PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Tytuł artykułu

Improved GETMe by adaptive mesh smoothing

Wybrane pełne teksty z tego czasopisma
Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Mesh smoothing improves mesh quality by node relocation without altering mesh topology. Such methods play a vital role in finite element mesh improvement with a direct consequence on the quality of the discretized solution. In this work, an improved version of the recently proposed geometric element transformation method (GETMe) for mesh smoothing is presented. Key feature is the introduction of adaptive concepts, which improve the resulting mesh quality, reduce the number of parameters, and enhance the parallelization capabilities. Implementational aspects are discussed and results of a more efficient version are presented, which demonstrate that GETMe adaptive smoothing yields high quality meshes, is particularly fast, and has a comparably low memory profile. Furthermore, results are compared to those of other state-of-the-art smoothing methods.
Rocznik
Strony
55--71
Opis fizyczny
Bibliogr. 45 poz., rys., tab., wykr.
Twórcy
  • Institute of Structural Analysis & Antiseismic Research National Technical University Athens (NTUA) Zografou Campus, 15780 Athens, Greece
  • NIKI Ltd. Digital Engineering, Research Center 205 Ethnikis Antistasis Street, 45500 Katsika, Ioannina, Greece
  • TWT GmbH Science & Innovation, Department for Mathematical Research & Services Bernhäuser Straße 40–42, 73765 Neuhausen, Germany
  • Institute of Structural Analysis & Antiseismic Research National Technical University Athens (NTUA) Zografou Campus, 15780 Athens, Greece
Bibliografia
  • [1] L.A. Freitag, C. Ollivier-Gooch. A cost/benefit analysis of simplicial mesh improvement techniques as measured by solution efficiency. Int. J. Comput. Geom. Appl., 10 (4): 361–382, 2000.
  • [2] G. Strang, G. Fix. An Analysis of the Finite Element Method . Wellesley-Cambridge Press, second edition, 2008.
  • [3] J.R. Shewchuk. What is a good linear finite element? Interpolation, conditioning, anisotropy, and quality measures (preprint). University of California at Berkeley , 2002.
  • [4] L.A. Freitag, C. Ollivier-Gooch. Tetrahedral mesh improvement using swapping and smoothing. Int. J. Numer. Meth. Eng., 40 (21): 3979–4002, 1997.
  • [5] B.M. Klingner, J.R. Shewchuk. Aggressive tetrahedral mesh improvement. In Proceedings of the 16th International Meshing Roundtable, 3–23, 2007.
  • [6] J.M. Escobar, R. Montenegro, E. Rodriguez, J.M. Gonzalez-Yuste. Smoothing and local refinement techniques for improving tetrahedral mesh quality. Comput. Struct., 83 (28–30): 2423–2430, 2005.
  • [7] M.-C. Rivara. New longest-edge algorithms for the refinement and/or improvement of unstructured triangulations. Int J Numer Methods Eng, 40 (18): 3313–3324, 1997.
  • [8] P.J. Frey, P.-L. George. Mesh Generation. Wiley-ISTE, second edition, 2008.
  • [9] S.H. Lo. A new mesh generation scheme for arbitrary planar domains. Int. J. Numer. Meth. Eng., 21 (8): 1403–1426, 1985.
  • [10] D.A. Field. Laplacian smoothing and Delaunay triangul ations. Commun. Appl. Numer. Methods, 4 (6): 709–712, 1988.
  • [11] L.A. Freitag. On combining Laplacian and optimization -based mesh smoothing techniques. In Trends in Unstructured Mesh Generation, 37–43, 1997.
  • [12] M. Zhihong, M. Lizhuang, Z. Mingxi, L. Zhong. A modified Laplacian smoothing approach with mesh saliency. Lect. Notes Comput. Sci., 4073 : 105–113, 2006.
  • [13] N. Amenta, M. Bern, D. Eppstein. Optimal point placement for mesh smoothing. J. Algorithms, 30 (2): 302–322, 1999.
  • [14] H. Xu, T.S. Newman. An angle-based optimization approach for 2D finite element mesh smoothing. Finite Elem. Anal. Des., 42 (13): 1150–1164, 2006.
  • [15] Y. Zhang, C. Bajaj, G. Xu. Surface smoothing and quality improvement of quadrilateral/hexahedral meshes with geometric flow. Commun. Numer. Methods Eng., 25 (1): 1–18, 2009.
  • [16] L. Chen. Mesh smoothing schemes based on optimal Delaunay triangulations. In Proceedings of the 13th International Meshing Roundtable, 109–120, 2004.
  • [17] L. Freitag Diachin, P. Knupp, T. Munson, S. Shontz. A comparison of two optimization methods for mesh quality improvement. Eng. Comput., 22 (2): 61–74, 2006.
  • [18] A. Egemen Yilmaz, M. Kuzuoglu. A particle swarm optimization approach for hexahedral mesh smoothing. Int. J. Numer. Meth. Fl., 60 (1): 55–78, 2009.
  • [19] S. Kulovec, L. Kos, J. Duhovnik. Mesh smoothing with global optimization under constraints. Strojniski vestnik – J. Mech. Eng., 57 (7–8): 555–567, 2011.
  • [20] Y. Sirois, J. Dompierre, M.-G. Vallet, F. Guibault. Hybrid mesh smoothing based on Riemannian metric non-conformity minimization. Finite Elem. Anal. Des., 46 (1–2): 47–60, 2010.
  • [21] P.M. Knupp. Algebraic mesh quality metrics. SIAM J. Sci. Comput., 23 (1): 193–218, 2001.
  • [22] P.M. Knupp. Remarks on mesh quality. In Proceedings of the 45th AIAA Aerospace Sciences Meeting and Exhibit, 2007.
  • [23] X. Jiao, D. Wang, H. Zha. Simple and effective variational optimization of surface and volume triangulations. In Proceedings of the 17th International Meshing Roundtable, 315–332, 2008.
  • [24] D. Vartziotis, T. Athanasiadis, I. Goudas, J. Wipper. M esh smoothing using the geometric element transformation method. Comput. Methods Appl. Mech. Eng., 197 (45–48): 3760–3767, 2008.
  • [25] D. Vartziotis, J. Wipper. The geometric element transformation method for mixed mesh smoothing. Eng. Comput., 25 (3): 287–301, 2009.
  • [26] D. Vartziotis, J. Wipper, B. Schwald. The geometric element transformation method for tetrahedral mesh smoothing. Comput. Methods Appl. Mech. Eng., 199 (1–4): 169–182, 2009.
  • [27] D. Vartziotis, J. Wipper. Characteristic parameter sets and limits of circulant Hermitian polygon transformations. Linear Algebra Appl., 433 (5): 945–955, 2010.
  • [28] D. Vartziotis, J. Wipper. Fast smoothing of mixed volume meshes based on the effective geometric element transformation method. Comput. Methods Appl. Mech. Eng., 201–204 : 65–81, 2012.
  • [29] D. Vartziotis, S. Huggenberger. Iterative geometric triangle transformations. Elemente der Mathematik, 67 (2): 68–83, 2012.
  • [30] D. Vartziotis, J. Wipper, M. Papadrakakis. Improving mesh quality and finite element solution accuracy by GETMe smoothing in solving the Poisson equation. Finite Elem. Anal. Des., 66: 36–52, 2013.
  • [31] D. Vartziotis, J. Wipper. Classification of symmetry generating polygon-transformations and geometric prime algorithms. Mathematica Pannonica , 20 (2): 167–187, 2009.
  • [32] D. Vartziotis, J. Wipper. A dual element based geometric element transformation method for all-hexahedral mesh smoothing. Comput. Methods Appl. Mech. Eng., 200 (9–12): 1186–1203, 2011.
  • [33] B. Stroustrup. The C++ Programming Language. Addison-Wesley, third edition, 2000.
  • [34] B.W. Kernighan, D.M. Ritchie. The C Programming Language . Prentice Hall, 1988.
  • [35] Khronos OpenCL Working Group. The OpenCL Specification, Version 1.2, Document Revision 15. Khronos Group, 2011.
  • [36] NVIDIA CUDA C Programming Guide, Version 4.2, NVIDIA, 2012.
  • [37] OpenACC Application Programming Interface, Version 1.0. OpenACC-Standard.org, 2011.
  • [38] M. Papadrakakis, G. Stavroulakis, A. Karatarakis. A new era in scientific computing: Domain decomposition methods in hybrid CPU-GPU architectures. Comput. Methods Appl. Mech. Eng., 200 (13–16): 1490–1508, 2011.
  • [39] OpenMP Architecture Review Board. OpenMP Application Program Interface, Version 3.1, 2011.
  • [40] Mesquite: mesh quality improvement toolkit, version 2.2.0. http://www.cs.sandia.gov/optimization/knupp/Mes-quite.html, accessed June 20, 2012.
  • [41] M. Brewer, L. Freitag Diachin, P. Knupp, T. Leurent, D. Melander. The Mesquite Mesh Quality Improvement Toolkit. In Proceedings of the 12th International Meshing Roundtable, 239–250, 2003.
  • [42] MPI: A Message-Passing Interface Standard, Version 2.2. Message Passing Interface Forum, University of Tennessee, Knoxville, Tennessee, 2009.
  • [43] GNU compiler collection, version 4.7.1. http://gcc.g nu.org/, accessed July 4, 2012.
  • [44] Drexel University, Geometric & Intelligent Computing Laboratory model repository. http://edge.cs.dre-xel.edu/repository/, accessed July 3, 2012.
  • [45] Aim@Shape mesh repository. http://shapes.aim-at-shape.net/, accessed July 17, 2012.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-7d130f35-de06-4a87-9cfb-4e00f244cc1b
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.