Efficiency Analysis of Discontinuous Galerkin Approaches for the Application Onto Quantum-Liouville Type Equations

Abstract The simulation of nano devices is computationally inefficient with current algorithms. The discontinuous Galerkin approach has been demonstrated in the field of computational fluid dynamics to deliver high order accuracy and efficiency due to its reliance on matrix-vector multiplications. The discontinuous Galerkin approach was previously successfully used in conjunction with the Finite Volume technique to solve the Liouville-von Neumann equation in center-mass coordinates and thus simulate nano devices. To exploit its full potential regarding high performance computing, this work aims to substitute the aforementioned Finite Volume technique with the discontinuous Galerkin method. To arrive at the said formalism, a Finite Element method is implemented as an intermediate step.