| Full atomistic Molecular Dynamics (MD) simulations are very accurate but too costly; however, atomistic resolution is not actually required everywhere in many problems. For this reason, a concurrent atomistic/continuum coupling method called Multiresolution Molecular Mechanics (MMM) has been developed. The method employs atomistic resolution in the localized regions of interest and coarser continuum description elsewhere. A number of such multiscale methods have been developed but they fail to demonstrate consistency, accuracy, adaptivity, flexibility, and efficiency all in one. The goal of this research is thus to develop a multiscale method that possesses these properties to outperform the MD method by 1) formulating new dynamics equations under the MMM framework, 2) developing an adaptivity scheme, and 3) implementing efficient algorithms for the method. First, the derivation of the governing MMM equations from a Hamiltonian that approximates the energy of the original system is presented. Second, the adaptivity analysis of the MMM method is presented. Refinement and coarsening mechanisms of the adaptivity scheme are described in detail and the step-by-step procedures are outlined. Third, the implementation and efficiency of the MMM software is presented. The structure of the software along with the associated technologies is introduced. Many improvements that contribute to the efficiency of the MMM software are described and demonstrated through benchmark tests. The efficiency of the software is found to be as good as one of the best state-of-the-art MD codes, i.e., LAMMPS. The speed-up of the code in proportion to reduction in the rep atom ratio is demonstrated. The scalability of the software is demonstrated and competing effects of multiscale modeling and parallelization is discussed. The dynamics, adaptivity, and efficiency of the method are demonstrated by numerical examples including wave and crack propagation, dislocation glide, nanoindentation, and modal analysis in 1/2/3 dimensions. All results agree well with the true full atomistic solutions. Ultimately, the MMM method demonstrates an improvement of 6.3 -- 8.3 times in efficiency over MD method by means of a combined reduction in simulation time and number of processors. In conclusion, this dissertation shows that the MMM method is consistent, accurate, flexible, and efficient. |
