Object-Oriented Software Tools for the Construction of Preconditioners

Article type: Research Article

Authors: Mossberg, Eva | Otto, Kurt | Thuné, Michael

Affiliations: Department of Scientific Computing, Uppsala University, Box 120, SE-751 04 Uppsala, Sweden; E-mail: {evam,kurt,michael}@tdb.uu.se

Abstract: In recent years, there has been considerable progress concerning preconditioned iterative methods for large and sparse systems of equations arising from the discretization of differential equations. Such methods are particularly attractive in the context of high-performance (parallel) computers. However, the implementation of a preconditioner is a nontrivial task. The focus of the present contribution is on a set of object-oriented software tools that support the construction of a family of preconditioners based on fast transforms. By combining objects of different classes, it is possible to conveniently construct any preconditioner within this family. The implementation is made in Fortran 90, and uses the language features for abstract data types. Numerical experiments show that the execution time of programs based on the new tools is comparable to that of corresponding programs where the preconditioner is hardcoded. Moreover, it is demonstrated that both the initial preconditioner construction and subsequent modifications are easily done with our software tools, whereas the same tasks are very cumbersome for a hardcoded program. The new tools are integrated into Cogito, which is a library of object-oriented software tools for finite difference methods on composite grids.

Journal: Scientific Programming, vol. 6, no. 3, pp. 285-295, 1997