Abstract
An improved peak-selection algorithm is proposed for mesh deformation. With the use of the newly derived block-based recurrence Cholesky (BRC) decomposition scheme, the computational complexity for solving the linear algebraic system in the data reducing procedure is reduced from O(Nc4/Np) to O(Nc3), where Nc denotes the total number of support nodes and Np denotes the number of support nodes added at a time. Because the BRC decomposition scheme introduces block matrices, it involves more multiplications between matrices rather than between vectors. Due to the fact that the computation of matrix multiplication is more efficient with the use of the linear algebraic library, the efficiency for solving the linear algebraic system can be further increased. Two deformation problems are applied to validate the algorithm. The results show that it significantly increases the efficiency for solving the linear algebraic system, allowing the time consumption of this process to be reduced to only one sixth. Moreover, the efficiency will increase with the mesh scale. The results also show that it allows the efficiency of the data reducing procedure to improve by two times. Furthermore, it is found that only 1.094 s in total is required to solve the linear algebraic system with serial computing by constructing a set of as many as 2999 support nodes in a large-scale mesh deformation problem. It is indicated that the bottleneck of mesh deformation caused by inefficient parallel computing for solving the linear algebraic system can thus be removed. This makes the algorithm favorable for large-scale engineering applications.
Highlights
Mesh deformation is an important area of computational fluid dynamics (CFD) research
Unlike other algorithms31 in which the errors are computed only at the selected boundary nodes, the errors of all boundary nodes are computed after m iterations in the GCB greedy algorithm, which can contribute to error control and ensure accuracy. Another challenge for radial basis functions (RBFs)-based mesh deformation is that the computational complexity for solving the linear algebraic system is as high as O(Nc4), where Nc denotes the number of support nodes
The based recurrence Cholesky (BRC) decomposition scheme is able to make the computational complexity for solving the linear algebraic system reduce from O(Nc4/Np∗) to O(Nc3) that is the same as the recurrence Cholesky (RC) one
Summary
Mesh deformation is an important area of computational fluid dynamics (CFD) research. The above-mentioned steps are iteratively conducted until the maximum error is within allowance With this procedure, the greedy algorithm greatly reduces the number of support nodes and the amount of computation for solving the linear algebraic system, which contributes to its use in practice. Unlike other algorithms in which the errors are computed only at the selected boundary nodes, the errors of all boundary nodes are computed after m iterations in the GCB greedy algorithm, which can contribute to error control and ensure accuracy Another challenge for RBF-based mesh deformation is that the computational complexity for solving the linear algebraic system is as high as O(Nc4), where Nc denotes the number of support nodes. The following sections first introduce the peak-selection algorithm in detail (section II), derive the BRC decomposition scheme (section III), and apply the ONERA M6 wing and the High Reynolds Number Aero-Structural Dynamics (HIRENASD) wind tunnel configuration for validation (section IV)
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