Computational framework for modeling one-dimensional subgrid components and phenomena in multidimensional microsystems

This paper presents a framework for modeling essentially 1D devices and components embedded in multi-dimensional spaces. The main characteristic and main advantage of the new methodology is that the 1D and multi-dimensional objects or domain are meshed completely independently of each other, without regard to their relative alignment or location, and subsequently combined into a single, unified composite mesh. The coupling of the solution between the different domains is handled fully-automatically in the solver, entirely through exchange of source terms between these domains of differing dimensionality. The source terms are evaluated locally on a cell-by-cell basis, depending on the solution values in these domains and the manner in which the 1D grids intersect the multi-dimensional grids. The capabilities and usefulness of the method are demonstrated with several examples.