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Element-Wise Mixed Implicit-Explicit Integration for Stable Dynamic Simulation of Deformable Objects

Basil Fierz, Jonas Spillmann, Matthias Harders
Procedings of the Symposium on Computer Animation


In order to evolve a deformable object in time, the underlying equations of motion have to be numerically integrated. This is commonly done by employing either an explicit or an implicit integration scheme. While explicit methods are only stable for small time steps, implicit methods are unconditionally stable. In this paper, we present a novel methodology to combine explicit and implicit linear integration approaches, based on element-wise stability considerations. First, we detect the ill-shaped simulation elements which hinder the stable explicit integration of the element nodes as a pre-computation step. These nodes are then simulated implicitly, while the remaining parts of the mesh are explicitly integrated. As a consequence, larger integration time steps than in purely explicit methods are possible, while the computation time per step is smaller than in purely implicit integration. During modifications such as cutting or fracturing, only newly created or modified elements need to be reevaluated, thus making the technique usable in real-time simulations. In addition, our method reduces problems due to numerical dissipation.

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  author = {Basil Fierz and Jonas Spillmann and Matthias Harders},
  title = {Element-Wise Mixed Implicit-Explicit Integration for Stable Dynamic Simulation of Deformable Objects},
  booktitle = {Procedings of the Symposium on Computer Animation},
  year = {2011},
  pages = {257–266},
  keywords = {Computer Graphics, Three-Dimensional Graphics and Realism, Animation}