Domain Decomposition Methods for Multiscale Modeling

Domain decomposition methods (DDM), which originate from the Schwarz alternating method to solve elliptic partial different equations, are largely extended and prove to have increasing influences on multiscale modeling of materials. We discuss some of the important extensions of the DDM in the fields of multiscale modeling for soft materials such as simple and complex fluids. To this end, we typically model the fluids in two or more levels of detail, which exploits the computational efficiency of the coarse model and physical accuracy of the fine description. For simple fluids, we take a continuum perspective to couple the molecular dynamics (MD) and Navier-Stokes equations by matching the state variables and/or fluxes across the hybrid interface. For complex fluids, we take a discrete perspective to encompass the complex structure of the molecules and couple the MD with coarse-grained MD by interpolating the forces between the two levels of descriptions.