Title: Multi-scale and Multi-physics Numerical Methods for Modeling Transport in Mesoscopic Systems
Abstract: 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.
Publication Year: 2012
Publication Date: 2012-09-05
Language: en
Type: report
Indexed In: ['crossref']
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