An edge-based computationally efficient formulation of Saint Venant-Kirchhoff tetrahedral finite elements

Ryo Kikuuwe, Hiroaki Tabuchi, Motoji Yamamoto

Research output: Contribution to journalArticlepeer-review

33 Citations (Scopus)

Abstract

This article describes a computationally efficient formulation and an algorithm for tetrahedral finite-element simulation of elastic objects subject to Saint Venant-Kirchhoff (StVK) material law. The number of floating point operations required by the algorithm is in the range of 15% to 27% for computing the vertex forces from a given set of vertex positions, and 27% to 38% for the tangent stiffness matrix, in comparison to a well-optimized algorithm directly derived from the conventional Total Lagrangian formulation. In the new algorithm, the data is associated with edges and tetrahedron-sharing edge-pairs (TSEPs), as opposed to tetrahedra, to avoid redundant computation. Another characteristic of the presented formulation is that it reduces to that of a spring-network model by simply ignoring all the TSEPs. The technique is demonstrated through an interactive application involving haptic interaction, being combined with a linearized implicit integration technique employing a preconditioned conjugate gradient method.

Original languageEnglish
Article number8
JournalACM Transactions on Graphics
Volume28
Issue number1
DOIs
Publication statusPublished - Jan 1 2009

All Science Journal Classification (ASJC) codes

  • Computer Graphics and Computer-Aided Design

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