Performance evaluation of numerical methods for the Maxwell–Liouville–von Neumann equations

  • Michael RieschEmail author
  • Nikola Tchipev
  • Sebastian Senninger
  • Hans-Joachim Bungartz
  • Christian Jirauschek
Part of the following topical collections:
  1. 2017 Numerical Simulation of Optoelectronic Devices


The Maxwell–Liouville–von Neumann (MLN) equations are a valuable tool in nonlinear optics in general and to model quantum cascade lasers in particular. Several numerical methods to solve these equations with different accuracy and computational complexity have been proposed in related literature. We present an open-source framework for solving the MLN equations and parallel implementations of three numerical methods using OpenMP. The performance measurements demonstrate the efficiency of the parallelization.


Quantum cascade lasers Maxwell–Bloch equations Liouville–von Neumann equation Parallelization 



This work was supported by the German Research Foundation (DFG) within the Heisenberg Program (JI 115/4-2) and under DFG Grant No. JI 115/9-1. Nikola Tchipev acknowledges the funding provided by Intel as part of the Intel Parallel Computing Center ExScaMIC-KNL. The authors gratefully acknowledge the Gauss Centre for Supercomputing e.V. ( for funding this project by providing computing time on the GCS Supercomputer SuperMUC at Leibniz Supercomputing Centre ( Finally, the authors thank Mariem Kthiri for her help in the development of the mbsolve project.


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Authors and Affiliations

  1. 1.Department of Electrical and Computer EngineeringTechnical University of Munich (TUM)MunichGermany
  2. 2.Department of InformaticsTechnical University of Munich (TUM)GarchingGermany

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