The electric arc furnace (EAF) is used to produce high quality steel from steel scraps. The EAF uses plasma arc to generate heat for melting scarp or direct reduced iron (DRI). The liquid metal should be drained from the tap hole. Manual tapping operation of the EAF in the hot environment around the furnace is a potentially dangerous and time consuming task for the workers. Therefore, it is ess...

In this paper we revisit the Horn and Schunck optical flow method [1], and focus on its interpretation as Gauss-Newton optimisation. We explicitly demonstrate that the standard incremental version of the Horn and Schunck (HS) method1 is equivalent to Gauss-Newton (GN) optimisation of the non-linearised energy, consisting of the sum of squared differences (SSD) criterion and diffusion regularisa...

Newton-Krylov methods are potentially well suited for the implicit solution of nonlinear problems whenever it is unreasonable to compute or store a true Jacobian. Krylov-Schwarz iterative methods are well suited for the parallel implicit solution of multidimensional systems of boundary value problems that arise in CFD. They provide good data locality so that even a high-latency workstation netw...

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 earliest example of bifurcation is the buckling of of an elastic beam. In engineering, buckling is a failure mode characterized by a sudden failure of a structure subjected to high compressive stresses, where the actual compressive stresses at failure are greater than the ultimate compressive stresses that the material is capable of withstanding. This mode of failure is also described as fa...

Newton-Krylov methods are potentially well suited for the implicit solution of nonlinear problems whenever it is unreasonable to compute or store a true Jacobian. Krylov-Schwarz iterative methods are well suited for the parallel implicit solution of multidimensional systems of boundary value problems that arise in CFD. They provide good data locality so that even a high-latency workstation netw...

The purpose of this paper is to present techniques to solve higher-order finite element discretizations on massively parallel architectures. Implicit schemes are considered as a means of achieving mesh independent convergence rates for both time dependent problems and steady state solutions obtained through pseudo-transient continuation. Domain decomposition preconditioners are presented for th...

In this paper we extend the micro-macro decomposition based asymptotic-preserving scheme developed in [3] for the single species Boltzmann equation to the multispecies problems. An asymptoticpreserving scheme for kinetic equation is very efficient in the fluid regime where the Knudsen number is small and the collision term becomes stiff. It allows coarse (independent of Knudsen number) mesh siz...

The paper begins with a review of screw algebra including dual numbers, unit line vectors, dual vectors, screws, line coordinates, and screw coordinates and summarizes the essential rules of operation for screw algebra. A significant advantage of the algebra is that geometric, kinematic, and dynamic equations of a rigid body can be expressed in a concise and compact form. Several physical quant...

Modern economic theory views the economy as a dynamical system in which rational decisions are made in the face of uncertainties. The dynamics includes changes over time of market behavior such as consumption, investment, labor supply, and technology innovation, all interpreted in a broad sense. The Euler equation arises as the first order optimality condition when solving an economic dynamics ...