Accelerating Monte Carlo estimation with derivatives of high-level finite element models. CMAME paper submitted with Jack and Paul. 

http://hdl.handle.net/10993/28618 Link

In this paper we demonstrate the ability of a derivative-driven Monte Carlo estimator to accelerate the propagation of uncertainty through two high-level non-linear finite element models. The use of derivative information amounts to a correction to the standard Monte Carlo estimation procedure that reduces the variance under certain conditions. We express the finite element models in variational form using the high-level Unified Form Language (UFL). We derive the tangent linear model automatically from this high-level description and use it to efficiently calculate the required derivative information. To study the effectiveness of the derivative-driven method we consider two stochastic PDEs; a one- dimensional Burgers equation with stochastic viscosity and a three-dimensional geometrically non-linear Mooney-Rivlin hyperelastic equation with stochastic density and volumetric material parameter. Our results show that for these problems the first-order derivative-driven Monte Carlo method is around one order of magnitude faster than the standard Monte Carlo method and at the cost of only one extra tangent linear solution per estimation problem. We find similar trends when comparing with a modern non-intrusive multi-level polynomial chaos expansion method. We parallelise the task of the repeated forward model evaluations across a cluster using the ipyparallel and mpi4py software tools. A complete working example showing the solution of the stochastic viscous Burgers equation is included as supplementary material.

Professor Nenad Bićanić passed away

My long-standing colleague Chris Pearce (University of Glasgow) just passed on the sad news of the passing of Professor Nenad Bićanić.

I will remember Nenad as a passionate, gentle and dedicated mentor and I am deeply saddened by his passing. I am sure he inspired many young engineers in the many years he taught the subject and as many researchers to follow the path of knowledge.

I would like to wish all the best to his family in these difficult times.

Stéphane Bordas

Modelling interfacial cracking with non-matching cohesive interface elements Paper out 

http://link.springer.com/article/10.1007/s00466-016-1314-y?wt_mc=Internal.Event.1.SEM.ArticleAuthorAssignedToIssue

Title 

Modelling interfacial cracking with non-matching cohesive interface elements  

Journal 

Computational Mechanics, 58(5), 731-746

DOI 

10.1007/s00466-016-1314-y

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]