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