Ω-an octree-based mixed element grid allocator for the simulation of complex 3-D device structures

The authors discuss an automatic mesh generator, Ω, developed as a front-end for the simulation of complex three-dimensional semiconductor devices. Grids generated with Ω exhibit smooth transitions from dense to coarse grid regions and a proper description of irregular geometries such as nonuniform surfaces and interfaces. In addition to the grid itself, Ω provides the dual lattice needed for the integration of the device equations. The underlying algorithm avoids the obtuse angle problem. It is shown how this problem can be formalized in 3-D, how badly shaped elements can be detected, and how they can be avoided by construction. Examples of simulations of complex 3-D devices, with grids with several tens of thousands of mesh points, demonstrate the capabilities of Ω