Summary
When applying higher order finite elements to curved 3D domains in large-scale accelerator simulations, complexities that arise include needing valid curved finite elements and the capability to track the movement of mesh refinement in the critical domains. This paper presents a procedure which combines Bézier mesh curving and size driven mesh adaptation technologies to address those requirements. The intelligent selection of local mesh modifications to eliminate invalid curved elements and properly control the size distribution are the two key technical components. The procedure has been successfully applied by SLAC to generate 3D moving curved meshes in the large-scale electromagnetic modeling of next generation accelerator designs. The results demonstrated that valid curvilinear meshes not only make the time domain simulations more reliable but also improve the computational efficiency up to 30%.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Babuska, I., Szabo, B.A., Katz, I.N.: The p-version of the finite element method. Int. J. Numer. Meth. Engng. 18(3), 515–545 (1981)
Luo, X.J., Shephard, M.S., Remacle, J.F., O’Bara, R.M., Beall, M.W., Szabo, B.A., Actis, R.: p-version mesh generation issues. In: Proc.of 11th Meshing Roundtable, pp. 343–354 (2002)
CUBIT geometry and mesh generation toolkit, http://cubit.sandia.gov
Simmetrix Inc. Enabling simulation-based design, http://www.simmetrix.com
Akcelik, V., Ko, K., Lee, L.Q., Li, Z.H., Ng, C.K., Xiao, L.L.: Shape determination for deformed electromagnetic cavities. J. Comput. Physics 227(3), 1722–1738 (2008)
Xiao, L., Adolphsen, C., Akcelik, V., Kabel, A., Ko, K., Lee, L.Q., Li, Z., Ng, C.K.: Modeling imperfection effects on dipole modes in TESLA cavity. In: Proc. of 2007 Particle Accelerator Conference (2007)
Lee, L.Q., Akcelik, V., Chen, S., Gl, X., Prudencio, E., Schussman, G., Uplenchwar, R., Ng, C., Ko, K., Luo, X.J., Shephard, M.S.: Enabling technologies for petascale electromagnetic accelerator simulation. J. of Physics 78(Conference Series), 012040 (2007)
Luo, X.J., Shephard, M.S., Obara, R.M., Nastasia, R., Beall, M.W.: Automatic p-version mesh generation for curved domains. Engineering with Computers 20, 265–285 (2004)
Luo, X.J.: An Automatic Adaptive Directional Variable p-Version Method in 3D Curved Domains. PhD Thesis, Rensselaer Polytechnic Institute, New York (2005)
Li, X.R., Shephard, M.S., Beall, M.W.: Accounting for curved domains in mesh adaptation. Int. J. Numer. Meth. Engng. 150, 247–276 (2003)
Li, X.R., Shephard, M.S., Beall, M.W.: 3D anisotropic mesh adaptation by mesh modification. Comp. Meth. Appl. Mech. Engng. 194, 4915–4950 (2005)
Seegyoung, E., Shephard, M.S.: Efficient distributed mesh data structure for parallel automated adaptive analysis. Engineering with Computers 22, 197–213 (2006)
Beall, M.W., Shephard, M.S.: A general topology-based mesh data structure. Int. J. Numer. Meth. Engng. 40(9), 1573–1596 (1997)
Farin, G.: Curves and Surfaces for Computer Aided Geometric Design. Academic Press, London (1992)
Sahni, O., Muller, J., Jansen, K.E., Shephard, M.S., Taylor, C.: Efficient anisotropic adaptive discretization of the cardiovascular system. Comput. Methods Appl. Mech. Engrg. 195(41-43), 5634–5655 (2006)
Wan, J.: An Automated Adaptive Procedure for 3D Metal Forming Simulations. PhD Thesis, Rensselaer Polytechnic Institute, New York (2006)
Chevaugeon, N., Hillewaert, K., Gallez, X., Ploumhans, P., Remacle, J.F.: Optimal numerical parameterization of discontinuous Galerkin method applied to wave propagation problems. J. Comput. Physics 223(1), 188–207 (2007)
Borouchaki, H., Hecht, F., Frey, P.J.: Mesh gradation control. Int. J. Numer. Meth. Engng. 43(6), 1143–1165 (1998)
Sun, D.K., Lee, J.F., Cendes, Z.: Construction of nearly orthogonal Nedelec bases for rapid convergence with multilevel preconditioned solvers. SIAM J. on Sci Comput. 23(4), 1053–1076 (2001)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Luo, X., Shephard, M.S., Lee, LQ., Ng, C., Ge, L. (2008). Tracking Adaptive Moving Mesh Refinements in 3D Curved Domains for Large-Scale Higher Order Finite Element Simulations. In: Garimella, R.V. (eds) Proceedings of the 17th International Meshing Roundtable. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-87921-3_35
Download citation
DOI: https://doi.org/10.1007/978-3-540-87921-3_35
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-87920-6
Online ISBN: 978-3-540-87921-3
eBook Packages: EngineeringEngineering (R0)