×

zbMATH — the first resource for mathematics

Subdivision-based nonlinear multiscale cloth simulation. (English) Zbl 1425.74297

MSC:
74K25 Shells
74B20 Nonlinear elasticity
65M55 Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs
65K10 Numerical optimization and variational techniques
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] J. C. Alexander and J. A. Yorke, The homotopy continuation method: Numerically implementable topological procedures, Trans. Amer. Math. Soc., 242 (1978), pp. 271–284, https://www.jstor.org/stable/1997737. · Zbl 0424.58003
[2] I. Babuška, The finite element method with penalty, Math. Comp., 27 (1973), pp. 221–228, https://doi.org/10.1090/S0025-5718-1973-0351118-5.
[3] K. Bandara and F. Cirak, Isogeometric shape optimisation of shell structures using multiresolution subdivision surfaces, Comput.-Aided Des., 95 (2018), pp. 62–71, https://doi.org/10.1016/j.cad.2017.09.006.
[4] D. Baraff and A. Witkin, Large steps in cloth simulation, in Proceedings of the 25th Annual Conference on Computer Graphics and Interactive Techniques, SIGGRAPH ’98, New York, 1998, ACM, pp. 43–54, https://doi.org/10.1145/280814.280821.
[5] J. W. Barrett and C. M. Elliott, Finite element approximation of the Dirichlet problem using the boundary penalty method, Numer. Math., 49 (1986), pp. 343–366, https://doi.org/10.1007/BF01389536. · Zbl 0614.65116
[6] A. Brandt, Multi-level adaptive solutions to boundary-value problems, Math. Comp., 31 (1977), pp. 333–390, https://doi.org/10.2307/2006422. · Zbl 0373.65054
[7] R. Bridson, R. Fedkiw, and J. Anderson, Robust treatment of collisions, contact and friction for cloth animation, ACM Trans. Graph., 21 (2002), pp. 594–603, https://doi.org/10.1145/566654.566623.
[8] R. Bridson, S. Marino, and R. Fedkiw, Simulation of clothing with folds and wrinkles, in SCA ’03: Proceedings of the 2003 ACM SIGGRAPH/Eurographics Symposium on Computer Animation, Eurographics Association, 2003, pp. 28–36.
[9] W. L. Briggs, V. E. Henson, and S. F. McCormick, A Multigrid Tutorial, 2nd ed., SIAM, Philadelphia, 2000, https://doi.org/10.1137/1.9780898719505.
[10] X.-C. Cai and D. E. Keyes, Nonlinearly preconditioned inexact Newton algorithms, SIAM J. Sci. Comput., 24 (2002), pp. 183–200, https://doi.org/10.1137/S106482750037620X. · Zbl 1015.65058
[11] X.-C. Cai and X. Li, Inexact Newton methods with restricted additive Schwarz based nonlinear elimination for problems with high local nonlinearity, SIAM J. Sci. Comput., 33 (2011), pp. 746–762, https://doi.org/10.1137/080736272. · Zbl 1227.65045
[12] C. Cartis, N. I. M. Gould, and P. L. Toint, An adaptive cubic regularization algorithm for nonconvex optimization with convex constraints and its function-evaluation complexity, IMA J. Numer. Anal., 32 (2012), pp. 1662–1695, https://doi.org/10.1093/imanum/drr035. · Zbl 1267.65061
[13] E. Catmull and J. Clark, Recursively generated B-spline surfaces on arbitrary topological meshes, Comput.-Aided Des., 10 (1978), pp. 350–355, https://doi.org/10.1016/0010-4485(78)90110-0.
[14] F. Cirak and M. Ortiz, Fully \(C^1\)-conforming subdivision elements for finite deformation thin-shell analysis, Internat. J. Numer. Methods Engrg., 51 (2001), pp. 813–833, https://doi.org/10.1002/nme.182. · Zbl 1039.74045
[15] F. Cirak, M. Ortiz, and P. Schröder, Subdivision surfaces: A new paradigm for thin-shell finite-element analysis, Internat. J. Numer. Methods Engrg., 47 (2000), pp. 2039–2072, https://doi.org/10.1002/(SICI)1097-0207(20000430)47:12%3C2039::AID-NME872%3E3.0.CO;2-1.
[16] D. Clyde, Numerical Subdivision Surfaces for Simulation and Data Driven Modeling of Woven Cloth, Ph.D. thesis, University of California, Los Angeles, 2017; available online at https://escholarship.org/uc/item/30g0h9r5.
[17] D. Clyde, J. Teran, and R. Tamstorf, Modeling and data-driven parameter estimation for woven fabrics, in Proceedings of the ACM SIGGRAPH/Eurographics Symposium on Computer Animation, SCA ’17, ACM, New York, 2017, 17, https://doi.org/10.1145/3099564.3099577.
[18] D. Clyde, J. Teran, and R. Tamstorf, Simulation of nonlinear Kirchhoff-Love thin shells using subdivision finite elements, in Proceedings of the ACM SIGGRAPH/Eurographics Symposium on Computer Animation, SCA ’17, ACM, New York, 2017, supplemental technical document, https://doi.org/10.1145/3099564.3099577.
[19] A. R. Conn, N. I. M. Gould, and P. L. Toint, Trust Region Methods, MOS-SIAM Ser. Optim., SIAM, Philadelphia, 2000, https://doi.org/10.1137/1.9780898719857.
[20] J. E. Dennis, Jr., and R. B. Schnabel, Numerical Methods for Unconstrained Optimization and Nonlinear Equations, SIAM, Philadelphia, 1996, https://doi.org/10.1137/1.9781611971200.
[21] A. Forsgren, On the Behavior of the Conjugate-Gradient Method on Ill-Conditioned Problems, Technical Report TRITA-MAT-2006-OS1, Department of Mathematics, Royal Institute of Technology, Stockholm, Sweden, 2006.
[22] M. W. Gee and R. S. Tuminaro, Nonlinear Algebraic Multigrid for Constrained Solid Mechanics Problems Using Trilinos, Technical Report SAND2006-2256, Sandia National Laboratories, Livermore, CA, 2006.
[23] S. Gratton, M. Mouffe, A. Sartenaer, P. L. Toint, and D. Tomanos, Numerical experience with a recursive trust-region method for multilevel nonlinear bound-constrained optimization, Optim. Methods Softw., 25 (2010), pp. 359–386, https://doi.org/10.1080/10556780903239295. · Zbl 1190.90209
[24] S. Gratton, A. Sartenaer, and P. L. Toint, Recursive trust-region methods for multiscale nonlinear optimization, SIAM J. Optim., 19 (2008), pp. 414–444, https://doi.org/10.1137/050623012. · Zbl 1163.90024
[25] S. Green and G. Turkiyyah, Second-order accurate constraint formulation for subdivision finite element simulation of thin shells, Internat. J. Numer. Methods Engrg., 61 (2004), pp. 380–405, https://doi.org/10.1002/nme.1070. · Zbl 1075.74645
[26] S. Green, G. Turkiyyah, and D. Storti, Subdivision-based multilevel methods for large scale engineering simulation of thin shells, in Proceedings of the Seventh ACM Symposium on Solid Modeling and Applications, SMA ’02, K. Lee and N. M. Patrikalakis, eds., ACM, New York, 2002, pp. 265–272, https://doi.org/10.1145/566282.566321.
[27] C. Groß, A Unifying Theory for Nonlinear Additively and Multiplicatively Preconditioned Globalization Strategies: Convergence Results and Examples from the Field of Nonlinear Elastostatics and Elastodynamics, Ph.D. thesis, Universität Bonn, Bonn, Germany, 2009, http://hss.ulb.uni-bonn.de/2009/1868/1868.htm.
[28] C. Groß and R. Krause, On the convergence of recursive trust-region methods for multiscale nonlinear optimization and applications to nonlinear mechanics, SIAM J. Numer. Anal., 47 (2009), pp. 3044–3069, https://doi.org/10.1137/08071819X. · Zbl 1410.90198
[29] W. Hackbusch, Multi-Grid Methods and Applications, Springer Ser. Comput. Math. 4, Springer-Verlag, Berlin, Heidelberg, 1985, https://doi.org/10.1007/978-3-662-02427-0.
[30] W. Hackbusch and A. Reusken, On global multigrid convergence for nonlinear problems, in Robust Multi-Grid Methods, Notes Numer. Fluid Mech. 23, Friedr. Vieweg, Braunschweig, 1989, pp. 105–113, https://doi.org/10.1007/978-3-322-86200-6_9.
[31] N. J. Higham, Accuracy and Stability of Numerical Algorithms, 2nd ed., SIAM, Philadelphia, 2002, https://doi.org/10.1137/1.9780898718027.
[32] T. Hughes, J. Cottrell, and Y. Bazilevs, Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement, Comput. Methods Appl. Mech. Engrg., 194 (2005), pp. 4135–4195, https://doi.org/10.1016/j.cma.2004.10.008. · Zbl 1151.74419
[33] F.-N. Hwang and X.-C. Cai, A class of parallel two-level nonlinear Schwarz preconditioned inexact Newton algorithms, Comput. Methods Appl. Mech. Engrg., 196 (2007), pp. 1603–1611, https://doi.org/10.1016/j.cma.2006.03.019. · Zbl 1173.76385
[34] Intel Developer Zone, Intel Math Kernel Library, 2007, https://software.intel.com/en-us/mkl.
[35] M. Juntunen and R. Stenberg, Nitsche’s method for general boundary conditions, Math. Comp., 78 (2009), pp. 1353–1374, https://doi.org/10.1090/S0025-5718-08-02183-2. · Zbl 1198.65223
[36] M. Keckeisen and W. Blochinger, Parallel implicit integration for cloth animations on distributed memory architectures, in Eurographics Workshop on Parallel Graphics and Visualization, D. Bartz, B. Raffin, and H.-W. Shen, eds., The Eurographics Association, 2004, https://doi.org/10.2312/EGPGV/EGPGV04/119-126.
[37] J. Kiendl, K.-U. Bletzinger, J. Linhard, and R. Wüchner, Isogeometric shell analysis with Kirchhoff-Love elements, Comput. Methods Appl. Mech. Engrg., 198 (2009), pp. 3902–3914, https://doi.org/10.1016/j.cma.2009.08.013. · Zbl 1231.74422
[38] G. Kirchhoff, Über das Gleichgewicht und die Bewegung einer elastischen Scheibe, J. Reine Angew. Math., 40 (1850), pp. 51–88, https://doi.org/10.1515/crll.1850.40.51.
[39] A. Klawonn, O. Rheinbach, and O. B. Widlund, An analysis of a FETI–DP algorithm on irregular subdomains in the plane, SIAM J. Numer. Anal., 46 (2008), pp. 2484–2504, https://doi.org/10.1137/070688675. · Zbl 1176.65135
[40] R. Kornhuber and R. Krause, Adaptive multigrid methods for Signorini’s problem in linear elasticity, Comput. Vis. Sci., 4 (2001), pp. 9–20, https://doi.org/10.1007/s007910100052. · Zbl 1051.74045
[41] R. Krause, A nonsmooth multiscale method for solving frictional two-body contact problems in 2D and 3D with multigrid efficiency, SIAM J. Sci. Comput., 31 (2009), pp. 1399–1423, https://doi.org/10.1137/070682514. · Zbl 1193.74103
[42] R. Krause, A. Rigazzi, and J. Steiner, A parallel multigrid method for constrained minimization problems and its application to friction, contact, and obstacle problems, Comput. Vis. Sci., 18 (2016), pp. 1–15, https://doi.org/10.1007/s00791-016-0267-1. · Zbl 1360.65175
[43] S. Lanquetin and M. Neveu, Reverse Catmull-Clark subdivision, in Conference Proceedings WSCG’2006, UNION Agency—Science Press, 2006.
[44] C. Loop, Smooth Subdivision Surfaces Based on Triangles, master’s thesis, Department of Mathematics, University of Utah, Salt Lake City, UT, 1987.
[45] S. G. Nash, A multigrid approach to discretized optimization problems, Optim. Methods Softw., 14 (2000), pp. 99–116, https://doi.org/10.1080/10556780008805795.
[46] J. Nocedal and S. J. Wright, Numerical Optimization, 2nd ed., Springer, New York, 2006, https://doi.org/10.1007/978-0-387-40065-5.
[47] Pixar Animation Studios, OpenSubdiv, 2017, http://graphics.pixar.com/opensubdiv.
[48] L. Pospíšil, Development of Algorithms for Solving Minimizing Problems with Convex Quadratic Function on Special Convex Sets and Applications, Ph.D. thesis, Vysoká škola báňská-Technická univerzita Ostrava, Czech Republic, 2015; available online at http://hdl.handle.net/10084/110918.
[49] M. J. D. Powell, A new algorithm for unconstrained optimization, in Nonlinear Programming, J. B. Rosen, O. L. Mangasarian, and K. Ritter, eds., Academic Press, 1970, pp. 31–65, https://doi.org/10.1016/B978-0-12-597050-1.50006-3.
[50] M. J. D. Powell, A hybrid method for nonlinear equations, in Numerical Methods for Nonlinear Algebraic Equations, P. Rabinowitz, ed., Gordon and Breach Science Publishers, London, 1970, pp. 87–114.
[51] Y. Saad, Iterative Methods for Sparse Linear Systems, SIAM, Philadelphia, 2003, https://doi.org/10.1137/1.9780898718003.
[52] F. Samavati, H.-R. Pakdel, C. Smith, and P. Prusinkiewicz, Reverse Loop Subdivision, Technical Report 2003-730-33, University of Calgary, Calgary, AB, Canada, 2003, https://doi.org/10.11575/PRISM/30995.
[53] O. Schenk and K. Gärtner, Solving unsymmetric sparse systems of linear equations with PARDISO, Future Gener. Comput. Syst., 20 (2004), pp. 475–487, https://doi.org/10.1016/j.future.2003.07.011.
[54] J. Stam, Exact evaluation of Catmull-Clark subdivision surfaces at arbitrary parameter values, in Proceedings of the 25th Annual Conference on Computer Graphics and Interactive Techniques, SIGGRAPH ’98, ACM, 1998, pp. 395–404, https://doi.org/10.1145/280814.280945.
[55] T. Steihaug, The conjugate gradient method and trust regions in large scale optimization, SIAM J. Numer. Anal., 20 (1983), pp. 626–637, https://doi.org/10.1137/0720042. · Zbl 0518.65042
[56] G. Strang and G. Fix, An Analysis of the Finite Element Method, 2nd ed., Wellesley-Cambridge Press, Wellesley, MA, 2008. · Zbl 1171.65081
[57] R. Tamstorf, T. Jones, and S. F. McCormick, Smoothed aggregation multigrid for cloth simulation, ACM Trans. Graph., 34 (2015), 245, https://doi.org/10.1145/2816795.2818081.
[58] M. Tang, H. Wang, L. Tang, R. Tong, and D. Manocha, CAMA: Contact-aware matrix assembly with unified collision handling for GPU-based cloth simulation, Comput. Graph. Forum, 35 (2016), pp. 511–521, https://doi.org/10.1111/cgf.12851.
[59] B. Thomaszewski, S. Pabst, and W. Blochinger, Parallel techniques for physically based simulation on multi-core processor architectures, Comput. Graph., 32 (2008), pp. 25–40, https://doi.org/10.1016/j.cag.2007.11.003.
[60] B. Thomaszewski, M. Wacker, and W. Straßer, A consistent bending model for cloth simulation with corotational subdivision finite elements, in ACM SIGGRAPH/Eurographics Symposium on Computer Animation, SCA ’06, The Eurographics Association, 2006, pp. 107–116, https://doi.org/10.2312/SCA/SCA06/107-116.
[61] F. Tisseur, Newton’s method in floating point arithmetic and iterative refinement of generalized eigenvalue problems, SIAM J. Matrix Anal. Appl., 22 (2001), pp. 1038–1057, https://doi.org/10.1137/S0895479899359837. · Zbl 0982.65040
[62] P. L. Toint, Towards an efficient sparsity exploiting Newton method for minimization, in Sparse Matrices and Their Uses, I. S. Duff, ed., Academic Press, London, 1981, pp. 57–88.
[63] D. Zorin, A method for analysis of \(C^1\)-continuity of subdivision surfaces, SIAM J. Numer. Anal., 37 (2000), pp. 1677–1708, https://doi.org/10.1137/S003614299834263X. · Zbl 0959.65021
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.