Acceleration of free-vibrations analysis with the Dual Reciprocity BEM based on ℋ-matrices and CUDA

Abstract

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...

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