Algorithms by design with illustrations to solid and structural mechanics/dynamics

• Published in: International journal for numerical methods in engineering Vol. 66; no. 11; pp. 1738 - 1790
• Main Authors: Zhou, X., Tamma, K. K.
• Format: Journal Article
• Language: English
• Published: Chichester, UK John Wiley & Sons, Ltd 11.06.2006; Wiley
• Subjects: Algorithms; Applied sciences; Computation; computational algorithms; Computational techniques; Dynamics; Education; Exact sciences and technology; Exposure; first and second order systems; Fundamental areas of phenomenology (including applications); Illustrations; INT; Mathematical methods in physics; Mechanical engineering. Machine design; Physics; Solid mechanics; Structural and continuum mechanics; structural dynamics; Tasks; time integration algorithms; time operators; Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...); Measurement; time integration algorithms; Numerical integration; Vibration; first and second order systems; Algorithmics; computational algorithms; Modeling; Engineering design; Design process; solid mechanics; Time domain method; structural dynamics; time operators; Structural analysis
• ISSN: 0029-5981; 1097-0207
• DOI: 10.1002/nme.1559

A novel procedure, concepts, and new ideas to tailor and design time operators under the notion of algorithms by design is formulated in this exposition with emphasis on applications to the broad area of computational mechanics, but with focus on solid and structural mechanics/dynamics as an illustration. The algorithms by design concepts capitalize upon: (i) the recently developed unified theory underlying computational algorithms (Int. J. Numer. Meth. Engng 2004; 59:597–668), and (ii) newly established design spaces and algorithmic measures for evaluating the quality of computational algorithms (Int. J. Numer. Meth. Engng 2005; 64:1841–1870). As a step in the forward direction, in this exposition we embark upon some challenging tasks with the objective to advance, tailor, and foster the design of computational algorithms for time‐dependent problems with desired and/or improved algorithmic attributes in the sense of accuracy, stability and other characteristics including algorithmic complexity in a well educated manner. The design process for computational algorithms is explained in the sense of the algorithms by design concepts via selected numerical illustrations of practical scenarios encountered in solid and structural mechanics/dynamics applications. Copyright © 2006 John Wiley & Sons, Ltd.