Reference : Taylor-Series Expansion Based Numerical Methods: A Primer, Performance Benchmarking a...
Scientific journals : Article
Engineering, computing & technology : Multidisciplinary, general & others
Computational Sciences
http://hdl.handle.net/10993/41983
Taylor-Series Expansion Based Numerical Methods: A Primer, Performance Benchmarking and New Approaches for Problems with Non-smooth Solutions
English
Jacquemin, Thibault Augustin Marie mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > >]
Tomar, Satyendra mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Engineering Research Unit >]
Agathos, Konstantinos mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Engineering Research Unit >]
Mohseni-Mofidi, Shoya [Fraunhofer-Institute for Mechanics of Materials IWM, Freiburg, Germany]
Bordas, Stéphane mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Engineering Research Unit > ; China Medical University Hospital, China Medical University, Taichung, Taiwan > Department of Medical Research > > ; Asia University, Taichung, Taiwan > Department of Computer Science and Information Engineering]
30-Aug-2019
Archives of Computational Methods in Engineering
International Center for Numerical Methods in Engineering
Yes
International
1134-3060
Barcelona
Spain
[en] We provide a primer to numerical methods based on Taylor series expansions such as generalized finite difference methods and collocation methods. We provide a detailed benchmarking strategy for these methods as well as all data files including input files, boundary conditions, point distribution and solution fields, so as to facilitate future benchmarking of new methods. We review traditional methods and recent ones which appeared in the last decade. We aim to help newcomers to the field understand the main characteristics of these methods and to provide sufficient information to both simplify implementation and benchmarking of new methods. Some of the examples are chosen within a subset of problems where collocation is traditionally known to perform sub-par, namely when the solution sought is non-smooth, i.e. contains discontinuities, singularities or sharp gradients. For such problems and other simpler ones with smooth solutions, we study in depth the influence of the weight function, correction function, and the number of nodes in a given support. We also propose new stabilization approaches to improve the accuracy of the numerical methods. In particular, we experiment with the use of a Voronoi diagram for weight computation, collocation method stabilization approaches, and support node selection for problems with singular solutions. With an appropriate selection of the above-mentioned parameters, the resulting collocation methods are compared to the moving least-squares method (and variations thereof), the radial basis function finite difference method and the finite element method. Extensive tests involving two and three dimensional problems indicate that the methods perform well in terms of efficiency (accuracy versus computational time), even for non-smooth solutions.
Researchers ; Professionals ; Students ; General public ; Others
http://hdl.handle.net/10993/41983
10.1007/s11831-019-09357-5
FnR ; FNR10318764 > Stéphane Bordas > Fretting fatigue > Multi-analysis of fretting fatigue using physical and virtualexperiments > 01/07/2016 > 30/06/2019 > 2015

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