Adaptive Conservative Cell Average Spectral Element Methods for Transient Wigner Equation in Quantum Transport
Adaptive Conservative Cell Average Spectral Element Methods for Transient Wigner Equation in Quantum Transport
复制标题
DOI：
10.4208/cicp.080509.310310s
复制
发表时间：
2011-03
影响因子：
3.7
通讯作者：
Sihong Shao;Tiao Lu;W. Cai
中科院分区：
文献类型：
--
作者：
Sihong Shao;Tiao Lu;W. Cai
提出了一种新的自适应细胞平均谱元法（SEM）来求解量子器件中随时间变化的输运维格纳方程。所提出的单元平均扫描电镜允许在相空间中自适应非均匀网格，以减少维格纳函数的高维计算成本，同时精确地保持数值解的质量守恒。该方法的主要特点是在k空间中Wigner函数的单元平均值（有限范围速度下的局部电子密度）与分布的点值之间建立了解析关系，从而通过快速正弦和余弦变换实现了离散Wigner方程的局部电子密度和局部通量之间的快速变换。数值结果表明，该方法具有较高的精度、守恒性、收敛性和降低成本的优点。
A new adaptive cell average spectral element method (SEM) is proposed to solve the time-dependent Wigner equation for transport in quantum devices. The proposed cell average SEM allows adaptive non-uniform meshes in phase spaces to reduce the high-dimensional computational cost of Wigner functions while preserving exactly the mass conservation for the numerical solutions. The key feature of the proposed method is an analytical relation between the cell averages of the Wigner function in the k-space (local electron density for finite range velocity) and the point values of the distribution, resulting in fast transforms between the local electron density and local fluxes 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.