Domain Decomposition Approach For Atomistic-to-Continuum Coupling Models

Atomistic-to-Continuum(A/C)coupling algorithms are in focus of researchers,as solely atomistic or solely continuum model can no longer serve as an adequate method in studying material domains.A/C methods enable studying atomistic effects in places where these may be important,but in the same time they limit the amount of calculation by applying the continuum model elsewhere.To start with,we give a brief introduction to line search methods and finite element methods which are background knowledge for atomistic-to-continuum coupling algorithms.Then we commit various approximation errors during the construction of a/c coupling methods.At last a specific alternating Schwarz algorithm is considered,as well as Domain Decomposition approach.We also carry out a convergence and error analysis.