Designing a Flexible Software Tool for RBF Approximations Applied to PDEs

Abstract:

This paper aims at addressing how to design a flexible software for RBF-based numerical solution of partial differential equations (PDEs). In the process, object-oriented analysis and design (OOAD) approach combined with feature modeling, is adopted to construct object models of PDE solvers. This project was mplemented in Fortran 90, emulating object oriented constructs by encapsulating particular data structures and subroutines in modules to represent classes.

The separation of mathematical domains and numerical domains as well as the introduction of the workflow manager and operations gives a significant flexibility and extendability for the software. For illustration, a solver for Dam seepage problem is constructed with the new design, compared with the one by the pre-existing reference code.