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

  • Authors:

  • Kenji Takizawa;Tayfun E. Tezduyar

  • Affiliations:

  • Department of Modern Mechanical Engineering and Waseda Institute for Advanced Study, Waseda University, Tokyo, Japan 169-8050;Department of Mechanical Engineering, Rice University, Houston, USA 77005

  • Venue:
  • Computational Mechanics
  • Year:
  • 2014

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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.