Design Sensitivity Analysis of Coupled MD-Continuum Systems Using Bridging Scale Approach

We present a design sensitivity analysis(DSA) method for multiscale problems based on bridging scale decomposition. In this paper, we utilize a bridging scale method for the coupled system analysis. Since the analysis of full MD systems requires huge amount of computational costs, a coupled system of MD-level and continuum-level simulation is usually preferred. The information exchange between the MD and continuum levels is taken place at the MD-continuum boundary. In the bridging scale method, a generalized Langevin equation(GLE) is introduced for the reduced MD system and the GLE force using a time history kernel is applied at the boundary atoms in the MD system. Therefore, we can separately analyze the MD and continuum level simulations, which can accelerate the computing process. Once the simulation of coupled problems is successful, the need for the DSA is naturally arising for the optimization of macro-scale design, where the macro scale performance of the system is maximized considering the micro scale effects. The finite difference sensitivity is impractical for the gradient based optimization of large scale problems due to the restriction of computing costs but the analytical sensitivity for the coupled system is always accurate. In this study, we derive the analytical design sensitivity to verify the accuracy and applicability to the design optimization of the coupled system.