Application of a Hybrid Discontinuous Galerkin Scheme onto Quantum-Liouville-type Equations for Heterostructure Devices

In addition to the high accuracy nature of conventional finite element formalisms, discontinuous Galerkin methods are suited for the realization of high performance computing. Therefore, this approach is applied onto the Liouville-von Neumann equation describing the electron transport in nanoscale heterostructure devices. Unfortunately, discontinuous Galerkin methods are prone to instability issues. As demonstrated, these inherent stability issues of the discontinuous Galerkin method can be alleviated by the use of a complex absorbing potential ensuring an efficient use of the Liouville-von Neumann equation.