Unified Modeling Language description of the object-oriented multi-scale adaptive finite element method for Step-and-Flash Imprint Lithography Simulations

Abstract

In the first part of the paper we present the multi-scale simulation of the Step-and-Flash Imprint Lithography (SFIL), a modern patterning process. The simulation utilizes the hp adaptive Finite Element Method (hp-FEM) coupled with Molecular Statics (MS) model. Thus, we consider the multi-scale problem, with molecular statics applied in the areas of the mesh where the highest accuracy is required, and the continuous linear elasticity with thermal expansion coefficient applied in the remaining part of the domain. The degrees of freedom from macro-scale element's nodes located on the macro-scale side of the interface have been identified with particles from nano-scale elements located on the nano-scale side of the interface. In the second part of the paper we present Unified Modeling Language (UML) description of the resulting multi-scale application (hp-FEM coupled with MS). We investigated classical, procedural codes from the point of view of the object-oriented (O-O) programming paradigm. The discovered hierarchical structure of classes and algorithms makes the UML project as independent on the spatial dimension of the problem as possible. The O-O UML project was defined at an abstract level, independent on the programming language used.