Asymptotically complexity diminishing schemes (ACDS) for kinetic equations in the diffusive scaling

In this work, we develop a new class of numerical schemes for collisional kinetic equations in the diffusive regime. The first step consists in reformulating the problem by decomposing the solution in the time evolution of an equilibrium state plus a perturbation. Then, the scheme combines a Monte Carlo solver for the perturbation with an Eulerian method for the equilibrium part, and is designed in such a way to be uniformly stable with respect to the diffusive scaling and to be consistent with the asymptotic diffusion equation. Moreover, since particles are only used to describe the perturbation part of the solution, the scheme becomes computationally less expensive – and is thus an asymptotically complexity diminishing scheme (ACDS) – as the solution approaches the equilibrium state due to the fact that the number of particles diminishes accordingly. This contrasts with standard methods for kinetic equations where the computational cost increases (or at least does not decrease) with the number of interactions. At the same time, the statistical error due to the Monte Carlo part of the solution decreases as the system approaches the equilibrium state: the method automatically degenerates to a solution of the macroscopic diffusion equation in the limit of infinite number of interactions. After a detailed description of the method, we perform several numerical tests and compare this new approach with classical numerical methods on various problems up to the full three dimensional case

Asymptotic-Induced Domain Decomposition Methods for Kinetic and Drift Diffusion Semiconductor Equations

This paper deals with domain decomposition methods for kinetic and drift diffusion semiconductor equations. In particular accurate coupling conditions at the interface between the kinetic and drift diffusion domain are given. The cases of slight and strong nonequilibrium situations at the interface are considered and some numerical examples are shown

Asymptotic-Induced Domain Decomposition Methods for Kinetic and Drift Diffusion Semiconductor Equations

This paper deals with domain decomposition methods for kinetic and drift diffusion semiconductor equations. In particular accurate coupling conditions at the interface between the kinetic and drift diffusion domain are given. The cases of slight and strong nonequilibrium situations at the interface are considered and some numerical examples are shown

Asymptotic-induced domain decomposition methods for kinetic and drift diffusion semiconductor equations

This paper deals with domain decomposition methods for kinetic and drift diffusion semiconductor equations. In particular accurate coupling conditions at the interface between the kinetic and drift diffusion domain are given. The cases of slight and strong nonequilibrium situations at the interface are considered and some numerical examples are shown. (orig.)Available from TIB Hannover: RO 5810(137)+a / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman

Asymptotic-Induced Domain Decomposition Methods for Kinetic and Drift Diffusion Semiconductor Equations

This paper deals with domain decomposition methods for kinetic and drift diffusion semiconductor equations. In particular accurate coupling conditions at the interface between the kinetic and drift diffusion domain are given. The cases of slight and strong nonequilibrium situations at the interface are considered and numerical examples are shown. 1 Introduction Semiconductor device simulations are usually done on the basis of drift diffusion or hydrodynamic equations. However in view of the ongoing miniaturization of semiconductor devices a more accurate modelling of the physics seems to be necessary. This is achieved by kinetic semiconductor equations. We refer to the books of Markowich et al. [16] and Selberherr [18] for a detailed description of semiconductor equations and further references. However, it is in general not necessary to model the whole region in the device by the computationally expensive kinetic equation. Only in particular sensitive regions, where the solution is f..