Automatic Adaptive and Targeted Localized Refinement in Transient Structural Dynamic Simulations Using the Multiresolution Finite Wavelet Domain Method

ABSTRACT The multiresolution finite wavelet domain method has been meticulously studied in numerous wave propagation simulations, showing excellent convergence properties and very fast computing times. The multiresolution procedure always starts with the coarse solution, and then finer solutions can be superimposed on the coarse solution until convergence is achieved. Based on repetitive observations on the multiple resolution components of the method, two indices have been developed: a residual‐based convergence indicator that reveals convergence at the coarse solution and a displacement‐based convergence metric that indicates convergence on the next step of the multiresolution process. Those convergence metrics are both rapidly applicable and straightforward, and can also divulge the spatial and temporal domains in which the already obtained solution needs to be enhanced, using quantitative and robust threshold parameters. In this way, targeted and automatic adaptive refinement techniques are proposed for the specific localized enrichment of the solution, only in the specific grid points and timesteps that refinement is actually needed. This is feasible due to the multiresolution equations of motion that permit the partial computation of the fine solutions. Numerical case studies regarding wave propagation in rods and beams manifest the effectiveness and accuracy of the proposed refinement techniques, as well as the excellent performance of the suggested convergence indicators.