An improved peak-selection algorithm using block-based recurrence Cholesky decomposition for mesh deformation

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.