We present parallel computation of 3D, unsteady, incompressible ow past a sphere. The Navier-Stokes equations of incompressible ows are solved using a stabilized-nite element formulation. Equal-order interpolation functions are used for velocity and pressure. The second-order accurate time-marching within the solution process is carried out in an implicit fashion. The coupled, nonlinear equatio...

We present parallel computation of 3D, unsteady, incompressible flow past a sphere. The Navier-Stokes equations of incompressible flows are solved using a stabilized finite element formulation. Equal-order interpolation functions are used for velocity and pressure. The second-order accurate time-marching within the solution process is carried out in an implicit fashion. The coupled, nonlinear e...

Real-time optimization (RTO) methods use measurements to offset the effect of uncertainty and drive the plant to optimality. Explicit RTO schemes, which are characterized by solving a static optimization problem repeatedly, typically require multiple iterations to steady state. In contrast, implicit RTO methods, which do not solve an optimization problem explicitly, can use transient measuremen...

Training of recurrent neural networks is typically formulated as unconstrained optimization problems. There is, however, an implicit constraint stating that the equations of state must be satisfied at every iteration in the optimization process. Such constraints can make a problem highly non-linear and thus difficult to solve. A potential remedy is to reformulate the problem into one in which t...

An analytical study is presented of the condensation of a pure saturated vapour on a cooled channel plate, including the interaction between the cooling liquid, the condensate and the vapour. The governing equations of co-, counterand cross-current condensation are derived, set dimensionless and solved in closed form. The resulting implicit expressions are evaluated numerically by iteration. In...

Many applications in computer vision and computer graphics require the definition of curves and surfaces. Implicit surfaces [7] are a popular choice for this because they are smooth, can be appropriately constrained by known geometry, and require no special treatment for topology changes. Given a scalar function f : Rd 7→ R, one can define a manifold S of dimension d− 1 wherever f(x) passes thr...

‎The object of this paper is to present a new iteration process‎. ‎We will show that our process is faster than the known recent iterative schemes‎. ‎We discuss stability results of our iteration and prove some results in the context of uniformly convex Banach space for Suzuki generalized nonexpansive mappings‎. ‎We also present a numerical example for proving the rate of convergence of our res...

In this note we show how the implicit filtering algorithm can be coupled with the BFGS quasi-Newton update to obtain a superlinearly convergent iteration if the noise in the objective function decays sufficiently rapidly as the optimal point is approached. We show how known theory for the noise-free case can be extended and thereby provide a partial explanation for the good performance of quasi...

A deeation procedure is introduced that is designed to improve the convergence of an implicitly restarted Arnoldi iteration for computing a few eigenvalues of a large matrix. As the iteration progresses the Ritz value approximations of the eigenvalues of A converge at diierent rates. A numerically stable scheme is introduced that implicitly deeates the converged approximations from the iteratio...

we introduce a new one-step iteration process to approximate common fixed points of twononexpansive mappings in banach spaces and prove weak convergence of the iterative sequence using (i)opial’s condition and (ii) kadec-klee property. strong convergence theorems are also established in banachspaces and uniformly convex banach spaces under the so-called condition ( a ), which is weaker thancom...