Faisal Saied

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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)
The nonlinear Poisson-Boltzmann equation (NPBE) provides a continuum description of the electrostatic field in an ionic medium around a macromolecule. Here, a novel approach to the solution of the full NPBE is developed. This robust and efficient algorithm combines multilevel techniques with a damped inexact Newton's method. The CPU time required for(More)
A. M. Abrahams,1,2,3 L. Rezzolla,1 M. E. Rupright,3 A. Anderson,3 P. Anninos,1 T. W. Baumgarte,1 N. T. Bishop,4 S. R. Brandt,1 J. C. Browne,5 K. Camarda,6 M. W. Choptuik,5 G. B. Cook,7 R. R. Correll,5 C. R. Evans,3 L. S. Finn,8 G. C. Fox,9 R. Gómez,10 T. Haupt,9 M. F. Huq,5 L. E. Kidder,8 S. A. Klasky,9 P. Laguna,6 W. Landry,7 L. Lehner,10 J. Lenaghan,3 R.(More)
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 quantum–mechanical effects in the electronic states of the device but also the granular atomistic representation of the underlying material are important. Approaches based on a(More)
A new method for solving the full nonlinear Poisson-Boltzmann equation is outlined. This method is robust and efficient, and uses a combination of the multigrid and inexact Newton algorithms. The novelty of this approach lies in the appropriate combination of the two methods, neither of which by themselves are capable of solving the nonlinear problem(More)
A realistic 40 nm InAs high electron mobility transistor is studied using a two-dimensional, full-band, and atomistic Schrödinger-Poisson solver based on the spds tightbinding 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)
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)
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)
G. B. Cook,1 M. F. Huq,2 S. A. Klasky,3 M. A. Scheel,1 A. M. Abrahams,4,5 A. Anderson,6 P. Anninos,4 T. W. Baumgarte,4 N. T. Bishop,7 S. R. Brandt,4 J. C. Browne,2 K. Camarda,8 M. W. Choptuik,2 R. R. Correll,2,9 C. R. Evans,6 L. S. Finn,10 G. C. Fox,3 R. Gómez,11 T. Haupt,3 L. E. Kidder,10 P. Laguna,8 W. Landry,1 L. Lehner,11 J. Lenaghan,6 R. L. Marsa,2 J.(More)