Multi-scale and Multi-physics Numerical Methods for Modeling Transport in Mesoscopic Systems
Abstract
In this project, we have accomplished in development of algorithms to model transport and eletromagnetic processes in mesoscopic systems such as nano-electronics and biological membrane, and layered inhomogeneous media. Specifically, the following results have been obtained resulting in the publication of 6 peer-referred journal papers and a third part of a Cambridge University Press book. (1) fast integral solver for quantum dots in 3-D layered media. The fast solver is based on a window accelerated method for computing the layered Green's function and wide band Fast multipole methods for Hankel waves. (2) a new linear scaling discontinuous Galerkin density functional theory, which provide a brand new approach in combining physics-based orbitals and piece-wise polynomial finite element basis in finding the ground state energy of the DFT for quantum systems. (3) numerical methods for computation of electrostatics in ion-channel transport, (4) a new parallel solver for elliptic PDEs by combining random walk Feynmann-Kac formula and local boundary integral equations for extreme computing, (5) an improved device adaptive inflow boundary condition for Wigner quantum transport equations.
Document Details
- Document Type
- Technical Report
- Publication Date
- Oct 13, 2014
- Accession Number
- ADA617374
Entities
People
- Wei Cai
Organizations
- University of North Carolina at Charlotte