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 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; and (f) creating, using an element creator, the refined elements having subindices linked to the existing indices.