Multi-scale and Multi-physics Numerical Methods for Modeling Transport in Mesoscopic Systems
Final rept. 15 Aug 2011-14 Aug 2014
NORTH CAROLINA UNIV AT CHARLOTTE
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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 Greens 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.
- Numerical Mathematics