Often scientists need to locate appropriate software for their problems and then select from among many alternatives. We have previously proposed an approach for dealing with this task by processing performance data of the targeted software. This approach has been tested using a customized implementation referred to as PYTHIA. This experience made us realize the complexity of the algorithmic discovery of knowledge from performance data and of the management of these data together with the discovered knowledge. To address this issue, we created PYTHIA-II-a modular framework and system which combines a general knowledge discovery in databases (KDD) methodology and recommender system technologies to provide advice about scientific software/hardware artifacts. The functionality and effectiveness of the system is demonstrated for two existing performance studies using sets of software for solving partial differential equations. From the end-user perspective, PYTHIA-II allows users to specify the problem to be solved and their computational objectives. In turn, PYTHIA-II (i) selects the software available for the user's problem, (ii) suggests parameter values, and (iii) assesses the recommendation provided. PYTHIA-II provides all the necessary facilities to set up database schemas for testing suites and associated performance data in order to test sets of software. Moreover, it allows easy interfacing of alternative data mining and recommendation facilities. PYTHIA-II is an open-ended system implemented on public domain software and
We consider the collocation method for linear, second-order elliptic problems on rectangular and general two-dimensionaldomains. An overview of the method is given for general domains, followed by a discussion of the improved efficiencies and simplifications possible for rectangular domains. A very-high-level description is given of three specific collocation algorithms that use Hermite bicubic basic functions, (1) GENCOL (collocation on general two-dimensional domains), (2) HERMCOL (collocation on rectangular domains with general linear boundary conditions), and (3) INTCOL (collocation on rectangular domains with uncoupled boundary conditions). The linear system resulting from INTCOL has half the bandwidth of that from HERMCOL, which provides substantial benefit in solving the system. We provide some examples showing the range of applicability of the algorithms and some performance profiles illustrating their efficiency. Fortran implementations of these algorithms are given in the companion papers [lo, 111.
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