Received: 9 April 2017 Revised: 25 August 2017 Accepted: 27 September 2017
DOI: 10.1002/nme.5710
RESEARCH ARTICLE
A parallel multiselection greedy method for the radial basis
function–based mesh deformation
Chao Li Xinhai Xu Jinyu Wang Liyang Xu Shuai Ye Xuejun Yang
State Key Laboratory of High Performance
Computing, College of Computer,
National University of Defense
Technology, Changsha, 410073, China
Correspondence
Xinhai Xu, State Key Laboratory of High
Performance Computing, College of
Computer, National University of Defense
Technology, Changsha 410073, China.
Email: xuxinhai@nudt.edu.cn
Funding information
National Key Research and Development
Program of China, Grant/Award Number:
2016YFB0201301 ; Science Challenge
Project, Grant/Award Number: TZ2016002
Abstract
Greedy algorithm has been widely adopted for the point selection procedure
of radial basis function–based mesh deformation. However, in large deforma-
tion simulations with thousands of points selected, the greedy point selection
will be too expensive and thus become a performance bottleneck. To improve
the efficiency of the point selection procedure, a parallel multiselection greedy
method has been developed in this paper. Multiple points are selected at each
step to accelerate the convergence speed of the greedy algorithm. In addition, 2
strategies are presented to determine the specific selecting number. The paral-
lelization of the greedy point selection is realized on the basis of a master-slave
model, and a hybrid decomposition algorithm is proposed to address the load
imbalance problem. Numerical benchmarks show that both our multiselection
method and the parallelization could obviously improve the point selection effi-
ciency. Specifically, total speedups of 20 and 55 are separately obtained for the 3D
undulating fish with 10
6
cell mesh and the 3D rotating hydrofoil with 11 million
cell mesh.
KEYWORDS
CFD mesh deformation, greedy algorithm, multiselection, parallelization, radial basis function
1 INTRODUCTION
Computational fluid dynamic (CFD) simulation with moving boundary is widely involved in fluid-structure interaction
applications, such as the aerodynamic shape optimization and hydrodynamic analysis for aquatic motions.
1-3
In these
cases, to keep in accordance with the motion of the boundary, it is often necessary to update the computational mesh as
the simulation proceeds. Since the quality of the updated mesh has a significant impact on the accuracy of the numerical
results, an effective mesh deformation method is required essentially.
Many mesh deformation methods have been demonstrated in literature in terms of accuracy, efficiency, and robustness.
The spring analogy,
4,5
which models the mesh edges as elastic springs, is widely applied in complex-aircraft aerodynamic
analysis. However, this method requires the total mesh connectivity information and thus constructs an equation sys-
tem equal to the mesh size, which has made it too expensive for large-scale problems. The linear elasticity analogy,
6,7
which models the mesh cells as elastic solid, solves the mesh motion system on the basis of partial differential equations.
This method is robust for large deformation problems, but still at a price of high computational cost. The transfinite
interpolation
8,9
is a simple method with high efficiency, but it is not applicable for unstructured meshes. Recently,
the radial basis function (RBF) interpolation
10,11
is gaining interest for its high robustness and accuracy. On the basis of
the well-established RBFs, the mesh motion is calculated by interpolating the displacements of the boundary points to
Int J Numer Meth Engng. 2018;113:1561–1588. wileyonlinelibrary.com/journal/nme Copyright © 2017 John Wiley & Sons, Ltd. 1561