J.A. Cuminato

Local Affine Multidimensional Projection

Multidimensional projection techniques have experienced many improvements lately, mainly regarding computational times and accuracy. However, existing methods do not yet provide flexible enough mechanisms for visualization-oriented fully interactive applications. This work presents a new multidimensional projection technique designed to be more flexible and versatile than other methods. This novel approach, called Local Affine Multidimensional Projection (LAMP), relies on orthogonal mapping theory to build accurate local transformations that can be dynamically modified according to user knowledge. The accuracy, flexibility and computational efficiency of LAMP is confirmed by a comprehensive set of comparisons. LAMPs versatility is exploited in an application which seeks to correlate data that, in principle, has no connection as well as in visual exploration of textual documents.

On the uniform convergence of a collocation method for a class of singular integral equations

We establish the uniform convergence of a collocation method for solving a class of singular integral equations. This method uses the Jacobi polynomials {Pn(α, β)} as basis elements and the zeros of a Chebyshev polynomial of the first kind as collocation points. Uniform convergence is shown to hold under the weak assumption that the kernel and the right-hand side are Hölder-continous functions. Convergence rates are also given.

A Stable Semi-Implicit Method for Free Surface Flows

The present work is concerned with a semi-implicit modification of the GENSMAC method for solving the two-dimensional time-dependent incompressible Navier-Stokes equations in primitive varinbles formulation with a free surface. A projection method is employed to uncouple the velocity components and pressure, thus allowing the solution of each variable separately (a segregated approach). The viscous terms are treated by the implicit backward method in time and a centered second order method in space, and the nonlinear convection terms are explicitly approximated by the high order upwind variable-order nonoscillatory scheme method in space. The boundary conditions at the free surface couple the otherwise segregated velocity and pressure fields. The present work proposes a method that allows the segregated solution of free surface flow problems to be computed by semi-implicit schemes that preserve the stability conditions of the related coupled semi-implicit scheme. The numerical method is applied to both the simulation of free surface and to confined flows. The numerical results demonstrate that the present technique eliminates the parabolic stabiliy restriction required by the original explicit GENSMAC method, and also found in segregated semi-implicit methods with time-lagged boundary conditions. For low Reynolds number flows, the method is robust and very efficient when compared to the original GENSMAC method.

Particle‐tracking within turbulent cylindrical electromagnetically‐driven flow

SUMMARY This paper discusses a simple model of electromagnetically stirred molten metal within a long cylinder, neglecting end effects. The radially-dependent velocity profiles of the molten metal are calculated using the Prandtl mixing length model for turbulence. The paths of non-conducting particles within the fluid are also computed numerically, under the influence of Stokes’ drag and a random force due to turbulence. The paths are calculated for a range of particle diameters and the general motion is observed. Copyright

Evaluation of a bounded high order upwind scheme for 3D incompressible free surface flow computations

In the context of normalized variable formulation (NVF) of Leonard and total variation diminishing (TVD) constraints of Harten, this paper presents an extension of a previous work by the authors for solving unsteady incompressible flow problems. The main contributions of the paper are threefold. First, it presents the results of the development and implementation of a bounded high order upwind adaptative QUICKEST scheme in the 3D robust code (Freeflow), for the numerical solution of the full incompressible Navier-Stokes equations. Second, it reports numerical simulation results for 1D shock tube problem, 2D impinging jet and 2D/3D broken dam flows. Furthermore, these results are compared with existing analytical and experimental data. And third, it presents the application of the numerical method for solving 3D free surface flow problems.

A multiresolution flow-based multiphase image segmentation

In this work a variational model is proposed for simultaneous smoothing and multiphase image segmentation. By assuming that the pixel intensities are independent samples from a mixture of Gaussians, and by interpreting the phase fields as probabilities of pixels belonging to a certain phase, the model formulation is obtained by maximizing the mutual information between image features and phase fields. The proposed energy functional Je consists of three parts: the smoothing term for the reconstructed image, the regularization for the boundaries in hard segmentation, and a likelihood estimator based on the density function. The segmentation and image denoising are performed simultaneously through the flow equation obtained by minimizing the energy functional with respect to the mixture of Gaussian coefficients and variance. Some experimental results on segmenting synthetic and natural color images are presented to illustrate the effectiveness of the proposed model.

On the uniform convergence of a perturbed collocation method for a class of Cauchy integral equations

Abstract This paper is concerned with the proof of convergence and derivation of convergence rates of a perturbed polynomial collocation method for the numerical solution of Cauchy-type singular integral equations. The analysis is restricted to the constant coefficients and nonnegative index case. The integrals involved in the compact operator are approximated by quadrature rules.

Numerical solution of cauchy-type integral equations of index −1 by collocation methods

This paper describes a collocation method for solving constant coefficient Cauchy-type singular integral equations of index −1. A technique for reducing the set of linear equations resulting from collocation to match the number of unknows is described. The uniform convergence analysis of the resulting method is presented and convergence rates based on the smoothness of the data are given.

Solution of a non-trivial space charge problem by the hodographic method

A numerical technique for solving the discontinuous injection space-charge problem is described. This technique is based upon the hodographic method studied by Budd and Wheeler. In order to avoid the difficulties introduced by the vanishing charge density the domain is split into two subdomains with an unknown common boundary. Each of these subproblems is then solved by the hodographic method, and an extra boundary condition is used to update the position of the unknown boundary.

An efficient adaptive boundary algorithm to reconstruct Neumann boundary data in the MFS for the inverse Stefan problem

Abstract In this exposition, a simple practical adaptive algorithm is developed for efficient and accurate reconstruction of Neumann boundary data in the inverse Stefan problem, which is a highly nontrivial task. Primarily, this algorithm detects the satisfactory location of the source points from the boundary in reconstructing the boundary data in the inverse Stefan problem efficiently. To deal with the ill-conditioning of the matrix generated by the MFS, we use Tikhonov regularization and the algorithm is designed in such a way that the optimal regularization parameter is detected automatically without any use of traditional methods like the discrepancy principle, the L-curve criterion or the generalized cross-validation (GCV) technique. Furthermore, this algorithm can be thought of as an alternative to the concept of Beck’s future temperatures for obtaining stable and accurate fluxes, but without it being necessary to specify data on any future time interval. A MATLAB code for the algorithm is discussed in more-than-usual detail. We have studied the effects of accuracy and measurement error (random noise) on both optimal location and number of source points. The effectiveness of the proposed algorithm is shown through several test problems, and numerical experiments indicate promising results.