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NEA-0488 POISSX.

POISSX, Poisson Equation on Rectangle with Various Boundary Condition

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1. NAME OR DESIGNATION OF PROGRAM:  POISSX.
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2. COMPUTERS
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Program name Package id Status Status date
POISSX NEA-0488/01 Tested 01-FEB-1978

Machines used:

Package ID Orig. computer Test computer
NEA-0488/01 IBM 370 series IBM 370 series
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3. NATURE OF PHYSICAL PROBLEM SOLVED

The subroutine POISSX solves the Poisson equation on a rectangle with either Dirichlet, Neumann or periodic boundary conditions.
More precisely, the program solves the linear equation system which  arises when the differential equation is discretized on a rectangular grid with m inner grid points in the x and n points in the y direction using second order finite difference approximations.  The values of m and n must be larger than one but are otherwise arbitrary. For more details see the references and the comment cards included in POISSX.
The main program and the subroutine case provided with POISSX set up 36 cases to test POISSX.
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4. METHOD OF SOLUTION

The solution is obtained by cyclic reduction; see references.
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5. RESTRICTIONS ON THE COMPLEXITY OF THE PROBLEM
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6. TYPICAL RUNNING TIME

For m = 128, n = 33, 0.3 sec. are required on  the IBM 370/168.
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7. UNUSUAL FEATURES OF THE PROGRAM

N is not restricted to powers of two as the older versions based on cyclic reduction. The Neumann boundary conditions correspond to a staggered grid.
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8. RELATED AND AUXILIARY PROGRAMS

POISSX is an extended version of POISSN described in ref. 1.
The standard test main program uses a subroutine ZEIT to determine the required CPU time. This subroutine is included but not necessarily required.
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9. STATUS
Package ID Status date Status
NEA-0488/01 01-FEB-1978 Tested at NEADB
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10. REFERENCES

- U. Schumann and R.A. Sweet:
  'A Direct Method for the Solution of Poisson's Equation with Neumann Boundary Conditions on a Staggered Grid of Arbitrary Size'      J. Comp. Phys. 20 (1970) 171-182.
- U. Schumann and R.A. Sweet ;
  'Direct Poisson Equation Solver for Potential and Pressure Fields on a Staggered Grid with Obstacles.'
  Lect. Notes in Physics 59 (1976) 398-403 (Proc. of the 5th Int.
  Conf. on Numerical Methods in Fluid Dynamics, Enschede, July
  1976).
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11. MACHINE REQUIREMENTS

FORTRAN compiler. The IBM FORTRAN-H extended compiler requires 300 k for translation.
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12. PROGRAMMING LANGUAGE(S) USED
Package ID Computer language
NEA-0488/01 FORTRAN-IV
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13. OPERATING SYSTEM OR MONITOR UNDER WHICH PROGRAM IS EXECUTED:  Any.
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14. ANY OTHER PROGRAMMING OR OPERATING INFORMATION OR RESTRICTIONS

For some applications underflows are possible which are admitted.
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15. NAME AND ESTABLISHMENT OF AUTHOR

    Dr. Ulrich Schumann
    Kernforschungszentrum Karlsruhe
    Institut fuer Reaktorentwicklung
    Postfach 3640
    D-75 Karlsruhe
    Germany, F.R.

    Dr. Roland A. Sweet
    National Center for Atmospheric Research
    P.O. Box 3000
    Boulder, Colorado 80303
    U.S.A.
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16. MATERIAL AVAILABLE
NEA-0488/01
File name File description Records
NEA0488_01.001 SOURCE PROGRAM F4-EBCDIC 1500
NEA0488_01.002 SUBROUTINES BAL 49
NEA0488_01.003 DEMONSTRATION PROGRAM OUTPUT 234
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17. CATEGORIES
  • P. General Mathematical and Computing System Routines

Keywords: finite difference method, poisson equation.