I,J)-X(I,J)))/MAX(ABS(X(I,J)))
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C
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C where the two maxima are taken over all I=1,2,...,M
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C and J=1,2,...,N, was computed. The value of E is
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C given in the table below for some typical values of
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C M and N.
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C
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C
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C M (=N) MPEROD NPEROD T(MSECS) E
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C ------ ------ ------ -------- ------
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C
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C 31 0-1 1-4 45 9.E-13
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C 31 1 1 21 4.E-13
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C 31 1 3 41 3.E-13
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C 32 0-1 1-4 51 3.E-12
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C 32 1 1 32 3.E-13
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C 32 1 3 48 1.E-13
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C 33 0-1 1-4 42 1.E-12
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C 33 1 1 30 4.E-13
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C 33 1 3 34 1.E-13
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C 63 0-1 1-4 186 3.E-12
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C 63 1 1 91 1.E-12
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C 63 1 3 173 2.E-13
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C 64 0-1 1-4 209 4.E-12
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C 64 1 1 128 1.E-12
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C 64 1 3 199 6.E-13
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C 65 0-1 1-4 143 2.E-13
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C 65 1 1 160 1.E-11
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C 65 1 3 138 4.E-13
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C
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C Portability American National Standards Institute FORTRAN.
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C The machine dependent constant PI is defined in
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C function PIMACH.
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C
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C Required COS
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C Resident
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C Routines
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C
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C Reference Schumann, U. and R. Sweet,'A Direct Method for
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C the Solution of Poisson's Equation With Neumann
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C Boundary Conditions on a Staggered Grid of
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C Arbitrary Size,' J. Comp. Phys. 20(1976),
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C pp. 171-182.
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C
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C * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
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C
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C***REFERENCES U. Schumann and R. Sweet, A direct method for the
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C solution of Poisson's equation with Neumann boundary
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C conditions on a staggered grid of arbitrary size,
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C Journal of Computational Physics 20, (1976),
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C pp. 171-182.
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C***ROUTINES CALLED POSTG2
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C***REVISION HISTORY (YYMMDD)
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C 801001 DATE WRITTEN
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C 861211 REVISION DATE from Version 3.2
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C 891214 Prologue converted to Version 4.0 format. (BAB)
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C 920501 Reformatted the REFERENCES section. (WRB)
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C***END PROLOGUE POISTG
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C
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C
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DIMENSION Y(IDIMY,*)
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DIMENSION W(*) ,B(*) ,A(*) ,C(*)
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C***FIRST EXECUTABLE STATEMENT POISTG
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IERROR = 0
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IF (M .LE. 2) IERROR = 1
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IF (N .LE. 2) IERROR = 2
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IF (IDIMY .LT. M) IERROR = 3
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IF (NPEROD.LT.1 .OR. NPEROD.GT.4) IERROR = 4
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IF (MPEROD.LT.0 .OR. MPEROD.GT.1) IERROR = 5
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IF (MPEROD .EQ. 1) GO TO 103
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DO 101 I=1,M
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IF (A(I) .NE. C(1)) GO TO 102
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IF (C(I) .NE. C(1)) GO TO 102
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IF (B(I) .NE. B(1)) GO TO 102
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101 CONTINUE
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GO TO 104
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102 IERROR = 6
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RETURN
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103 IF (A(1).NE.0. .OR. C(M).NE.0.) IERROR = 7
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104 IF (IERROR .NE. 0) RETURN
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IWBA = M+1
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IWBB = IWBA+M
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IWBC = IWBB+M
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IWB2 = IWBC+M
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IWB3 = IWB2+M
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IWW1 = IWB3+M
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IWW2 = IWW1+M
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IWW3 = IWW2+M
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IWD = IWW3+M
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IWTCOS = IWD+M
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IWP = IWTCOS+4*N
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DO 106 I=1,M
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K = IWBA+I-1
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W(K) = -A(I)
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K = IWBC+I-1
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W(K) = -C(I)
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K = IWBB+I-1
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W(K) = 2.-B(I)
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DO 105 J=1,N
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Y(I,J) = -Y(I,J)
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105 CONTINUE
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106 CONTINUE
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NP = NPEROD
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MP = MPEROD+1
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GO TO (110,107),MP
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107 CONTINUE
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GO TO (108,108,108,119),NPEROD
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108 CONTINUE
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CALL POSTG2 (NP,N,M,W(IWBA),W(IWBB),W(IWBC),IDIMY,Y,W,W(IWB2),
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1 W(IWB3),W(IWW1),W(IWW2),W(IWW3),W(IWD),W(IWTCOS),
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2 W(IWP))
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IPSTOR = W(IWW1)
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IREV = 2
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IF (NPEROD .EQ. 4) GO TO 120
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109 CONTINUE
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GO TO (123,129),MP
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110 CONTINUE
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C
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C REORDER UNKNOWNS WHEN MP =0
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C
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MH = (M+1)/2
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MHM1 = MH-1
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MODD = 1
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IF (MH*2 .EQ. M) MODD = 2
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DO 115 J=1,N
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DO 111 I=1,MHM1
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MHPI = MH+I
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MHMI = MH-I
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W(I) = Y(MHMI,J)-Y(MHPI,J)
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W(MHPI) = Y(MHMI,J)+Y(MHPI,J)
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111 CONTINUE
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W(MH) = 2.*Y(MH,J)
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GO TO (113,112),MODD
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112 W(M) = 2.*Y(M,J)
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113 CONTINUE
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DO 114 I=1,M
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Y(I,J) = W(I)
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114 CONTINUE
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115 CONTINUE
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K = IWBC+MHM1-1
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I = IWBA+MHM1
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W(K) = 0.
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W(I) = 0.
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W(K+1) = 2.*W(K+1)
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GO TO (116,117),MODD
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116 CONTINUE
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K = IWBB+MHM1-1
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W(K) = W(K)-W(I-1)
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W(IWBC-1) = W(IWBC-1)+W(IWBB-1)
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GO TO 118
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117 W(IWBB-1) = W(K+1)
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118 CONTINUE
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GO TO 107
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119 CONTINUE
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C
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C REVERSE COLUMNS WHEN NPEROD = 4.
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C
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IREV = 1
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NBY2 = N/2
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NP = 2
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120 DO 122 J=1,NBY2
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MSKIP = N+1-J
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DO 121 I=1,M
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A1 = Y(I,J)
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Y(I,J) = Y(I,MSKIP)
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Y(I,MSKIP) = A1
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121 CONTINUE
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122 CONTINUE
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GO TO (108,109),IREV
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123 CONTINUE
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DO 128 J=1,N
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DO 124 I=1,MHM1
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MHMI = MH-I
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MHPI = MH+I
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W(MHMI) = .5*(Y(MHPI,J)+Y(I,J))
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W(MHPI) = .5*(Y(MHPI,J)-Y(I,J))
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124 CONTINUE
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W(MH) = .5*Y(MH,J)
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GO TO (126,125),MODD
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125 W(M) = .5*Y(M,J)
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126 CONTINUE
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DO 127 I=1,M
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Y(I,J) = W(I)
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127 CONTINUE
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128 CONTINUE
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129 CONTINUE
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C
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C RETURN STORAGE REQUIREMENTS FOR W ARRAY.
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C
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W(1) = IPSTOR+IWP-1
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RETURN
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END
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