Discrete-to-continuum bridging based on multigrid principles Original Research Article

The paper presents a new concurrent multiscale approach based on multigrid principles with intent of solving large molecular statics and molecular dynamics systems. We show that the coarse model effective stiffness matrix obtained by variational restriction of the atomistic model effective stiffness matrix coincides with the effective stiffness matrix of the equivalent continuum scale model. The equivalent continuum model is defined for both molecular statics and molecular dynamics cases and theoretical estimates of the rate of convergence for the proposed concurrent multiscale approach are obtained.