Convergence of Adaptive Finite Element Approximations for Nonlinear Eigenvalue Problems

In this paper, we study an adaptive finite element method for a class of a nonlinear eigenvalue problems that may be of nonconvex energy functional and consider its applications to quantum chemistry. We prove the convergence of adaptive finite element approximations and present several numerical examples of micro-structure of matter calculations that support our theory.Comment: 24 pages, 12 figure

Energy-Conserving Lattice Boltzmann Thermal Model in Two Dimensions

A discrete velocity model is presented for lattice Boltzmann thermal fluid dynamics. This model is implemented and tested in two dimensions with a finite difference scheme. Comparison with analytical solutions shows an excellent agreement even for wide temperature differences. An alternative approximate approach is then presented for traditional lattice transport schemes

A Lattice Boltzmann method for simulations of liquid-vapor thermal flows

We present a novel lattice Boltzmann method that has a capability of simulating thermodynamic multiphase flows. This approach is fully thermodynamically consistent at the macroscopic level. Using this new method, a liquid-vapor boiling process, including liquid-vapor formation and coalescence together with a full coupling of temperature, is simulated for the first time.Comment: one gzipped tar file, 19 pages, 4 figure

Global convergence analysis of the bat algorithm using a markovian framework and dynamical system theory

The bat algorithm (BA) has been shown to be effective to solve a wider range of optimization problems. However, there is not much theoretical analysis concerning its convergence and stability. In order to prove the convergence of the bat algorithm, we have built a Markov model for the algorithm and proved that the state sequence of the bat population forms a finite homogeneous Markov chain, satisfying the global convergence criteria. Then, we prove that the bat algorithm can have global convergence. In addition, in order to enhance the convergence performance of the algorithm and to identify the possible effect of parameter settings on convergence, we have designed an updated model in terms of a dynamic matrix. Subsequently, we have used the stability theory of discrete-time dynamical systems to obtain the stable parameter ranges for the algorithm. Furthermore, we use some benchmark functions to demonstrate that BA can indeed achieve global optimality efficiently for these functions

Corner detector based on global and local curvature properties

This paper proposes a curvature-based corner detector that detects both fine and coarse features accurately at low computational cost. First, it extracts contours from a Canny edge map. Second, it computes the absolute value of curvature of each point on a contour at a low scale and regards local maxima of absolute curvature as initial corner candidates. Third, it uses an adaptive curvature threshold to remove round corners from the initial list. Finally, false corners due to quantization noise and trivial details are eliminated by evaluating the angles of corner candidates in a dynamic region of support. The proposed detector was compared with popular corner detectors on planar curves and gray-level images, respectively, in a subjective manner as well as with a feature correspondence test. Results reveal that the proposed detector performs extremely well in both fields. © 2008 Society of Photo-Optical Instrumentation Engineers.published_or_final_versio