Projection finite element methods for semiconductor device equations

A finite element formulation for the hydrodynamic semiconductor device equations

A new formulation employing the Galerkin/least-squares finite element method is presented for the simulation of the hydrodynamic model of semiconductor devices. Numerical simulations are performed on the coupled Poisson and hydrodynamic equations for one carrier devices. The hydrodynamic equations for a single carrier, i.e. for the electrons or holes, resemble the compressible Navier-Stokes equ...

Error Estimates for a Finite Element Method for the Drift-diffusion Semiconductor Device Equations

In this paper, optimal error estimates are obtained for a method for numerically solving the so-called unipolar model (a one-dimensional simpliied version of the drift-diiusion semiconductor device equations). The numerical method combines a mixed nite element method using a continuous piecewise-linear approximation of the electric eld with an explicit upwinding nite element method using a piec...

Consistent Local Projection Stabilized Finite Element Methods

Abstract. This work establishes a formal derivation of local projection stabilized methods as a result of an enriched Petrov-Galerkin strategy for the Stokes problem. Both velocity and pressure finite element spaces are enhanced with solutions of residual-based local problems, and then the static condensation procedure is applied to derive new methods. The approach keeps degrees of freedom unch...

Finite element methods for Maxwell's equations

Adaptive finite element methods for Maxwell equations

We report our recent efforts in developing adaptive finite element methods for solving electromagnetic problems. We shall first introduce the method for the Maxwell cavity problem with discontinuous coefficients. We then consider the eddy current model with voltage excitations for complicated three dimensional structures. Unique continuation on analytic curve and its application to Inverse Prob...