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Akcelik, V., Bielak, J., Biros, G., Epanomeritakis, I., Fernandez, A., Ghattas, O., et al. (2003) High Resolution Forward and Inverse Earthquake Modeling on Terasacale Computers. Proceedings of SC2003, Phoenix, 15-21 November 2003.

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• TITLE: Adaptive Reduced Basis Methods Applied to Structural Dynamic Analysis

  AUTHORS: Yonghui Huang, Yi Huang

  KEYWORDS: Reduced Basis Method, Mode Superposition, Direct Integration, Greedy Algorithm, Structural Dynamic Problem

  JOURNAL NAME: American Journal of Computational Mathematics, Vol.5 No.3, September 7, 2015

  ABSTRACT: The reduced basis methods (RBM) have been demonstrated as a promising numerical technique for statics problems and are extended to structural dynamic problems in this paper. Direct step-by-step integration and mode superposition are the most widely used methods in the field of the finite element analysis of structural dynamic response and solid mechanics. Herein these two methods are both transformed into reduced forms according to the proposed reduced basis methods. To generate a reduced surrogate model with small size, a greedy algorithm is suggested to construct sample set and reduced basis space adaptively in a prescribed training parameter space. For mode superposition method, the reduced basis space comprises the truncated eigenvectors from generalized eigenvalue problem associated with selected sample parameters. The reduced generalized eigenvalue problem is obtained by the projection of original generalized eigenvalue problem onto the reduced basis space. In the situation of direct integration, the solutions of the original increment formulation corresponding to the sample set are extracted to construct the reduced basis space. The reduced increment formulation is formed by the same method as mode superposition method. Numerical example is given in Section 5 to validate the efficiency of the presented reduced basis methods for structural dynamic problems.