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Mathematical Fidelity and Open Source Libraries for Large Scale Simulation and Optimization
- Publisher: European Association of Geoscientists & Engineers
- Source: Conference Proceedings, 78th EAGE Conference and Exhibition 2016, May 2016, Volume 2016, p.1 - 5
Abstract
Optimization algorithms used to solve inverse problems in geoscience have abstract mathematical descriptions – many of them (Conjugate Gradient iteration, Newton’s method,…) are so–called matrix free algorithms, that is, they manipulate their mathematical objects (vectors, functions) without reference to their internal details. Similarly, time-stepping algorithms for dynamical simulation may be described in terms of update rules for dynamical states, without reference to the internal structure of these states or the precise action of the rules. Both of these algorithmic settings provide opportunities for creation of reusable open source code bases, applying to many different tasks. Not only do such libraries save programmer effort and reduce the incidence of errors, but also they could potentially make possible comparison of inversion techniques by providing common implementations for common components. This paper lays out some examples of features that computational types should inherit from their mathematical models, and some solutions to the programming problems that arise in implementing such types.