Exploring the inherent capacity of the multiresolution finite wavelet domain method to provide convergence indicators in transient dynamic simulations

The advantages of the multiresolution finite wavelet domain method in terms of convergence speed and solution localization capabilities have been demonstrated in dynamic simulations of one- and two-dimensional solids. The first step in the multiresolution procedure entails a coarse solution, which is subsequently enriched by the calculation of finer solutions, so convergence is achieved without discarding the previous results obtained at coarser resolutions. In this work, the multiresolution structure of the method is thoroughly explored to develop two novel convergence indicators which can provide error indices for the first two steps of the process and focus the fine solutions on specific subregions, enhancing accuracy and computational speed. The first convergence indicator is based on force residuals and the second relies on the maximum ratio of the fine to total solution. Detailed examination of the multiresolution components results in profound comprehension of the way they participate to the total solution. Based on repeated observations, it is deduced that the participation of fine components to the total solution constitute metrics of convergence, permitting the termination of the hierarchical analysis without requiring convergence checks. The proposed convergence indicators can guide targeted refinement techniques and may provide the basis for a new computational paradigm.