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Parallel mesh adaptation for high-order finite element methods with curved element geometry

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Abstract

This paper presents 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 that explicitly consider the influence of the curved mesh entities on element shape. Applications of the curved mesh adaptation procedure have been developed to support the parallel automated adaptive accelerator simulations at SLAC National Accelerator Laboratory.

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Notes

  1. Note that this criterion is different from the one being discussed in Sect. 3.3 and can be used only in such particular cases that the element is in fact valid since it could eventually stop. In other cases, the incremental criterion should be used.

Abbreviations

\(\Upomega_\upsilon\) :

Domain of interest, υ = G, M, where G denotes the geometric model and M denotes the mesh model

\(\partial \Upomega_\upsilon\) :

Boundary of the domain \(\Upomega_\upsilon\)

G d i :

ith geometric model entity of dimension d.

M d i :

ith mesh entity of dimension d. d = 0, 1, 2, 3 and represents mesh vertex, edge, face and region, respectively.

\(\sqsubset\) :

Classification symbol used to indicate the association of one or more entities from the mesh model M with the geometric model G.

M d :

Unordered group of mesh topological entities of dimension d.

\(M_i^{d_i}\{M_j^{d_j}\}\) :

First-order adjacency sets of individual mesh entity \(M_i^{d_i}\) defined as the set of mesh entities of dimension d j adjacent to mesh entity \(M_i^{d_i}\).

P (n) i (M d j ):

the ith control point of a nth order Bézier polynomial associated with the mesh entity M d j .

X (n)(M 3 j ):

the nth order Bézier polynomial representation of a general tetrahedron.

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Acknowledgments

This work is supported by the US Department of Energy. The RPI portions of the work are supported by the SciDAC Grant No. DE-FC02-06ER25769 and a DOE SBIR Grant No. BEE101/DE-SC0002089. The Simmetrix portions of the work are supported by the SBIR grant. The authors would like to thank Dr Lixin Ge, Dr Cho-Kuen Ng and Dr Kwok Ko at SLAC National Accelerator Laboratory for providing the accelerator models and access to the ACE3P solvers.

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Authors and Affiliations

  1. Scientific Computation Research Center, Rensselaer Polytechnic Institute, Troy, NY, USA

    Qiukai Lu & Mark S. Shephard

  2. Simmetrix Inc, Clifton Park, NY, USA

    Saurabh Tendulkar & Mark W. Beall

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  1. Qiukai Lu
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  2. Mark S. Shephard
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  4. Mark W. Beall
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Correspondence to Qiukai Lu.

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Lu, Q., Shephard, M.S., Tendulkar, S. et al. Parallel mesh adaptation for high-order finite element methods with curved element geometry. Engineering with Computers 30, 271–286 (2014). https://doi.org/10.1007/s00366-013-0329-7

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