Login | Register

Isogeometric Computation Reuse Method for Complex Objects with Topology-Consistent Volumetric Parameterization

Title:

Isogeometric Computation Reuse Method for Complex Objects with Topology-Consistent Volumetric Parameterization

Xu, Gang, Kwok, Tsz Ho ORCID: https://orcid.org/0000-0001-7240-1426 and Wang, Charlie C.L. (2017) Isogeometric Computation Reuse Method for Complex Objects with Topology-Consistent Volumetric Parameterization. Computer-Aided Design, 91 . pp. 1-13.

[thumbnail of CADReuseIGA.pdf]
Preview
Text (application/pdf)
CADReuseIGA.pdf - Accepted Version
Available under License Spectrum Terms of Access.
613kB

Official URL: http://dx.doi.org/10.1016/j.cad.2017.04.002

Abstract

Volumetric spline parameterization and computational efficiency are two main challenges in isogeometric analysis (IGA). To tackle this problem, we propose a framework of computation reuse in IGA on a set of three-dimensional models with similar semantic features. Given a template domain, B-spline based consistent volumetric parameterization is first constructed for a set of models with similar semantic features. An efficient quadrature-free method is investigated in our framework to compute the entries of stiffness matrix by Bezier extraction and polynomial approximation. In our approach, evaluation on the stiffness matrix and imposition of the boundary conditions can be pre-computed and reused during IGA on a set of CAD models. Examples with complex geometry are presented to show the effectiveness of our methods, and efficiency similar to the computation in linear finite element analysis can be achieved for IGA taken on a set of models.

Divisions:Concordia University > Gina Cody School of Engineering and Computer Science > Mechanical, Industrial and Aerospace Engineering
Item Type:Article
Refereed:Yes
Authors:Xu, Gang and Kwok, Tsz Ho and Wang, Charlie C.L.
Journal or Publication:Computer-Aided Design
Date:October 2017
Digital Object Identifier (DOI):10.1016/j.cad.2017.04.002
Keywords:Computation reuse, Isogeometric analysis, Consistent volume parameterization
ID Code:983467
Deposited By: Tsz Ho Kwok
Deposited On:05 Feb 2018 14:24
Last Modified:05 Feb 2018 14:24

References:

Hughes T.J.R., Cottrell J.A., Bazilevs Y. Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement Comput Methods Appl Mech Engrg, 194 (39–41) (2005), pp. 4135-4195

Cottrell J.A., Hughes T.J.R., Bazilevs Y. Isogeometric analysis: toward integration of CAD and FEA Bautechnik, 88 (6) (2011), p. 423

Kwok T.-H., Zhang Y., Wang C.C. Constructing common base domain by cues from Voronoi diagram Graph Models, 74 (4) (2012), pp. 152-163

Kwok T.-H., Zhang Y., Wang C.C.L. Efficient optimization of common base domains for cross parameterization IEEE Trans Vis Comput Graphics, 18 (10) (2012), pp. 1678-1692

Kraevoy V., Sheffer A. Cross-parameterization and compatible remeshing of 3D models ACM SIGGRAPH 2004 Papers, SIGGRAPH’04, ACM, New York, NY, USA (2004), pp. 861-869

Schreiner J., Asirvatham A., Praun E., Hoppe H. Inter-surface mapping ACM SIGGRAPH 2004 Papers, SIGGRAPH’04, ACM, New York, NY, USA (2004), pp. 870-877

Li X., Guo X., Wang H., He Y., Gu X., Qin H. Harmonic volumetric mapping for solid modeling applications Proceedings of the 2007 ACM symposium on solid and physical modeling, ACM, New York, NY, USA (2007), pp. 109-120

Xia J., He Y., Yin X., Han S., Gu X. Direct-product volumetric parameterization of handlebodies via harmonic fields 2010 shape modeling international conference (2010), pp. 3-12

Xia J., He Y., Han S., Fu C.W., Luo F., Gu X. Parameterization of star-Shaped volumes using Green’s functions Mourrain B., Schaefer S., Xu G. (Eds.), Advances in geometric modeling and processing: 6th international conference, Castro Urdiales, Spain, June 16–18, 2010. Proceedings, Springer, Berlin, Heidelberg, Berlin, Heidelberg (2010), pp. 219-235

Martin T., Cohen E., Kirby R.M. Volumetric parameterization and trivariate B-spline fitting using harmonic functions Comput Aided Geom Design, 26 (6) (2009), pp. 648-664

Aigner M., Heinrich C., Jüttler B., Pilgerstorfer E., Simeon B., Vuong A.V. Swept volume parameterization for isogeometric analysis Hancock E.R., Martin R.R., Sabin M.A. (Eds.), Mathematics of Surfaces XIII: 13th IMA International Conference York, UK, September 7–9, 2009 Proceedings, Springer, Berlin, Heidelberg, Berlin, Heidelberg (2009), pp. 19-44

Escobar J.M., Cascón J.M., Rodríguez E., Montenegro R. A new approach to solid modeling with trivariate T-splines based on mesh optimization Comput Methods Appl Mech Engrg, 200 (45–46) (2011), pp. 3210-3222

Zhang Y., Wang W., Hughes T.J.R. Solid T-spline construction from boundary representations for genus-zero geometry Comput Methods Appl Mech Engrg, 249–252 (2012), pp. 185-197 Higher Order Finite Element and Isogeometric Methods

Wang W., Zhang Y., Liu L., Hughes T.J.R. Trivariate solid T-spline construction from boundary triangulations with arbitrary genus topology Comput Aided Des, 45 (2) (2013), pp. 351-360 Solid and Physical Modeling 2012

Xu G., Mourrain B., Duvigneau R., Galligo A. Parameterization of computational domain in isogeometric analysis: Methods and comparison Comput Methods Appl Mech Engrg, 200 (23–24) (2011), pp. 2021-2031

Xu G., Mourrain B., Duvigneau R., Galligo A. Analysis-suitable volume parameterization of multi-block computational domain in isogeometric applications Comput Aided Des, 45 (2) (2013), pp. 395-404

Pettersen K.F., Skytt V. Spline volume fairing Boissonnat J.-D., Chenin P., Cohen A., Gout C., Lyche T., Mazure M.-L., Schumaker L. (Eds.), Curves and surfaces: 7th international conference. Avignon, France, June 24–30, 2010, revised selected papers, Springer, Berlin, Heidelberg, Berlin, Heidelberg (2012), pp. 553-561

Zhang Y., Wang W., Hughes T.J.R. Conformal solid T-spline construction from boundary T-spline representations Comput Mech, 51 (6) (2013), pp. 1051-1059

Kwok T.-H., Wang C.C.L. Domain construction for volumetric cross-parameterization Comput Graph, 38 (2014), pp. 86-96

Karatarakis A., Karakitsios P., Papadrakakis M. GPU accelerated computation of the isogeometric analysis stiffness matrix Comput Methods Appl Mech Engrg, 269 (2014), pp. 334-355

Hughes T.J.R., Reali A., Sangalli G. Efficient quadrature for NURBS-based isogeometric analysis Comput Methods Appl Mech Engrg, 199 (5–8) (2010), pp. 301-313 Computational Geometry and Analysis

Antolin P., Buffa A., Calabr F., Martinelli M., Sangalli G. Efficient matrix computation for tensor-product isogeometric analysis: The use of sum factorization Comput Methods Appl Mech Engrg, 285 (2015), pp. 817-828

Bartoň M., Calo V.M. Optimal quadrature rules for odd-degree spline spaces and their application to tensor-product-based isogeometric analysis Comput Methods Appl Mech Engrg, 305 (2016), pp. 217-240

Bartoň M., Calo V.M. Gauss–Galerkin quadrature rules for quadratic and cubic spline spaces and their application to isogeometric analysis Comput Aided Des, 82 (2017), pp. 57-67 Isogeometric Design and Analysis

Calabró F., Sangalli G., Tani M. Fast formation of isogeometric Galerkin matrices by weighted quadrature Comput Methods Appl Mech Engrg, 316 (2017), pp. 606-622 Special issue on isogeometric analysis: progress and challenges

Johannessen K.A. Optimal quadrature for univariate and tensor product splines Comput Methods Appl Mech Engrg, 316 (2017), pp. 84-99 Special issue on isogeometric analysis: progress and challenges

Mantzaflaris A., Jüttler B. Integration by interpolation and look-up for Galerkin-based isogeometric analysis Comput Methods Appl Mech Engrg, 284 (2015), pp. 373-400 Isogeometric analysis special issue

Wang C.C.L., Hui K.-C., Tong K.M. Volume parameterization for design automation of customized free-form products IEEE Trans Autom Sci Eng, 4 (1) (2007), pp. 11-21

Praun E., Sweldens W., Schröder P. Consistent mesh parameterizations Proceedings of the 28th annual conference on computer graphics and interactive techniques, SIGGRAPH’01, ACM, New York, NY, USA (2001), pp. 179-184

Farin G., Hoschek J., Kim M.S. Handbook of computer aided geometric design ELSEVIER (2002), pp. 771-795

Borden M.J., Scott M.A., Evans J.A., Hughes T.J.R. Isogeometric finite element data structures based on Bézier extraction of NURBS Internat J Numer Methods Engrg, 87 (1–5) (2011), pp. 15-47

Scott M.A., Borden M.J., Verhoosel C.V., Sederberg T.W., Hughes T.J.R. Isogeometric finite element data structures based on Bézier extraction of T-splines Internat J Numer Methods Engrg, 88 (2) (2011), pp. 126-156

Wang X., Qian X. An optimization approach for constructing trivariate B-spline solids Comput Aided Des, 46 (2014), pp. 179-191

Hu Q., Xu H. Constrained polynomial approximation of rational Bézier curves using reparameterization J. Comput Appl Math, 249 (249) (2013), pp. 133-143

Shi M, Deng J. Approximating rational Bézier curves by constrained Bézier curves of arbitrary degree. arXiv:1212.3385 [math.NA], 2012

Wang G.J., Sederberg T.W., Chen F. On the Convergence of Polynomial Approximation of Rational Functions J Approx Theory, 89 (3) (1997), pp. 267-288
All items in Spectrum are protected by copyright, with all rights reserved. The use of items is governed by Spectrum's terms of access.

Repository Staff Only: item control page

Downloads per month over past year

Research related to the current document (at the CORE website)
- Research related to the current document (at the CORE website)
Back to top Back to top