Dr. Nicola Botta, Cezar Ionescu
Potsdam Institute for Climate Impact Research (PIK)
Software components for relation-based distributed computations Abstract: Descriptions of numerical methods for scientific computing are often based on a few commonly accepted abstraction, like for instance that of a 'domain', of a 'grid', of a 'sparse matrix' or of a finite function space.
Often, such descriptions are very "generic": they describe algorithms which, "in principle", do not depend on, for instance, whether the actual 'grid elements' are two- or three-dimensional bodies or on their shape.
Such descriptions allow one to reason about algorithms by abstracting away details which are understood to be features not of the algorithm itself but of the specific context in which the algorithm might be applied or of the computing architecture.
In a specific context, of course, it does matter whether the coordinates of grid points are given in a Cartesian or in a spherical coordinate system, whether a particular grid covers a plane or a curved domain or whether a computation is done on a parallel distributed architecture or on a single CPU machine.
Mapping "generic" description of numerical methods into "generic" software components has turned out to be extremely difficult. This is particularly true in scientific computing where "overspecification" -- the failure to account for a context dependent variability, e.g., the kind of coordinate system -- may prevent the usage of existing software in a specific application domain -- e.g., climate research. In scientific computing, the reuse of software for parallel computations out of its specific development context has been very rare and / or very inefficient.
In our presentation, we consider two typical descriptions of numerical methods for scientific computing. We argue that some of the above mentioned abstractions -- in particular that of a "grid" -- are not suitable for building the core of reusable software components for parallel computations.
We propose a framework for SPMD distributed computations of grid algorithms which is based on simpler abstractions: finite relations between integer intervals and relation-based algorithms.
We discuss a formalism for specifying standard problems that arise when dealing with distributed representations of finite relations and distributed computation of relation-based algorithms.
For one specific problem, we derive a solution algorithm in the proposed formalism. We discuss how this algorithm can be implemented with a small set of c++ data structures.
| Zeit: | Freitag, 1. Juli, 2005, 14.15 (Kaffee/Tee um 15.30 p.m.) |
| Ort: | FU Berlin, Arnimallee 2-6, Raum 032 im EG |