The article presents a new scalable iterative method for linear programming called the “apex method”. key feature of this is constructing path close to optimal on surface feasible region from certain starting point exact solution problem. refers minimum length according Euclidean metric. apex based predictor—corrector framework and proceeds in two stages: quest (predictor) target (corrector). s...

Constraint reduction is an essential method because the computational cost of the interior point methods can be effectively saved. Park and O’Leary proposed a constraint-reduced predictor-corrector algorithm for semidefinite programming with polynomial global convergence, but they did not show its superlinear convergence. We first develop a constraintreduced algorithm for semidefinite programmi...

Mehrotra-type predictor-corrector algorithm, as one of most efficient interior point methods, has become the backbones of most optimization packages. Salahi et al. proposed a cut strategy based algorithm for linear optimization that enjoyed polynomial complexity and maintained its efficiency in practice. We extend their algorithm to P∗(κ) linear complementarity problems. The way of choosing cor...

In this paper, the non-Fourier heat conduction in a semi-infinite body was examined. The heat wave non-Fourier heat conduction model was used for thermal analysis. Thermal conductivity was assumed temperature-dependent which resulted in a non-linear equation. The heat source was also considered temperature-dependent which resulted in a non-homogeneous equation. The Mac-Cormack predictor-correct...

In this paper, the sharp interface, direct forcing immersed boundary method developed by Yang and Stern (A simple and efficient direct forcing immersed boundary framework for fluidstructure interactions, J. Comput. Phys. 231 (2012) 5029-5061) is applied to the fully resolved simulation of particulate flow. This method uses a discrete forcing approach and maintains a sharp profile of the fluid/s...

We present a generalization of the finite volume evolution Galerkin scheme [17, 18] for hyperbolic systems with spatially varying flux functions. Our goal is to develop a genuinely multi-dimensional numerical scheme for wave propagation problems in a heterogeneous media. We illustrate our methodology for acoustic waves in a heterogeneous medium but the results can be generalized to more complex...

A linear multistep method for solving first order initial value problems of ordinary differential equations is presented in this paper. The approach of collocation approximation is adopted in the derivation of the scheme and then the scheme is applied as simultaneous integrator to first order initial value problems of ordinary differential equations. This implementation strategy is more accurat...