This paper reports the first numerical solver for the Boltzmann transport equation (BTE) that uses wavelets as basis functions. The main advantage of wavelets is that they offer modern compression and adaptation techniques that could cope with the "curse of dimensionality" of the 6-dimensional phase space. An adequate numerical method for the BTE has been developed which combines a conservative discontinuous Galerkin (DG) formulation with a Multi-Wavelets (MW) basis. NIN device simulations in a 3-dimensional phase space prove that the DG formulation performs well together with MWs. On the other hand, it shows that MWs provide a very efficient basis for the BTE. The number of degrees of freedom can be compressed to about 1-10% in comparison to other modern solvers. Even greater advantages are expected for higher-dimensional phase spaces.
This paper presents an important improvement of the current-based one-particle Monte-Carlo method. By regionwise coupling a semi-analytical solution of the Boltzmann equation to a full solution, the usage of computationally intensive Monte Carlo Boltzmann solvers can be limited to only those regions where they are needed. The advantages and drawbacks of this new method are reviewed and the problems arising from the coupling scheme are discussed.
This paper reports the first numerical solver for the Boltzmann transport equation (BTE) that uses wavelets as basis functions. The main advantage of wavelets is that they offer modern compression and adaptation techniques that could cope with the "curse of dimensionality" of the 6-dimensional phase space. An adequate numerical method for the BTE has been developed which combines a conservative discontinuous Galerkin (DG) formulation with a Multi-Wavelets (MW) basis. NIN device simulations in a 3-dimensional phase space prove that the DG formulation performs well together with MWs. On the other hand, it shows that MWs provide a very efficient basis for the BTE. The number of degrees of freedom can be compressed to about 1-10% in comparison to other modern solvers. Even greater advantages are expected for higher-dimensional phase spaces.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.