Software considerations for the “black box” solver FIDISOL for partial differential equations

ABSTRACT

FIDISOL is a program package for the solution of nonlinear systems of two-dimensional and three-dimensional elliptic and parabolic partial differential equations (PDEs) with nonlinear boundary conditions (BCs) on the boundaries of a rectangular domain. A finite difference method (FDM) with an arbitrary grid and arbitrary consistency order is used, these are either prescribed by the user or are self-adapted for a given relative tolerance. FIDISOL has been designed to be fully vectorizable on vector computers. In this paper we discuss several problems from the viewpoint of software development and user interface, for example, how to deliver the PDEs and BCs to FIDISOL and how to allow a flexible use by a suitable parameter list.

REFERENCES

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INDEX TERMS

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

Additional Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.8 Partial Differential Equations
          Subjects: Parabolic equations; Elliptic equations
  G.4 MATHEMATICAL SOFTWARE

      Nouns: FIDOSOL

General Terms:
Algorithms, Design