Abstract
• Wave dispersion error with both the spatial isogeometric elements and direct time integration method is first studied. • New generalized numerical algorithm is proposed to calculate the dispersion errors. • New isogeometric analysis for wave problems are proposed with desirable accuracy and computation efficiency. A uniform quadratic b-spline isogeometric element is exclusively considered for wave propagation problem with the use of desirable implicit time integration scheme. A generalized numerical algorithm is proposed for dispersion analysis of one-dimensional (1-D) and two-dimensional (2-D) wave propagation problems where the quantified influence of the defined CFL number on wave velocity error is analyzed and obtained. Meanwhile, the optimal CFL (Courant–Friedrichs–Lewy) number for the proposed 1-D and 2-D problems is suggested. Four representative numerical simulations confirm the effectiveness of the proposed method and the correctness of dispersion analysis when appropriate spatial element size and time increment are adopted. The desirable computation efficiency of the proposed isogeometric method was confirmed by conducting time cost and calculation accuracy analysis of a 2-D numerical example where the referred FEM was also tested for comparison.
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