It has been observed that in many optimization problems, nonsmooth objective functions often appear smooth on naturally arising manifolds. This has led to the development of optimization algorithms which attempt to exploit this smoothness. Many of these algorithms follow the same two step pattern: first predict a direction of decrease, and second make a correction step to return to the manifold...

We propose an alternative implementation of preconditioning techniques for the solution of non-linear problems. Within the framework of Newton-Krylov methods, preconditioning techniques are needed to improve the performance of the solvers. We propose a different implementation approach to re-utilize existing semiimplicit methods to precondition fully implicit non-linear schemes. We propose a pr...

The Mizuno–Todd–Ye predictor–corrector method based on two neighborhoods DðaÞ DðaÞ of the central path of a monotone homogeneous linear complementarity problem is analyzed, where DðaÞ is composed of all feasible points with d-proximity to the central path less than or equal to a. The largest allowable value for a is 1.76. For a specific choice of a and a a lower bound of vn= ffiffiffi n p is ob...

We describe the design, development and testing of a prototype simulator to study problems associated with robust and efficient solution of dynamic process problems, particularly for systems with models containing moderately to very stiff ordinary differential equations and associated algebraic equations. A new predictor-corrector integration strategy and modular dynamic simulator architecture ...

Parallel methods are not usually applied to the time domain because the sequential nature of time is considered to be a handicap for the development of competitive algorithms. However, this sequential nature can also play to our advantage by ensuring convergence within a given number of iterations. The novel parallel algorithm presented in this paper acts as a predictor corrector improving both...

A recent article [1] presents a semi-analytical method to solve the Landau-Lifshitz (LL) equation. Spin motion is computed analytically as precession about the effective field H, where H is assumed fixed over the time step. However, the exchange field dominates at short range and varies at the time scale of neighbor spin precessions, undermining the fixed field assumption. We present an axis co...

In this paper, we study iteration complexities of Mizuno-Todd-Ye predictor-corrector (MTY-PC) algorithms in SDP and symmetric cone programs by way of curvature integrals. The curvature integral is defined along the central path, reflecting the geometric structure of the central path. The idea to exploit the curvature of the central path for the analysis of iteration complexities is based on the...

In this work, two-dimensional inviscid supersonic flow around a wedge has been investigated using CFD scheme. The employed scheme is McCormack’s predictor-corrector scheme. Our own code, CFMOD was written using MATLAB environment. Proper boundary conditions and the grid parameters were decided on the basis of standard techniques. The results are verified using classic theories for supersonic fl...