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

Xiangmin Zhou, K. K. Tamma

Research output: Contribution to journalArticlepeer-review

43 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)1738-1790
Number of pages53
JournalInternational Journal for Numerical Methods in Engineering
Volume66
Issue number11
DOIs
StatePublished - Jun 11 2006

Keywords

  • Computational algorithms
  • First and second order systems
  • Solid mechanics
  • Structural dynamics
  • Time integration algorithms
  • Time operators

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