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A multigrid method is presented for the numerical solution of the linearized Poisson-Boltzmann equation arising in molecular biophysics. The equation is discretized with the finite volume method, and the numerical solution of the discrete equations is accomplished with multiple grid techniques originally developed for two-dimensional interface problems… (More)

We present a robust and efficient numerical method for solution of the nonlinear Poisson-Boltzmann equation arising in molecular biophysics. The equation is discretized with the box method, and solution of the discrete equations is accomplished with a global inexact-Newton method, combined with linear multilevel techniques we have described in a paper… (More)

A realistic 40 nm InAs high electron mobility transistor is studied using a two-dimensional, full-band, and atom-istic Schrödinger-Poisson solver based on the sp 3 d 5 s * tight-binding model. Bandstructure non-parabolicity effects, strain, alloy disorder in the InGaAs and InAlAs barriers, as well as band-to-band tunneling in the transistor OFF-state are… (More)

- Gerhard Klimeck, Shaikh S Ahmed, Hansang Bae, Neerav Kharche, Rajib Rahman, Gerhard Klimeck +31 others
- 2013

Atomistic simulation of realistically sized nanodevices using NEMO 3-D-Part I: Models and benchmarks" (2007). Other Nanotechnology Publications. Paper 92. Abstract—Device physics and material science meet at the atomic scale of novel nanostructured semiconductors, and the distinction between new device or new material is blurred. Not only the… (More)

- Marek Korkusinski, Faisal Saied, Haiying Xu, Seungwon Lee, Mohamed Sayeed, Sebastien Goasguen +1 other
- 2005

Extended Abstract Introduction NEMO3D is a quantum mechanical based simulation tool created to provide quantitative predictions for nanometer-scaled semiconductor devices. NEMO3D computes strain field using an atomistic valence force field method and electronic quantum states using an atomistic tight-binding Hamiltonian. Target applications for NEMO3D… (More)

The eigenvector corresponding to the second smallest eigenvalue of the Laplacian of a graph, known as the Fiedler vector, has a number of applications in areas that include matrix reordering, graph partitioning, protein analysis, data mining, machine learning, and web search. The computation of the Fiedler vector has been regarded as an expensive process as… (More)

We consider the solution of parabolic PDEs in three spatial dimensions by multigrid methods on parallel architectures. The objective is to develop high performance multigrid solvers for large scale time-dependent problems. We begin with temporal semi-discretizations with several explicit and implicit schemes, followed by a uniform spatial discretization in… (More)

We consider multigrid and domain decomposition methods for the numerical solution of electrostatics problems arising in biophysics. We compare multigrid methods designed for discontinuous coefficients with domain decomposition methods, including comparisons of standard multigrid methods , algebraic multigrid methods, additive and multiplicative Schwarz… (More)