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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)

In this paper we present the development and performance of a three-dimensional phase field dislocation dynamics (PFDD) model for large-scale dislocation-mediated plastic deformation on high-performance architectures. Through the parallelization of this algorithm, efficient run times can be achieved for large-scale simulations. The algorithm's performance… (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)

In this paper, we report on some computational experience in solving ocean acoustic propagation problems in three dimensions on supercomputers. The underlying Helmholtz equation is transformed into a parabolic-type equation in the Lee-Saad-Schultz model [5], which has a natural alternating direction implicit (ADI) implementation. We give estimates of the… (More)