1. A system comprising one or more processors configured to execute one or more executable modules including: a preprocessor configured to determine a surface mesh of a component to be manufactured based on a geometric description of the component, wherein the surface mesh comprises a plurality of triangular surface elements; a surface element analyzer configured to determine one or more element properties of each surface element in the plurality of surface elements and to determine one or more nodal properties of each surface element in the plurality of surface elements; a feature edge locator configured to locate one or more feature edges of the surface mesh using the element properties of a plurality of the surface elements; a subsurface classifier configured to assign each surface element in the plurality of surface elements to one of a plurality of subsurfaces according to a bending curvature of the surface element, wherein the subsurface classifier is configured to identify one or more subsurface properties and any surface loops for each subsurface of the plurality of subsurfaces; a remesher configured to coarsen or refine a mesh of one of the subsurfaces according to a specified edge length; a subsurface matcher configured to determine a first plurality of the surface elements that define a 2.5D-analysis portion of a hybrid mesh solution domain and a different second plurality of the surface elements that define a 3D-analysis portion of the hybrid mesh solution domain, wherein the subsurface matcher is configured to categorize each subsurface into one or more categories including a matched category, an unmatched category, and an edge category, and wherein the subsurface matcher is configured to assign a respective thickness to at least the subsurfaces categorized into the matched category; a first solution domain discretizer configured to define one or more wedge elements using the first plurality of the surface elements and to discretize the 2.5D-analysis portion; an interface element locator configured to define one or more interface elements along a boundary between the 2.5D-analysis portion and the 3D-analysis portion; a second solution domain discretizer configured to define one or more tetrahedral elements using the second plurality of the surface elements and to discretize the 3D-analysis portion; and an equation solver configured to determine a solution for a distribution of one or more process variables throughout the hybrid mesh solution domain, wherein the solution for each process variable is given as a function of time.