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Polyhedral Finite Elements Using Harmonic Basis Functions

Finite element simulations in computer graphics are typically based on tetrahedral or hexahedral elements, which enables simple and efficient implementations, but in turn requires complicated remeshing in case of topological changes or adaptive refinement. We propose a flexible finite element method for arbitrary polyhedral elements, thereby effectively avoiding the need for remeshing. Our polyhedral finite elements are based on harmonic basis functions, which satisfy all necessary conditions for FEM simulations and seamlessly generalize both linear tetrahedral and trilinear hexahedral elements. We discretize harmonic basis functions using the method of fundamental solutions, which enables their flexible computation and efficient evaluation. The versatility of our approach is demonstrated on cutting and adaptive refinement within a simulation framework for corotated linear elasticity.

Polyhedral Finite Elements Using Harmonic Basis Functions

Posted by christopherbatty on June 5th, 2008 Posted in Deformables, Fracture

2 Comments

  1. maantas says:
    August 23, 2008 at 4:45 am

    hei, i am sure u have already read thuse papers, but just in case not – might be interesting for you:
    http://3dideas.wordpress.com/2008/05/07/32-fracture-formation-in-growing-surfaces/
    andhttp://3dideas.wordpress.com/2008/05/07/3-dimensional-tree-generation-research-and-further-development-bark-synthesis/
    look at the picture descriptions u will find othor names ant so on,
    all the best to u.
    btw i think our blogs are a bit similar, but u describe things more from scientifick view and me more from “art’istick” 🙂
    m.

  2. maantas says:
    August 23, 2008 at 4:47 am

    dono why second link doesnt posted so well
    trying again:
    http://3dideas.wordpress.com/2008/05/
    07/3-dimensional-tree-generation-research-and-further-development-bark-synthesis/

    just ignor “enter” in a midle of link

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