Algorithms for computing symbolic representations of basic e-sums and their application to composites. (May 2016)

• Record Type: Journal Article
• Authors: Nawalaniec, Wojciech
• Is Part Of: Journal of symbolic computation. Volume 74(2016)
• Page Start: 328
• Page End: 345
• Publication Date: 2016-05
• Subjects: Computer algebra -- Symbol manipulation -- Symbolic computations -- Basic sums -- Effective conductivity -- Optimal packing problem; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2015.08.001
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: The main goal of the paper is to present an algorithm to realize the theoretical method byBerlyand and Mityushev (2001, 2005) for computations of the effective conductivity of fibrous composites expressed in therms of the linear combinations of the basic e -sums. Algorithms are presented in Mathematical Pseudo-language with examples in Mathematica ® . A method for simplifying the basic e -sums by reducing mirror terms is presented. Developed algorithms are applied to the optimal packing problem of disks in the plane.