Adaptive Conservative Cell Average Spectral Element Methods for Transient Wigner Equation in Quantum Transport (Communications in Computational Physics, 2011)
A new adaptive cell average spectral element method (SEM) is proposedto solve the time-dependent Wigner equation for transport in quantum devices. Theproposed cell average SEM allows adaptive non-uniform meshes in phase spaces toreduce the high-dimensional computational cost of Wigner functions while preservingexactly the mass conservation for the numerical solutions. The key feature of the proposedmethod is an analytical relation between the cell averages of the Wigner functionin the k-space (local electron density for finite range velocity) and the point values ofthe distribution, resulting in fast transforms between the local electron density and localfluxes of the discretized Wigner equation via the fast sine and cosine transforms.Numerical results with the proposed method are provided to demonstrate its high accuracy,conservation, convergence and a reduction of the cost using adaptive meshes.