We revisit the classification problem and focus on nonlinear methods for classification on manifolds. For multivariate datasets lying on an embedded nonlinear Riemannian manifold within the higher-dimensional space, our aim is to acquire a classification boundary between the classes with labels. Motivated by the principal flow [14], a curve that moves along a path of the maximum variation of th...

The effect of airfoil shape parameterization on optimum design and its influence on the convergence of the evolutionary optimization process is presented. Three popular airfoil parametric methods including PARSEC, Sobieczky and B-Spline (Bezier curve) are studied and their efficiency and results are compared with those of a new method. The new method takes into consideration the characteristics...

In this work the collocation method based on quartic B-spline is developed and applied to two-point boundary value problem in ordinary diferential equations. The error analysis and convergence of presented method is discussed. The method illustrated by two test examples which verify that the presented method is applicable and considerable accurate.

A new design approach for a delicate treatment of complex geometries such as wing/body configuration is arranged using overset mesh technique under large scale computing environment. For the in-depth study of the flow physics and highly accurate design, several special overlapped structured blocks such as collar grid, tip-cap grid, and etc. which are commonly used in refined drag prediction are...

We investigate how the choice of either no-slip or stress-free boundary conditions affects numerical models of rapidly rotating flow in Earth's core by computing solutions of the weakly-viscous magnetostrophic equations within a spherical shell, driven by a prescribed body force. For non-axisymmetric solutions, we show that models with either choice of boundary condition have thin boundary laye...

The main purpose of this work is to investigate the porous medium and diffusion-thermo effects on unsteady combined convection magneto hydrodynamics boundary layer flow of viscous electrically conducting fluid over a vertical permeable surface embedded in a high porous medium, in the presence of first order chemical reaction and thermal radiation. The slip boundary condition is applied at the p...

The purpose of this paper is twofold: first, to establish sufficient conditions under which the mean curvature flow supported on a hypersphere with exterior Dirichlet boundary exists globally in time and converges to a minimal surface, and second, to illustrate the application of Killing vector fields in the preservation of graphicality for the mean curvature flow with free boundary. To this en...

in recent years, the number of research works devoted to applying the highly accurate numerical schemes, in particular compact finite difference schemes, to numerical simulation of complex flow fields with multi-scale structures, is increasing. the use of compact finite-difference schemes are the simple and powerful ways to reach the objectives of high accuracy and low computational cost. compa...

[1] Critical issues facing basin-scale groundwater flow models are the estimation of representative hydraulic conductivity for the model units and the impact of nonrepresentation of within-unit conductivity heterogeneity on the model flow prediction. In this study, high-resolution, fully heterogeneous basin-scale hydraulic conductivity map is generated by scaling up an experimental stratigraphy...