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There are numerous large-scale applications requiring mesh adaptivity, e.g., computational fluid dynamics and weather prediction. Parallel processing is needed for simulations involving large-scale adaptive meshes. In this paper, we propose a parallel variational mesh quality improvement algorithm for use with distributed memory machines. Our method parallelizes the serial variational mesh quality improvement method by Huang and Kamenski. Their approach is based on the use of the Moving Mesh PDE method to adapt the mesh based on the minimization of an energy functional for mesh equidistribution and alignment. This leads to a system of ordinary differential equations (ODEs) to be solved which determine where to move the interior mesh nodes. An efficient solution is obtained by solving the ODEs on subregions of the mesh with overlapped communication and computation. Strong and weak scaling experiments on up to 128 cores for meshes with up to 160M elements demonstrate excellent results.
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This content will become publicly available on March 1, 2026
Proceedings of the 2025 SIAM International Meshing Roundtable; Parallelization of the Finite Element-based Mesh Warping Algorithm Using Hybrid Parallel Programming
Warping large volume meshes has applications in biomechanics, aerodynamics, image processing, and cardiology. However, warping large, real-world meshes is computationally expensive. Existing parallel implementations of mesh warping algorithms do not take advantage of shared-memory and one-sided communication features available in the MPI-3 standard. We describe our parallelization of the finite element-based mesh warping algorithm for tetrahedral meshes. Our implementation is portable across shared and distributed memory architectures, as it takes advantage of shared memory and one-sided communication to precompute neighbor lists in parallel. We then deform a mesh by solving a Poisson boundary value problem and the resulting linear system, which has multiple right-hand sides, in parallel. Our results demonstrate excellent efficiency and strong scalability on up to 32 cores on a single node. Furthermore, we show a 33.9% increase in speedup with 256 cores distributed uniformly across 64 nodes versus our largest single node speedup while observing sublinear speedups overall.
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- PAR ID:
- 10621870
- Editor(s):
- Si, Hang; Shepherd, Kendrick M; Zhang, Yongjie Jessica
- Publisher / Repository:
- Society for Industrial and Applied Mathematics
- Date Published:
- ISBN:
- 978-1-61197-857-5
- Page Range / eLocation ID:
- 140-153
- Subject(s) / Keyword(s):
- mesh warping, parallel computing, hybrid parallel programming, MPI-3, shared and distributed memory, strong scalability
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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