Algebraic Riccati equations (ARE) of large dimension arise when using approximations to design controllers for systems modelled by partial differential equations. We use a modified Newton method to solve the ARE that takes advantage of several special features of these problems. The modified Newton method leads to a right-hand side of rank equal to the number of inputs regardless of the weights...

The main di culty in the implementation of most standard implicit Runge-Kutta (IRK) methods applied to (sti ) ordinary di erential equations (ODE's) is to e ciently solve the nonlinear system of equations. In this article we propose the use of a preconditioner whose decomposition cost for a parallel implementation is equivalent to the cost for the implicit Euler method. The preconditioner is ba...

[1] We present a general formulation of the basic equations of large-scale magnetosphereionosphere coupling in terms of Euler potentials and describe a specific numerical implementation of this formulation in the context of the Rice Convection Model (RCM). When written in terms of Euler potentials, both the Vasyliunas magnetosphere-ionosphere coupling equation and the expression for bounce-aver...

A Newton-Krylov unstructured flow solver is developed for higher-order computation of the Euler equations using an upwind scheme. The Generalized Minimal Residual (GMRES) algorithm is used for solving the linear system arising from implicit time discretization of the governing eqautions. An Incomplete Lower-Upper factorization technique is employed as the preconditioning strategy, and an approx...

The studies in aerial vehicles modeling and control have been increased rapidly recently. In this paper , a coordination of two types of heterogeneous robots , namely unmanned aerial vehicle (UAV) and unmanned ground vehicle (UGV) is considered. In this paper the UAV plays the role of a virtual leader for the UGVs. The system consists of a vision- based target detection algorithm that uses the ...

In this paper, we design stable and accurate numerical schemes for conservation laws with stiff source terms. A prime example and the main motivation for our study is the reactive Euler equations of gas dynamics. Furthermore, we consider widely studied scalar model equations. We device one-step IMEX (implicit-explicit) schemes for these equations that treats the convection terms explicitly and ...

Background: Winsor & Newton Ltd. has been one of the main fine art products providers since its establishment in 1832, being responsible for the manufacture of a wide assortment of materials ranging from oils and pigments to brushes and papers. All the items produced over the years have been indexed in a comprehensive historical archive. Original Winsor & Newton handbooks are a powerful resourc...

In this paper, we consider the problem of efficiently computing the eigenvalues of limited-memory quasi-Newton matrices that exhibit a compact formulation. In addition, we produce a compact formula for quasi-Newton matrices generated by any member of the Broyden convex class of updates. Our proposed method makes use of efficient updates to the QR factorization that substantially reduces the cos...

A general, two-way coupled, point-particle formulation that accounts for the disturbance created by dispersed particles in obtaining undisturbed fluid flow field needed accurate computation of force closure models is presented. Specifically, equations presence are first derived based on inter-phase momentum coupling a finite-volume formulation. Solution to obtained using two approaches: (i) dir...

Today, robots and unmanned aerial vehicles are being used extensively in modern societies. Due to a wide range of applications, it has attracted much attention among scientists over the past decades. This paper deals with the problem of the stability of a four-rotor flying robot called quadrotor, which is an under-actuated system, in the presence of operator or sensor failures. The dynamica...