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/

\\

  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.

\\

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/

\\

  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.

\\

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/

\\

  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.

\\

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/

\\

  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.

\\

Isogeometric finite element analysis of time-harmonic exterior acoustic scattering problems

New paper with Tahsin Khajah and Xavier Antoine. 

https://arxiv.org/abs/1610.01694

Isogeometric finite element analysis of time-harmonic exterior acoustic scattering problems

Tahsin Khajah, Xavier Antoine, Stéphane P.A. Bordas

(Submitted on 6 Oct 2016)

We present an isogeometric analysis of time-harmonic exterior acoustic problems. The infinite space is truncated by a fictitious boundary and (simple) absorbing boundary conditions are applied. The truncation error is included in the exact solution so that the reported error is an indicator of the performance of the isogeometric analysis, in particular of the related pollution error. Numerical results performed with high-order basis functions (third or fourth orders) showed no visible pollution error even for very high frequencies. This property combined with exact geometrical representation makes isogeometric analysis a very promising platform to solve high-frequency acoustic problems.

Subjects: Computational Physics (physics.comp-ph); Numerical Analysis (cs.NA); Numerical Analysis (math.NA)

Cite as: arXiv:1610.01694 [physics.comp-ph]

  (or arXiv:1610.01694v1 [physics.comp-ph] for this version)

Submission history

From: Tahsin Khajah [view email] 

Isogeometric finite element analysis of time-harmonic exterior acoustic scattering problems

New paper with Tahsin Khajah and Xavier Antoine. 

https://arxiv.org/abs/1610.01694

Isogeometric finite element analysis of time-harmonic exterior acoustic scattering problems

Tahsin Khajah, Xavier Antoine, Stéphane P.A. Bordas

(Submitted on 6 Oct 2016)

We present an isogeometric analysis of time-harmonic exterior acoustic problems. The infinite space is truncated by a fictitious boundary and (simple) absorbing boundary conditions are applied. The truncation error is included in the exact solution so that the reported error is an indicator of the performance of the isogeometric analysis, in particular of the related pollution error. Numerical results performed with high-order basis functions (third or fourth orders) showed no visible pollution error even for very high frequencies. This property combined with exact geometrical representation makes isogeometric analysis a very promising platform to solve high-frequency acoustic problems.

Subjects: Computational Physics (physics.comp-ph); Numerical Analysis (cs.NA); Numerical Analysis (math.NA)

Cite as: arXiv:1610.01694 [physics.comp-ph]

  (or arXiv:1610.01694v1 [physics.comp-ph] for this version)

Submission history

From: Tahsin Khajah [view email] 

University of Luxembourg now 86th in Europe and 178th in the World

https://www.timeshighereducation.com/world-university-rankings/university-luxembourg?ranking-dataset=589595

The University of Luxembourg embodies the idea of a European research university, with our dynamism resulting from the pioneering spirit of our academics. Although we were only founded recently (2003) and we are a relatively small institution, we have international reach. This is thanks to our focus on a targeted range of exciting research fields:

  • ICT and computational sciences
  • systems biomedicine;
  • European law;
  • finance
  • educational sciences.

Situated on the new Belval Campus (VIDEO) on reconverted industrial land and in the City of Luxembourg, our research teams and 550 PhD students work within three faculties and two interdisciplinary centres.

With 6,200 students and 250 academics from Europe and beyond, our University provides a truly multilingual learning experience. Whether it be English-French or German-French, many degree programmes are bilingual, and Master’s degrees taught entirely in English are also on offer. Nearly 80 partner universities worldwide boost the cosmopolitan profile further, with all Bachelor’s students studying abroad for at least one semester. Cross-border degrees are also available.

Luxembourg is a hub for innovative knowledge industries such as finance, high-end manufacturing and ICT. As the motor of the national research and innovation system, the University gives strong support to entrepreneurial activities. We are also well connected to European institutions, banks and businesses, technology companies, and Luxembourg’s multicultural society. The result is a unique mix of international excellence and local relevance to students and scientists from across the globe