1. A computer-enabled method for refining a topological indexed mesh, comprising the steps of: (a) selecting, using a user interface, an existing coarse element of an existing coarse mesh having existing nodes and existing indices; (b) inputting, using the user interface, a quantity of refined elements to be created along an element edge; (c) generating, using a grid generator, a parametric grid on the existing coarse element; (d) placing, using a node placer, refined nodes at parametric grid locations, and having subindices linked to the existing indices; (e) deleting, using an element deleter, the existing coarse element; (f) creating, using an element creator, the refined elements of a refined mesh having subindices linked to the existing indices; (g) reverting the refined mesh to the original coarse mesh based on one or more links between the subindices of the refined mesh and the existing indices of the existing coarse mesh to generate a coarse mesh of a finite element model while maintaining the links between the refined elements and the existing course elements.