Local discontinuous Galerkin methods for moment models in device simulations: formulation and one dimensional results

We report, our preliminary work in applying the local discontinuous Galerkin (LDG) finite element method to solve various time dependent and steady state moment models for semiconductor device simulations, in which both the first derivative convection terms and second derivative diffusion (heat conduction) terms exist and are discretized by the discontinuous Galerkin method and the local discontinuous Galerkin method (Cockburn and Shu, 2001) respectively. The potential equation for the electrical field is also discretized by the local discontinuous Galerkin method. This is an ongoing project, with the objective of developing a numerical tool based on the discontinuous Galerkin and local discontinuous Galerkin methodology, capable of solving various models for semiconductor device simulations (hydrodynamic models, energy transport models, quantum drift-diffusion or quantum hydrodynamic models, kinetic models, etc.) in a unified treatment of first and higher spatial derivatives, including those for the potential equations, which would allow easy k-p adaptivity and efficient parallel implementation.