Article: On the Role of Mathematical Abstractions for Scientific Computing
Authors: Krister Åhlander , Magne Haveraaen , Hans Munthe-Kaas
Journal: The architecture of scientific software (Boisvert and Tang eds.), Kluwer acad. publ. (2001), pp. 145-159.
Abstract: A distinguished feature of scientific computing is the necessity to design software abstractions for approximations. The approximations are themselves abstractions of mathematical models, which also are abstractions. In this paper, the relation between different mathematical abstraction levels and scientific computing software is discussed, in particular with respect to the simulation of partial differential equations (PDEs). It is found that software based on continuous abstractions have more chances of being modular, than software based on discrete approximations of the continuous abstractions. Moreover, it is stated that coordinate-free abstractions are a solid foundation for the simulation of PDEs.
Hindsight notes: None yet.
12 Jul 2000