Real-time error estimation and adaptivity

https://arxiv.org/submit/1687902
Title: Real-time error controlled adaptive mesh refinement: Application to
  needle insertion simulation

Authors: Huu Phuoc Bui (1 and 2), Satyendra Tomar (2), R\’emi Bessard-Duparc

  (3), Hadrien Courtecuisse (1), St\’ephane Cotin (3), St\’ephane Bordas (2 and

  4) ((1) University of Strasbourg, CNRS, ICube, Strasbourg, France, (2)

  University of Luxembourg, Luxembourg, (3) Inria Nancy Grand Est,

  Villers-les-Nancy, France, (4) Cardiff University, Wales, UK)

Categories: cs.NA

Comments: 20 pages, 15 figures

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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  This paper presents the first real-time discretization-error-driven adaptive

finite element approach for corotational elasticity problems involving strain

localization. We propose a hexahedron-based finite element method, combined

with a posteriori error estimation driven local h-refinement, for simulating

soft tissue deformation. This enables to control the local error and global

error level in the mechanical fields (e.g. displacement or gradient) during the

simulation. The local error level is used to refine the mesh only where it is

needed, while maintaining a coarser mesh elsewhere. We investigate the

convergence of the algorithm on academic examples, and demonstrate its

practical usability on a percutaneous procedure involving needle insertion in a

liver. For the latter case, we compare the force displacement curves obtained

from the proposed adaptive algorithm with that obtained from a uniform

refinement approach.

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