APL and finite elements for solving convection-diffusion problems, with examples from gas bearing design

ABSTRACT

The increasing popularity of finite element techniques to solve fluid flow problems has been due, in large part, to its geometric flexibility and adaptability. APL shares that property. Therefore, it is a natural companion to finite element modelling. The closeness of control that APL allows during algorithm and program development is especially welcome during the pre-processing stages of the solution of field problems, in particular during grid generation. This leads to very reasonable “door-to-door” solution times, especially for problems that occur in a R&D environment, where a large percentage of the time is spent formulating, changing and maintaining code. Using examples from engineering practice, the adaptability of APL is illustrated in gas bearing design, as applied to magnetic sliders in hard disk files and laser mirror scanners in electrophotographic printers. APL was also used to teach finite element techniques and grid generation. It proved effective in affording a more immediate view of the key steps of finite element modelling, such as assembly of the stiffness matrix, and the effect of node numbering on the bandwidth of the sparse linear system.

REFERENCES

• 1: W.A. Gross et. al., "Fluid Film Lubrication," John Wiley & Sons, New York, 1980.
• 2: Franco P. Preparata , Michael I. Shamos, Computational geometry: an introduction, Springer-Verlag New York, Inc., New York, NY, 1985
• 3: C. Garcia-Suarez, "Use of an Upwinding Scheme for Air Bearing Calculations," ASLE Special Publication SP-19, Am. sot . Lubr. Engrs. 838 Busse Highway, Park Ridge, IL 60068, USA, 1984, pp. 90-96.

INDEX TERMS

Primary Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.8 Partial Differential Equations
          Subjects: Finite element methods

Additional Classification:
  D. Software
  D.3 PROGRAMMING LANGUAGES
      D.3.2 Language Classifications

          Nouns: APL

  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.3 Numerical Linear Algebra
          Subjects: Linear systems (direct and iterative methods)

  I. Computing Methodologies
  I.3 COMPUTER GRAPHICS
      I.3.5 Computational Geometry and Object Modeling
          Subjects: Curve, surface, solid, and object representations

  J. Computer Applications
  J.2 PHYSICAL SCIENCES AND ENGINEERING
      Subjects: Engineering

General Terms:
Algorithms, Languages