A flexible tool for physics simulations and its application to power diodes

This document addresses the design and implementation of a simulation tool which is flexible and powerful enough to be used to solve most of the partial differential equations (PDEs) that arise in a very wide variety of disciplines, including applied physics. The features which are appropriate for such a tool were identified, in part by considering specific applications in solid-state physics and plasma physics, and implemented in the Simulation Generation (SimGen) framework. These features include the following: (1) The automatic generation of code to solve a very general class of PDEs starting from a very compact specification of the discretized form of the PDEs and making use of symbolic differentiation of the PDEs and associated functions to generate efficient and robust code. This code is automatically linked to numerical algorithm modules to solve the discrete problem. (2) The implementation of user-defined functions to simplify coding and to facilitate use of complex models of physical parameters. User-defined functions and their derivatives may be computed and stored in arrays to eliminate redundant calculations and increase computational efficiency. (3) The automatic mesh generation and refinement and a mesh labeling format which makes specification of equations and boundary conditions straightforward and largely mesh-independent.; SimGen is applied to the design and optimization of a power semiconductor diode with multiple field limiting rings. The optimization is accomplished in part by means of principles drawn from the statistical design of experiments. In addition to accomplishing the design, this project illustrates the power and flexibility of the tool.