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Recent Developments in CAD/analysis Integration [article]

H. Lian, S. P. A. Bordas, R. Sevilla, R. N. Simpson
2012 arXiv   pre-print
Examples include B-spline subdivision surfaces, isogeometric analysis, NURBS-enhanced FEM and parametric-based implicit boundary definitions.  ...  We review in this paper a subset of such methods centred on tighter coupling between computer aided design (CAD) and analysis (finite element or boundary element methods).  ...  For topology optimisation, the initial method is cell-based or element-based, where the geometry can be represented by level sets [112] or splines.  ... 
arXiv:1210.8216v1 fatcat:jtnvz2hyvbghfoh7r2anr5osdi

Subdivision surfaces with isogeometric analysis adapted refinement weights

Qiaoling Zhang, Malcolm Sabin, Fehmi Cirak
2018 Computer-Aided Design  
Subdivision surfaces provide an elegant isogeometric analysis framework for geometric design and analysis of partial differential equations defined on surfaces.  ...  In finite element analysis the optimised subdivision weights for either cup- or saddle-like shapes are chosen depending on the shape of the solution field around an extraordinary vertex.  ...  Parameterisation of the subdivision surface, at least a local one, is essential in order to associate the so far discrete representation based on control vertices with a continuous differentiable representation  ... 
doi:10.1016/j.cad.2018.04.020 fatcat:wndedu37pfc3tdu7evif7bxwy4

Shape optimisation with multiresolution subdivision surfaces and immersed finite elements

Kosala Bandara, Thomas Rüberg, Fehmi Cirak
2016 Computer Methods in Applied Mechanics and Engineering  
With the immersed finite element method there is no need to maintain an analysis suitable domain mesh.  ...  In some of the presented two- and three-dimensional elasticity examples the topology derivative is used for creating new holes inside the domain.  ...  Acknowledgements The partial support of the EPSRC through grant # EP/G008531/1 and EC through Marie Curie Actions (IAPP) program CASOPT project is gratefully acknowledged.  ... 
doi:10.1016/j.cma.2015.11.015 fatcat:tjme4fh4izaepg23ze2nwlicni

Boundary element based multiresolution shape optimisation in electrostatics

Kosala Bandara, Fehmi Cirak, Günther Of, Olaf Steinbach, Jan Zapletal
2015 Journal of Computational Physics  
The multiresolution approach effectively prevents the appearance of non-physical geometry oscillations in the optimised shapes.  ...  The geometry of the domain is described with subdivision surfaces and different resolutions of the same geometry are used for optimisation and analysis.  ...  J.Z. thanks for the support provided by the European Regional Development Fund in the IT4Innovations Centre of Excellence project (CZ.  ... 
doi:10.1016/j.jcp.2015.05.017 fatcat:2vk7dtomtbd7zjfiid277aeg6e

Laplace-Beltrami based Multi-Resolution Shape Reconstruction on Subdivision Surfaces [article]

A. M. A. Alsnayyan, B. Shanker
2021 arXiv   pre-print
The method relies on subdivision basis sets to construct both boundary element isogeometric methods for analysis and surface finite elements to construct manifold harmonics.  ...  These eigenfunctions or manifold harmonics, provide the means to smoothly interpolate data on a manifold.  ...  Acknowledgments The authors would acknowledge computing support from the HPC Center at Michigan State University and financial support from NSF via CMMI-  ... 
arXiv:2104.04027v1 fatcat:3r26g4ob75dt7hvzf6winwrng4

Assessment of an isogeometric approach with Catmull–Clark subdivision surfaces using the Laplace–Beltrami problems

Zhaowei Liu, Andrew McBride, Prashant Saxena, Paul Steinmann
2020 Computational Mechanics  
An isogeometric approach for solving the Laplace-Beltrami equation on a two-dimensional manifold embedded in threedimensional space using a Galerkin method based on Catmull-Clark subdivision surfaces is  ...  The scalar-valued Laplace-Beltrami equation requires only C 0 continuity and is adopted to elucidate key features and properties of the isogeometric method using Catmull-Clark subdivision surfaces.  ...  Acknowledgements This work was supported by the UK Engineering and Physical Sciences Research Council grant EP/R008531/1 for the Glasgow Computational Engineering Centre.  ... 
doi:10.1007/s00466-020-01877-3 fatcat:q4m3e27z2ncgtjtohsyo2rwkvi

Elliptic grid generation techniques in the framework of isogeometric analysis applications

J. Hinz, M. Möller, C. Vuik
2018 Computer Aided Geometric Design  
Acknowledgements This project (MOTOR) has received funding from the European Union's Horizon 2020 research and innovation program under grant agreement No. 678727.  ...  In the following, we shall present a numerical solution technique for the approximate solution of (6) that is based on the principles of Isogeometric Analysis (IgA).  ...  , our focus is not only on generating analysis-suitable parameterisations of high quality but also on aspects of computational efficiency.  ... 
doi:10.1016/j.cagd.2018.03.023 fatcat:swj4bhwuwvbybptvq3ddfjegdu

Using Deep Learning to Extend the Range of Air-Pollution Monitoring and Forecasting [article]

Philipp Haehnel, Jakub Marecek, Julien Monteil, Fearghal O'Donncha
2019 arXiv   pre-print
We demonstrate a deep-learning framework for air-pollution monitoring and forecasting that provides the ability to train across different model domains, as well as a reduction in the run-time by two orders  ...  It presents a first-of-a-kind implementation that combines deep-learning and domain-decomposition techniques to allow model deployments extend beyond the domain(s) on which the model has been trained.  ...  More generally, one could explore links to isogeometric analysis of [68] , which integrates solving PDEs with geometric modelling.  ... 
arXiv:1810.09425v2 fatcat:3t2lktgvxbhtniormfteiofkpi

Subdivision surfaces with isogeometric analysis adapted refinement weights

Q Zhang, M Sabin, Fehmi Cirak, Apollo-University Of Cambridge Repository, Apollo-University Of Cambridge Repository
2018
Subdivision surfaces provide an elegant isogeometric analysis framework for geometric design and analysis of partial differential equations defined on surfaces.  ...  In finite element analysis the optimised subdivision weights for either cup- or saddle-like shapes are chosen depending on the shape of the solution field around an extraordinary vertex.  ...  Parameterisation of the subdivision surface, at least a local one, is essential in order to associate the so far discrete representation based on control vertices with a continuous differentiable representation  ... 
doi:10.17863/cam.26231 fatcat:czx4womtxnbv5at5rfvla43pwu

Assessment of an Isogeometric Approach with Catmull-Clark Subdivision Surfaces using the Laplace-Beltrami Problems [article]

Zhaowei Liu, Andrew McBride, Prashant Saxena, Paul Steinmann
2020 arXiv   pre-print
An isogeometric approach for solving the Laplace-Beltrami equation on a two-dimensional manifold embedded in three-dimensional space using a Galerkin method based on Catmull-Clark subdivision surfaces  ...  The scalar-valued Laplace-Beltrami equation requires only C0 continuity and is adopted to elucidate key features and properties of the isogeometric method using Catmull-Clark subdivision surfaces.  ...  Acknowledgements This work was supported by the UK Engineering and Physical Sciences Research Council grant EP/R008531/1 for the Glasgow Computational Engineering Centre.  ... 
arXiv:1909.11180v2 fatcat:33j7rm3o4jhztjfxf4pvdpr3ku

Geometric Modeling: Interoperability and New Challenges (Dagstuhl Seminar 21471)

Falai Chen, Tor Dokken, Géraldine Morin
2022
This seminar was initially planned on May 2021, and was delayed due to the pandemic. The seminar took place as a hybrid version with on site and remote participants.  ...  This report summarizes the seminar communications, first by providing the abstracts of the talks which present recent results in geometric modeling.  ...  The organisers are really grateful to have been given the possibility to have some on-site participants, who were very active in keeping the seminar lively.  ... 
doi:10.4230/dagrep.11.10.111 fatcat:i6fblwscefdpdhu6kr4kxbwpka

CAD-CAE integration and isogeometric analysis: trivariate multipatch and applications

Marco Brino, E. Bonisoli
2015
Element Method, in Section 2 both B-splines and NURBS are analysed with their properties, in Section 3 the isogeometric analysis concepts are presented and applied on examples composed by single-patch  ...  Section 6, analyses some added studies on parallel tests on the application of topological optimisation and the conversion from a boundary surface representation of a patch to a single tri-variate description  ...  Tutti questi nomi sento, in un modo o nell'altro, aver dato un contibuto a questo traguardo e perciò desidero ringraziarli caldamente.  ... 
doi:10.6092/polito/porto/2588580 fatcat:vpgvovn3u5g25jj6mj5o5qgzfi

Dagstuhl Reports, Volume 11, Issue 10, October 2021, Complete Issue [article]

2022
The recent emergence of the level set topology optimization approach has decoupled the geometry update of the optimization operation to the analysis and the implicit level set design representation opens  ...  This important problem arises, for example, in unfitted finite element methods and in isogeometric analysis on trimmed computational domains.  ...  In the talk, we focus on one particular step of the analysis, which deals with a seemingly noneffective use of a limit inferior.  ... 
doi:10.4230/dagrep.11.10 fatcat:mqui2qttdrdt7p6y3nbkkodoci

Dagstuhl Reports, Volume 7, Issue 5, May 2017, Complete Issue [article]

2018
This talk is based upon work from COST Action CA15140 on Improving Applicability of Nature-Inspired Optimisation by Joining Theory and Practice (ImAppNIO), supported by COST (European Cooperation in Science  ...  First, we propose an alternative image based representation for the 3D content, generated by peers and collected in a sprite tree.  ...  How to introduce analysis-based design in CAD systems with isogeometric analysis in mind?  ... 
doi:10.4230/dagrep.7.5 fatcat:ipv6ltpp6ngejao35zzoqko2ry

Self-adaptive isogeometric discretisations of the second-order forms of the neutron transport equation with dual weighted residual or goal-based error measures

Charles Latimer, Michael Bluck, Matthew Eaton, Engineering And Physical Sciences Research Council, Rolls-Royce Group Plc
2021
In this thesis several second-order forms of the neutron transport equation (NTE) are spatially discretised with isogeometric analysis (IGA).  ...  method.  ...  This does not imply that the number of control points is the same. 121 Conclusions In this chapter a constraint based method for the local refinement of NURBS based isogeometric analysis (IGA) has  ... 
doi:10.25560/89086 fatcat:mbs6vmnccjgrpbp2zphzf45uke
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