Adaptive grid generation for VSLI device simulation

A grid refinement methodology suitable for arbitrary spatial dimensions and geometries is developed. Using just the structural description of a device-specified by the user or taken directly from the output of a process simulator-strategies for creating an initial grid are proposed, embodying whatever knowledge the simulator can have about how the solution will behave. After solving the PDEs, a grid is adapted by examining the local error involved in the discretization process. A set of procedures is proposed for this purpose and shown to be nearly optimal in terms of cost and efficiency. The key to implementing a robust and efficient scheme lies in the choice of a suitable error indicator; it is shown that some of the more obvious candidates can perform quite poorly. The initial grid construction and error indicator schemes are used to show how the full adaptation procedure works on some practical examples