Novel Graph-based Adaptive Triangular Mesh Refinement for Finite-volume Discretizations

A novel graph-based adaptive mesh refinement technique for triangular finite-volume discretizations in order to solve second-order partial differential equations is described. Adaptive refined meshes are built in order to solve time-dependent problems aiming low computational costs. In the approach proposed, flexibility to link and traverse nodes among neighbors in different levels of refinement is admitted; and volumes are refined using an approach that allows straightforward and strictly local update of the data structure. In addition, linear equation system solvers based on the minimization of functionals can be easily used; specifically, the Conjugate Gradient Method. Numerical and analytical tests were carried out in order to study the required execution time and the data storage cost. These tests confirmed the advantages of the approach proposed in elliptic and parabolic problems

Malhas móveis para solução numérica de equações diferenciais parciais

Neste trabalho, abordam-se malhas móveis para a resolução numérica de equações diferenciais parciais. Conceitos importantes neste contexto são descritos, bem como indicados trabalhos existentes para a solução de equações diferenciais parciais pelos métodos dos volumes finitos e dos elementos finitos ambos com malhas móveis

A Systematic Review of Algorithms with Linear-time Behaviour to Generate Delaunay and Voronoi Tessellations

Triangulations and tetrahedrizations are important geometrical discretization procedures applied to several areas, such as the reconstruction of surfaces and data visualization. Delaunay and Voronoi tessellations are discretization structures of domains with desirable geometrical properties. In this work, a systematic review of algorithms with linear-time behaviour to generate 2D/3D Delaunay and/or Voronoi tessellations is presented

An adaptive graph for volumetric mesh visualization

AbstractThis work presents an adaptive strategy in order to visualize volumetric data generated from numerical simulations of partial differential equations. The mesh is represented by a graph data structure. Moreover, the Autonomous Leaves Graph is extended to the three-dimensional case. This scheme intends to achieve better transversal cost than a treelike (e.g., bintree, quadtree and octree) space arrangement approach. Furthermore, this strategy intends to reduce the computational cost of constructing the discretization and the visualization of data. The total-ordering of the mesh volumes used in the discretization and the visualization processes is by the 3D Modified Hilbert space-filling Curve. To evaluate the performance, the strategy is applied on a Heat Conduction simulation problem using finite difference discretizations and the experimental results are discussed. Comparisons are made between numerical results obtained when using the Hilbert Curve and its modified version. In addition, experiments are shown when visualization is made from inside and outside the volume. The results expose the efficiency of using this strategy

Metaheuristic-based Heuristics for Symmetric-matrix Bandwidth Reduction: A Systematic Review

AbstractComputational and storage costs of resolution of large sparse linear systems Ax=b can be performed by reducing the bandwidth of A. Bandwidth reduction consists of carrying out permutations of lines and columns so that they allow coefficients to remain near the main diagonal.When considering an adjacency matrix of a graph, bandwidth reduction can be considered in the sense of modifying the order in which the graph vertices are numbered. Heuristics for bandwidth reduction are revised in this study, aiming at determining which of them offers the higher bandwidth reduction with a reasonable computational cost. Specifically, metaheuristic-based heuristics are reviewed in this systematic review. Moreover, 29 metaheuristic-based heuristics tested for bandwidth reduction were found. Among them, 4 are recommended as possible state-of-the-art heuristics for addressing the problem

Low-cost heuristics for matrix bandwidth reduction combined with a Hill-Climbing strategy

This paper studies heuristics for the bandwidth reduction of large-scale matrices in serial computations. Bandwidth optimization is a demanding subject for a large number of scientific and engineering applications. A heuristic for bandwidth reduction labels the rows and columns of a given sparse matrix. The algorithm arranges entries with a nonzero coefficient as close to the main diagonal as possible. This paper modifies an ant colony hyper-heuristic approach to generate expert-level heuristics for bandwidth reduction combined with a Hill-Climbing strategy when applied to matrices arising from specific application areas. Specifically, this paper uses low-cost state-of-the-art heuristics for bandwidth reduction in tandem with a Hill-Climbing procedure. The results yielded on a wide-ranging set of standard benchmark matrices showed that the proposed strategy outperformed low-cost state-of-the-art heuristics for bandwidth reduction when applied to matrices with symmetric sparsity patterns

fingerprint

On the line width influence i

Enhancing fingerprint images . . . Gabor Filter

This work demonstrates an application of an adaptive Gabor filter technique to enhance fingerprint images. Firstly, average ridge and valley regions are evaluated as well as their direction by the directional field obtained. Secondly, the fingerprint topological structure is enhanced by Gabor filter using parameters according to their region. That is, filter orientations and frequencies vary according to the fingerprint area. Experimental tests indicate that the use of appropriate filter parameters enhances such images and shows an accurate final result on the recognition processes. This is done without any application of sophisticated techniques, such as those that heuristically evaluate empirical values or use artificial intelligence processes, such as neural networks