Parallel Curved Mesh Adaptation for Large Scale High-Order Finite Element Simulations

This paper presents the development of a parallel adaptive mesh control procedure designed to operate with high-order finite element analysis packages to enable large scale automated simulations on massively parallel computers. The curved mesh adaptation procedure uses curved entity mesh modification operations. Applications of the curved mesh adaptation procedure have been developed to support the parallel automated adaptive accelerator simulations at SLAC National Accelerator Laboratory.

[1]  Sailkat Dey,et al.  Curvilinear Mesh Generation in 3D , 1999, IMR.

[2]  Patrick M. Knupp,et al.  Introducing the target-matrix paradigm for mesh optimization via node-movement , 2012, Engineering with Computers.

[3]  Mark S. Shephard,et al.  3D anisotropic mesh adaptation by mesh modification , 2005 .

[4]  Christophe Geuzaine,et al.  Geometrical validity of curvilinear finite elements , 2011, J. Comput. Phys..

[5]  J. Z. Zhu,et al.  The superconvergent patch recovery and a posteriori error estimates. Part 1: The recovery technique , 1992 .

[6]  Robert M. O'Bara,et al.  Construction of near optimal meshes for 3D curved domains with thin sections and singularities for p-version method , 2010, Engineering with Computers.

[7]  Mark S. Shephard,et al.  Parallel refinement and coarsening of tetrahedral meshes , 1999 .

[8]  Paul-Louis George,et al.  Construction of tetrahedral meshes of degree two , 2012 .

[9]  Leif Kobbelt,et al.  Convergence of subdivision and degree elevation , 1994, Adv. Comput. Math..

[10]  Mark S. Shephard,et al.  Accounting for curved domains in mesh adaptation , 2003 .

[11]  William Roshan Quadros,et al.  Proceedings of the 20th International Meshing Roundtable , 2012 .

[12]  A. U.S.,et al.  Curved Mesh Generation and Mesh Refinement using Lagrangian Solid Mechanics , 2009 .

[13]  Frédéric Alauzet,et al.  Parallel anisotropic 3D mesh adaptation by mesh modification , 2006, Engineering with Computers.

[14]  Thomas W. Sederberg,et al.  COMPUTER AIDED GEOMETRIC DESIGN , 2012 .

[15]  Patrick M. Knupp,et al.  Tetrahedral Element Shape Optimization via the Jacobian Determinant and Condition Number , 1999, IMR.

[16]  Ron Goldman,et al.  On the smooth convergence of subdivision and degree elevation for Bézier curves , 2001, Comput. Aided Geom. Des..

[17]  Robert M. O'Bara,et al.  Towards curvilinear meshing in 3D: the case of quadratic simplices , 2001, Comput. Aided Des..

[18]  B. Joe,et al.  Relationship between tetrahedron shape measures , 1994 .

[19]  I. Babuska,et al.  Finite Element Analysis , 2021 .

[20]  Misbah Mubarak,et al.  A parallel ghosting algorithm for the flexible distributed mesh database , 2013, Sci. Program..

[21]  Mark S. Shephard,et al.  Moving curved mesh adaptation for higher-order finite element simulations , 2010, Engineering with Computers.

[22]  Gerald Farin,et al.  Curves and surfaces for computer aided geometric design , 1990 .