Evaluating the coupling quality of domain decomposition methods
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Domain decomposition methods are widely used in computational mechanics to efficiently simulate systems which are coupled by domains computed through different modeling strategies. We introduce a mapping approach [1] designed to thoroughly evaluate the coupling quality of such methods, particularly when bridging different types of computational domains as, e.g., continua and particle-based regions. Our method facilitates a comparison of strain distributions across one loading axis of coupled domains, offering a robust measure of coupling effectiveness. This involves slicing a three-dimensional simulation domain into smaller segments, computing weighted mean displacements of particle and node displacements, their standard deviations, and deriving strain measures from these quantities. By establishing a one-dimensional reference framework, we can directly assess the accuracy and consistency of the coupled simulation results. This comparison is leveraged by the computation of different strain error measures, providing insights into both local and overall coupling performance. We demonstrate the effectiveness of this technique [2] by the example of the Capriccio method, a concurrent multiscale domain decomposition technique: The Capriccio method's ability to accurately couple finite element (FE) and molecular dynamics (MD) domains is assessed and criticized through detailed strain analysis on various FE-MD coupled materials. In addition, we provide an insight into how this analysis has contributed to the Capriccio method’s methodological improvement. By our results, we show a promising evaluation method and thus pave the way for improved computational strategies for various domain decomposition methods. As such, we provide a generalizable framework for quantifying the coupling quality in multiscale simulations, offering a valuable tool for both method development and the optimization of existing domain decomposition techniques.