NEA-0488 POISSX.

POISSX, Poisson Equation on Rectangle with Various Boundary Condition

NAME OR DESIGNATION OF PROGRAM, COMPUTER, NATURE OF PHYSICAL PROBLEM SOLVED, METHOD OF SOLUTION, RESTRICTIONS, TYPICAL RUNNING TIME, UNUSUAL FEATURES OF THE PROGRAM, RELATED AND AUXILIARY PROGRAMS, STATUS, REFERENCES, MACHINE REQUIREMENTS, LANGUAGE, OPERATING SYSTEM OR MONITOR UNDER WHICH PROGRAM IS EXECUTED, ANY OTHER PROGRAMMING OR OPERATING INFORMATION OR RESTRICTIONS, NAME AND ESTABLISHMENT OF AUTHOR, MATERIAL, CATEGORIES

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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.