We introduce a well-developed Newton iterative (truncated Newton) algorithm for solving large-scale nonlinear systems. The framework is an inexact Newton method globalized by backtracking. Trial… (More)

Globalized inexact Newton methods are well suited for solving large-scale systems of nonlinear equations. When combined with a Krylov iterative method, an explicit Jacobian is never needed, and the… (More)

In this paper, we conduct a goal-oriented a posteriori analysis for the error in a quantity of interest computed from a cell-centered finite volume scheme for a semilinear elliptic problem. The a… (More)

We consider multiphysics applications from algorithmic and architectural perspectives, where “algorithmic” includes both mathematical analysis and computational complexity and “architectural”… (More)

An implicit structured-adaptive-mesh-refinement (SAMR) solver for 2D reduced magnetohydrodynamics (MHD) is described. The time-implicit discretization is able to step over fast normal modes, while… (More)

Multigrid methods for solving the steady-state incompressible Navier-Stokes equations require an appropriate smoother and coarse grid solution strategy to be effective. Classical pressure-correction… (More)

This work presents a forecaster based on an Elman artificial neural network trained with resilient backpropagation algorithm for predicting the daily peak temperatures one day ahead. The available… (More)

Domain decomposition methods are studied in a scalable parallel solver for the Cahn-Hilliard equation in 3D. The discretization is based on a stabilized implicit cell-centered finite difference… (More)