Simulation systems, manufacturing systems, software products and controllers are provided with multi-scale modeling in which a coarse mesh and a fine mesh that models a stimulus are decoupled. The fine mesh can be moved within the coarse mesh with a cut and paste operation. The coarse mesh is updated by sparsely propagated effects through the coarse mesh. Simulations of the invention can be conducted in real-time, and be used as controllers in manufacturing systems, such as additive manufacturing systems. A number of efficient methods are provided for solving meshing determinations that arise from movement of a stimulus modeled within a fine mesh.