Performance Comparison and Workload Analysis of Mesh Untangling and Smoothing Algorithms
This paper compares methods for simultaneous mesh untangling and quality improvement that are based on repositioning the vertices. The execution times of these algorithms vary widely, usually with a trade-off between different parameters. Thus, computer p
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Abstract This paper compares methods for simultaneous mesh untangling and quality improvement that are based on repositioning the vertices. The execution times of these algorithms vary widely, usually with a trade-off between different parameters. Thus, computer performance and workloads are used to make comparisons. A range of algorithms in terms of quality metric, approach and formulation of the objective function, and optimization solver are considered. Among them, two new objective function formulations are proposed. Triangle and tetrahedral meshes and three processors architectures are also used in this study. We found that the execution time of vertex repositioning algorithms is more directly proportional to a new workload measure called mesh element evaluations than other workload measures such as mesh size or objective function evaluations. The comparisons are employed to propose a performance model for sequential algorithms. Using this model, the workload required by each mesh vertex is studied. Finally, the effects of processor architecture on performance are also analyzed.
1 Introduction Mesh optimizing techniques reduce the total time to solution and improve the accuracy of results of PDE solvers. Processing a mesh can spend up to 25% of the overall running time of a PDE-based application [5]. When a mesh element is inverted, standard finite element simulation algorithms cannot numerically solve the PDE, although some methods are being investigated to solve a PDE on a tangled mesh [20]. Thus, researchers and practitioners recommend untangling the mesh prior to analysis using commercial packages.
D. Benitez () · J. M. Escobar · R. Montenegro · E. Rodriguez SIANI Institute & DIS Department, University of Las Palmas de Gran Canaria, Las Palmas de Gran Canaria, Spain e-mail: [email protected] © Springer Nature Switzerland AG 2019 X. Roca, A. Loseille (eds.), 27th International Meshing Roundtable, Lecture Notes in Computational Science and Engineering 127, https://doi.org/10.1007/978-3-030-13992-6_21
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Vertex repositioning algorithms (VrPA) have been adopted by a vast majority of mesh optimization applications [6, 7, 17], including hex meshes [11, 14]. VrPA algorithms improve the quality of a mesh by moving its free vertices. They can be posed as numerical techniques in which the following parameters are considered [6]: objective function approach (A) and formulation (f ), element quality metric (q), minimization method (NM) and convergence or termination criteria (T C). The execution times of these numerical algorithms vary widely, usually with a trade-off between parameters. There are few studies that compare the performance of mesh optimization algorithms. Diachin et al. compared the performance of two VrPA algorithms [6]. One of them employed an inexact Newton method and the all-vertex approach to numerically optimize the global objective function. The other algorithm used a coordinate descent method and the single-vertex approach. Sastry and Shontz compared the per
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