**Grid Refinement and Criteria - Algorithms**

The Refine command for the grid generation code LaGriT uses various criteria to tag grid elements for refinement or derefinement. When utilizing unstructured grids generated by LaGriT for applications such as solution of partial differential equations (PDE) for physical systems, it is desirable to modify the grid in order to optimize it for the particular problem based on several principles. The goal is to produce a better solution by creating better grid elements in various regions of the domain of the PDE’s. This can involve physical criteria such as choosing smaller elements where physical variables are rapidly changing or larger elements where the variables are relatively constant in order not to waste computational effort. Grid elements can also be chosen on various geometric criteria related to their shape such as different formulations of an aspect ratio. In time dependent problems, it may be necessary to refine and derefine the grid after each time step in order to follow various changing phenomena such as moving concentration fronts, shock waves, or advancing oxide layers. These factors make mesh refinement crucial to the practical solution of physical modeling problems. We therefore will detail several algorithms that are currently implemented for identifying which grid elements should be refined or derefined based on geometric and physical criteria. New algorithms will be added to this list and the current ones modified as we obtain feed back from users.

II. Faces: Each face is tested separately for refinement or derefinement.

III. Tets: Each tetrahedron is tested separately for refinement or derefinement

IV . Face Edges: Same algorithms of the Faces category except all edges of the face are tagged for refinement or derefinement if the condition is met for the face.

V. Tet Edges: Same algorithms of the tet category except all edges of the tet are tagged for refinement or derefinement if the condition is met for the tet.