Many physical processes of great importance to science and technology require numerical methods that couple modeling of the interactions of individual atoms in small regions with modeling of the interactions among larger sets of atoms (continuum models) in the remaining regions. An important example is crack growth, where practical predictive models require the accuracy of the detailed interaction of the atoms in a small region near the crack tip, along with the efficiency of continuum modeling in the larger surrounding material.
Although the greatest accuracy could be achieved by a computer simulation of the interactions of all of the atoms in the material, the large number of atoms in the material makes this approach infeasible for even the fastest computers. The quasicontinuum method can make possible such simulations without sacrificing the accuracy needed for reliable prediction by coupling an atomistic model in the neighborhood of the crack tip with a continuum model in the surrounding material. The continuum model achieves the desired accuracy with a major reduction in computational work by replacing the large numbers of atoms in selected regions with representative atoms.
The principal investigator proposes to develop analysis and adaptive algorithms for quasicontinuum methods that will ensure their reliability and improve their efficiency. Theory and rigorous numerical experiments will be developed to determine the most accurate and efficient atomistic-continuum coupling. The development of the quasicontinuum method has the potential to facilitate the design of new materials better able to resist failure and having other properties important for science and technology.
