### 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 language | English |
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Article number | 8 |

Journal | ACM Transactions on Graphics |

Volume | 28 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jan 1 2009 |

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### All Science Journal Classification (ASJC) codes

- Computer Graphics and Computer-Aided Design

### Cite this

*ACM Transactions on Graphics*,

*28*(1), [8]. https://doi.org/10.1145/1477926.1477934

**An edge-based computationally efficient formulation of Saint Venant-Kirchhoff tetrahedral finite elements.** / Kikuuwe, Ryo; Tabuchi, Hiroaki; Yamamoto, Motoji.

Research output: Contribution to journal › Article

*ACM Transactions on Graphics*, vol. 28, no. 1, 8. https://doi.org/10.1145/1477926.1477934

}

TY - JOUR

T1 - An edge-based computationally efficient formulation of Saint Venant-Kirchhoff tetrahedral finite elements

AU - Kikuuwe, Ryo

AU - Tabuchi, Hiroaki

AU - Yamamoto, Motoji

PY - 2009/1/1

Y1 - 2009/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=60349089176&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=60349089176&partnerID=8YFLogxK

U2 - 10.1145/1477926.1477934

DO - 10.1145/1477926.1477934

M3 - Article

AN - SCOPUS:60349089176

VL - 28

JO - ACM Transactions on Graphics

JF - ACM Transactions on Graphics

SN - 0730-0301

IS - 1

M1 - 8

ER -