The purpose of this project is to reduce the errors associated with numerical solution of wave propagation problems and their computational costs. In high-frequency regimes, the solution of conventional FEM sufferers from pollution error which is due to dispersion and can be visualized as a phase shift of the numerical solution. To maintain a desired level of pollution error in conventional FEM, it is necessary to increase discretization density faster than the wave number which rapidly increase the computational cost. On the other hand, the geometrical accuracy of the scattering surfaces play an important role in accuracy of the solution. The possibility of representing man-made objects exactly in IGA even with very coarse meshes and the convenience of its refinement makes it a desirable platform to perform scattering analysis. The convergence graphs obtained for scattering problems performed in IGA platform approves the anticipated properties and makes it possible to increase the solution accuracy even for very high-frequency analysis. [http://mechanical907.rssing.com/browser.php?indx=25030677&last=1&item=1], [http://hdl.handle.net/10993/28982].
submitted to the International Journal for Numerical Methods in Bioengineering. This is collaborative work with @tomar.sk here at Legato (on ERC RealTCut), @phuoc who starts with us in a few weeks and was funded by my Strasbourg Institute of Advanced Studies Fellowship and the team of Stéphane Cotin (Inria MEMESIS) and Hadrien Courtecuisse (former post-doc now at ICube in Strasbourg). Congratulations to everyone. This paper shows is the result of a long-lasting collaboration between Mathematics, Computer Science and Engineering and shows that error estimators can be useful also in real-time simulations through an example in liver surgery.
Congratulations to the whole team! Great collaboration with Inria MIMESIS Team led by Stéphane Cotin.
Congrats to Paul Hauseux and Jack Hale.
||Title: A well-conditioned and optimally convergent XFEM for 3D linear elastic fracture
Author(s): Agathos, Konstantinos; Chatzi, Eleni; Bordas, Stephane P. A.; et al.
Source: INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING Volume: 105 Issue: 9 Pages: 643-677 Published: MAR 2 2016
Times Cited: 0
||Title: A fast, certified and “tuning free” two-field reduced basis method for the metamodelling of affinely-parametrised elasticity problems
Author(s): Hoang, K. C.; Kerfriden, P.; Bordas, S. P. A.
Source: COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING Volume: 298 Pages: 121-158 Published: JAN 1 2016
Times Cited: 0
||Title: Virtual and smoothed finite elements: A connection and its application to polygonal/polyhedral finite element methods
Author(s): Natarajan, Sundararajan; Bordas, Stephane P. A.; Ooi, Ean Tat
Source: INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING Volume: 104 Issue: 13 Pages: 1173-1199 Published: DEC 28 2015
Times Cited: 0
of elliptic PDEs. The main difficulty is the lack of a full description of the diffusion coefficients.
We overcome this obstacle by representing them as a random a field. Under this …
It was observed in [1, 2] that the strain smoothing technique over higher order elements and arbitrary polytopes yields less accurate solutions than other techniques such as the conventional polygonal finite element method. In this work, we propose a linear strain smoothing scheme that improves the accuracy of linear and quadratic approximations over convex polytopes. The main idea is to subdivide the polytope into simplicial subcells and use a linear smoothing function in each subcell to compute the strain. This new strain is then used in the computation of the stiffness matrix. The convergence properties and accuracy of the proposed scheme are discussed by solving few benchmark problems. Numerical results show that the proposed linear strain smoothing scheme makes the approximation based on polytopes to deliver improved accuracy and pass the patch test to machine precision.
|Francis, Amrita |
|Ortiz-Bernardin, Alejandro |
|Bordas, Stéphane [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Engineering Research Unit >]|
|Natarajan, Sundararajan |
The isogeometric boundary element method (IGABEM) based on NURBS is adopted to model fracture problem in 3D. The NURBS basis functions are used in both crack representation and physical quantity approximation. A stable quadrature scheme for singular integration is proposed to enhance the robustness of the method in dealing with highly distorted element. The convergence study in crack opening displacement is performed for penny-shaped crack and elliptical crack. Two ways to extract stress intensity factors (SIFs), the contour $M$ integral and virtual crack closure integral, are implemented based on the framework of dual integral equations. An algorithm is outlined and validated to be stable for fatigue crack growth, thanks to the smoothness not only in crack geometry but also in stress/SIFs solution brought by IGABEM.
Thank you to Xuan Peng, PhD Student on the ITN INSIST Project, and to Elena Atroshchenko.