A Mathematical Analysis of Atomistic to Continuum Coupling Methods
نویسنده
چکیده
a. Mathematical upscaling: derivation of coarse-scale equations directly from atomistic equations using Generalized Mathematical Homogenization theory (Fish, Chen, Li, 2007). b. Computational upscaling: reducing the complexity of solving an atomistic problem to a manageable size that can be adapted based on available computational resources. Our model reduction approach is based on the space-time multilevel method (Li, Waisman, Fish, 2007). In the regions where the Generalized Mathematical Homogenization is estimated to be inaccurate (Nuggehally et al, 2007), a concurrent AtC bridging approach is employed (Fish et al, 2007) ( Badia et al, 2007). c. Model calibration: solving an inverse problem for calibration of fine scale parameters (interatomic potentials) by minimizing the error between the experimental data and multiscale simulations (Oskay, Fish, 2007).
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