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Application of Gröbner bases and quantifier elimination for insightful engineering design

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  • Sawada, Hiroyuki
  • Yan, Xiu-Tian

Abstract

Engineering design is a process of generating a design solution satisfying customers’ various requirements. As the design proceeds, more and more parameters are introduced to define the design solution. As more design parameters come into design consideration, designers face increasing difficulties in gaining insights into the relationships among these parameters. This research aims at overcoming the above difficulties by applying techniques of Gröbner basis (GB) and quantifier elimination (QE). The new constraint-solving methods derived from these techniques help designers in gaining important insights during engineering design. These constraint-solving methods have been evaluated through case studies of multidisciplinary engineering design. The evaluation results have illustrated these constraint-solving methods are useful for gaining insights that help designers in making informed design decisions.

Suggested Citation

  • Sawada, Hiroyuki & Yan, Xiu-Tian, 2004. "Application of Gröbner bases and quantifier elimination for insightful engineering design," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 67(1), pages 135-148.
    • Handle: RePEc:eee:matcom:v:67:y:2004:i:1:p:135-148
    DOI: 10.1016/j.matcom.2004.05.014
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    References listed on IDEAS

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    1. Sundaram,Rangarajan K., 1996. "A First Course in Optimization Theory," Cambridge Books, Cambridge University Press, number 9780521497190.
    2. Unknown, 1997. "Newsletter Spring 1997," Institute on Global Conflict and Cooperation, Working Paper Series qt9gw5x4mw, Institute on Global Conflict and Cooperation, University of California.
    3. Unknown, 1996. "Newsletter Spring 1996," Institute on Global Conflict and Cooperation, Working Paper Series qt0kg7492b, Institute on Global Conflict and Cooperation, University of California.
    4. Sundaram,Rangarajan K., 1996. "A First Course in Optimization Theory," Cambridge Books, Cambridge University Press, number 9780521497701.
    5. Unknown, 1993. "Newsletter Spring 1993," Institute on Global Conflict and Cooperation, Working Paper Series qt6zc5m57p, Institute on Global Conflict and Cooperation, University of California.
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    Cited by:

    1. Wester, Michael J. & Yaacob, Yuzita & Steinberg, Stanly, 2011. "Computing integrals over polynomially defined regions and their boundaries in 2 and 3 dimensions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 82(1), pages 79-101.

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