Purpose -The purpose of this paper is to present a novel strategy used for acceleration of free-vibration analysis, in which the hierarchical matrices structure and Compute Unified Device Architecture (CUDA) platform is applied to improve the performance of the traditional dual reciprocity boundary element method (DRBEM). Design/methodology/approach -The DRBEM is applied in forming integral equation to reduce complexity. In the procedure of optimization computation, ℋ-Matrices are introduced by applying adaptive cross-approximation method. At the same time, this paper proposes a high-efficiency parallel algorithm using CUDA and the counterpart of the serial effective algorithm in ℋ-Matrices for inverse arithmetic operation. Findings -The analysis for free-vibration could achieve impressive time and space efficiency by introducing hierarchical matrices technique. Although the serial algorithm based on ℋ-Matrices could obtain fair performance for complex inversion operation, the CUDA parallel algorithm would further double the efficiency. Without much loss in accuracy according to the examination of the numerical example, the relative error appeared in approximation process can be fixed by increasing degrees of freedoms or introducing certain amount of internal points. Originality/value -The paper proposes a novel effective strategy to improve computational efficiency and decrease memory consumption of free-vibration problems. ℋ-Matrices structure and parallel operation based on CUDA are introduced in traditional DRBEM. Accelerationof freevibrations analysis for engineers. Compared with FEM and FDM, the BEM, due to the advantages such as dimensionality reduction, high precision, is much more suitable for fast pretreatment, self-adaptive structural analysis in engineering software. That leads to the possibility for integrating engineering analysis process into CAD, as discussed by Wang (2009) and Wang et al. (2013) about their research in elastostaics. Meanwhile, boundary face method is an efficient solution method to the boundary integral equation and makes direct use of the B-rep data of a solid entity that available in all CAD packages (Zhang et al., 2009;Qin et al., 2010). In this paper, the efficiency of new strategy with BEM for free-vibration problems is discussed. Rizzo introduced boundary integral element method into elastostatics first (Rizzo, 1967), which marks the beginning of systematic development of BEM for numerical problems. Banaugh and Goldsmith (1963) applied BEM into dynamics for steady plane elastodynamics, Tai and Shaw (1974) and De Mey (1976) utilized BEM for free-vibration problems. Many researchers, such as Niwa et al., Beskos, Dominguez, Friedman, made effort for applying BEM into elastodynamics either time-domain or frequency-domain (Rizos and Karabalis, 1998;Michel, 1987;Banerjee et al., 1986;Karabalis and Beskos, 1984, 1985Dominguez and Roesset, 1978a. Nevertheless, the non-symmetric, fully populated matrix and low stability in numerical results of BEM would result in huge workload in co...
Finite Element Method (FEM1) is pervasively used in most of 3D product design analysis, in which Computer Aided Design (CAD) models need to be converted in to mesh models first and then enriched with some material features and boundary conditions data, etc. The interaction between CAD models and FEM models is intensive. Boundary Element Method (BEM) has been expected to be advantageous in large-scale problems in recent years owing to its reduction of the dimensionality and its reduced complexity in mesh generation. However, the BEM application has so far been limited to relatively small problems due to the memory and computational complexity for matrix buildup are O(N2). The fast multipole BEM (FMBEM) combined with BEM and fast multipole method (FMM) can overcome the defect of the traditional BEM, and provides an effective method to solve the large-scale problem. Combining GPU parallel computing with FMBEM can further improve its efficiency significantly. Based on the three-dimensional elastic mechanics problems, the parallelisms of the multipole moment (ME), multipole moment to multipole moment (M2M) translation, multipole moment to local expansion (M2L) translation, local expansion to local expansion (L2L) translation and near-field direct calculation were analyzed respectively according to the characteristics of the FMM, and the parallel strategies under CUDA were presented in this paper. Three main major parts are included herein: (1) FMBEM theory in 3D elastostatics, (2) the parallel FMBEM algorithm using CUDA, and (3) comparison the GPU parallel FMBEM with BEM, FEM and FMBEM respectively by engineering examples. Numerical example results show the 3D elastostatics GPU FMBEM not only can speed up the boundary element calculation process, but also save memory which can be effective to solve the large-scale engineering problems.
The translation from multipole moments to local moments (M2L) in the fast multipole boundary element method (FMBEM) costs too much time; we compare three methods of M2L optimization from the three following aspects: accuracy, efficiency and memory usage with an engineering numerical example, and then present a GPU parallel algorithm using CUDA for one of the front three methods which transfers child cell's coefficients to their father cell, meanwhile, improve the tree structure by redefining the whole cells in different levels which can avoid writing data conflict in the parallel strategy. Finally, we use the threedimensional elastic BEM problems of chassis parts to verify the algorithm, and the result shows that the accelerating effect of this method is significant.
Finite Element Method (FEM) is pervasively used in most of 3D elastostatic numerical simulations, in which Computer Aided Design (CAD) models need to be converted into mesh models first and then enriched with semantic data (e.g. material parameters, boundary conditions). The interaction between CAD models and FEM models stated above is very intensive. Boundary Element Method (BEM) has been used gradually instead of FEM in recent years because of its advantage in meshing. BEM can reduce the dimensionality of the problem by one so that the complexity in mesh generation can be decreased greatly. In this paper, we present a Boundary Element parallel computation method for 3D elastostatics. The parallel computation runs on Graphics Processing Unit (GPU) using Computing Unified Device Architecture (CUDA). Three major components are included in such method: (1) BEM theory in 3D elastostatics and the boundary element coefficient integral methods, (2) the parallel BEM algorithm using CUDA, and (3) comparison the parallel BEM using CUDA with conventional BEM and FEM respectively by examples. The dimension reduction characteristics of BEM can dispose the 3D elastostatic problem by 2D meshes, therefore we develop a new faceting function to make the ACIS facet meshes suitable for Boundary Element Analysis (BEA). The examples show that the GPU parallel algorithm in this paper can accelerate BEM computation about 40 times.
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