Computational Mechanics

, Volume 53, Issue 1, pp 91–99

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

Authors

  • Kenji Takizawa
    • Department of Modern Mechanical Engineering and Waseda Institute for Advanced StudyWaseda University
    • Department of Mechanical EngineeringRice University
Original Paper

DOI: 10.1007/s00466-013-0895-y

Cite this article as:
Takizawa, K. & Tezduyar, T.E. Comput Mech (2014) 53: 91. doi:10.1007/s00466-013-0895-y

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 techniquesContinuous representation in timeSmooth solution in timeNURBS in timeSuccessive projectionDirect computation

Copyright information

© Springer-Verlag Berlin Heidelberg 2013