A high-order multiscale discontinuous Galerkin method for two-dimensional Schrödinger equation in quantum transport
A high-order multiscale discontinuous Galerkin method for two-dimensional Schrödinger equation in quantum transport
复制标题
量子输运中二维薛定谔方程的高阶多尺度间断伽辽金法
DOI：
10.1016/j.cam.2022.114701
复制
发表时间：
2023
影响因子：
2.4
通讯作者：
Wang, Wei
中科院分区：
文献类型：
--
作者：
Dong, Bo;Wang, Wei
发展并分析了求解二维量子输运薛定谔方程的高阶多尺度间断Galerkin（DG）方法。所考虑问题的解主要在一个方向上具有振荡，因此我们在该方向上包括振荡的非多项式基函数，并在另一个方向上使用多项式基来近似解。我们证明了所得到的方法收敛时，网格尺寸足够小的最佳顺序。数值上，我们观察到，该方法收敛于粗网格，并达到最佳高阶收敛时，网格尺寸细化到波长的规模。数值结果表明，该方法可以捕捉薛定谔方程的高振荡的解决方案比标准DG方法的多项式基更有效。
We develop and analyze a high-order multiscale discontinuous Galerkin (DG) method for two-dimensional stationary Schrödinger equations in quantum transport. The solution of the problem under consideration has oscillations mainly in one direction, so we include oscillatory non-polynomial basis functions in that direction and use polynomial basis in the other direction to approximate the solution. We prove that the resulting method converges with an optimal order when the mesh size is sufficiently small. Numerically we observe that the method converges on coarse meshes and achieves optimal higher-order convergence when the mesh size is refined to the scale of the wave length. Numerical results show that the method can capture highly oscillating solutions of Schrödinger equations more effectively than standard DG methods with polynomial basis.