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Computational Mechanics

, Volume 53, Issue 1, pp 91–99 | Cite as

Space–time computation techniques with continuous representation in time (ST-C)

  • Kenji Takizawa
  • Tayfun E. Tezduyar
Original Paper

Abstract

We introduce space–time computation techniques with continuous representation in time (ST-C), using temporal NURBS basis functions. This gives us a temporally smooth, NURBS-based solution, which is desirable in some cases, and a more efficient way of dealing with the computed data. We propose two versions of ST-C. In the first version, the smooth solution is extracted by projection from a solution computed with a different temporal representation, typically a discontinuous one. We use a successive projection technique with a small number of temporal NURBS basis functions at each projection, and therefore the extraction can take place as the solution with discontinuous temporal representation is being computed, without storing a large amount of time-history data. This version is not limited to solutions computed with ST techniques. In the second version, the solution with continuous temporal representation is computed directly by using a small number of temporal NURBS basis functions in the variational formulation associated with each time step.

Keywords

Space–time techniques Continuous representation in time Smooth solution in time NURBS in time Successive projection Direct computation 

Notes

Acknowledgments

This work was supported in part by the Rice–Waseda research agreement (first author). It was also supported in part by ARO Grant W911NF-12-1-0162 (second author).

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Department of Modern Mechanical Engineering and Waseda Institute for Advanced StudyWaseda UniversityTokyoJapan
  2. 2.Department of Mechanical EngineeringRice UniversityHoustonUSA

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