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

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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.

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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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Authors and Affiliations

  1. Department of Modern Mechanical Engineering and Waseda Institute for Advanced Study, Waseda University, 1-6-1 Nishi-Waseda, Shinjuku-ku, Tokyo, 169-8050, Japan

    Kenji Takizawa

  2. Department of Mechanical Engineering, Rice University, MS 321, 6100 Main Street, Houston, TX, 77005, USA

    Tayfun E. Tezduyar

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  1. Kenji Takizawa
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  2. Tayfun E. Tezduyar
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Takizawa, K., Tezduyar, T.E. Space–time computation techniques with continuous representation in time (ST-C). Comput Mech 53, 91–99 (2014). https://doi.org/10.1007/s00466-013-0895-y

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