** **

**1. NAME AND TITLE**

POISSX**: **Poisson Equation on Rectangle with
Various Boundary Conditions.

**2. CONTRIBUTOR**

Institut
fuer Reaktorentwicklung, Karlsruhe, Germany and the National Center for
Atmospheric Research, Boulder, Colorado USA through the OECD Nuclear Energy
Agency Data Bank, Issy-les-Moulineaux, France.

**3. CODING LANGUAGE
AND COMPUTER**

Fortran IV; IBM 370 Series (C00819I037000).

**4. NATURE OF
PROBLEM SOLVED**

POISSX solves the Poisson equation on a rectangle with 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. The main program and the subroutine case provided with POISSX set up 36 cases to test POISSX.

**5. METHOD OF
SOLUTION**

The solution is obtained by cyclic reduction.

**6. RESTRICTIONS OR
LIMITATIONS**

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.

**7. TYPICAL RUNNING
TIME**

For m = 128, n = 33, 0.3 sec. are required on the IBM 370/168.

**8. COMPUTER
HARDWARE REQUIREMENTS**

IBM 370 Series - FORTRAN compiler. The IBM FORTRAN-H extended compiler requires 300 k for translation.

**9. COMPUTER
SOFTWARE REQUIREMENTS**

IBM 370 OS.

**10. REFERENCES**

**a) Included Documentation**

** **None listed.

**b) Background Documentation**

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).

** **

**11. CONTENTS OF CODE
PACKAGE**

The package is distributed on a CD with a compressed zip file including source files, sample data and output.

**12. DATE OF ABSTRACT**

December 2013.

**KEYWORDS**: FINITE
DIFFERENCE METHOD, POISSON EQUATION