Grid structure impact in sparse point representation of derivatives

In the Sparse Point Representation (SPR) method the principle is to retain the function data indicated by significant interpolatory wavelet coefficients, which are defined as interpolation errors by means of an interpolating subdivision scheme. Typically, a SPR grid is coarse in smooth regions, and refined close to irregularities. Furthermore, the computation of partial derivatives of a function from the information of its SPR content is performed in two steps. The first one is a refinement procedure to extend the SPR by the inclusion of new interpolated point values in a security zone. Then, for points in the refined grid, such derivatives are approximated by uniform finite differences, using a step size proportional to each point local scale. If required neighboring stencils are not present in the grid, the corresponding missing point values are approximated from coarser scales using the interpolating subdivision scheme. Using the cubic interpolation subdivision scheme, we demonstrate that such adaptive finite differences can be formulated in terms of a collocation scheme based on the wavelet expansion associated to the SPR. For this purpose, we prove some results concerning the local behavior of such wavelet reconstruction operators, which stand for SPR grids having appropriate structures. This statement implies that the adaptive finite difference scheme and the one using the step size of the finest level produce the same result at SPR grid points. Consequently, in addition to the refinement strategy, our analysis indicates that some care must be taken concerning the grid structure, in order to keep the truncation error under a certain accuracy limit. Illustrating results are presented for 2D Maxwell's equation numerical solutions.

Logarithmically proportional objective function for planar surfaces recognition in 3D point cloud

3D laser scanning is becoming a standard technology to generate building models of a facility's as-is condition. Since most constructions are constructed upon planar surfaces, recognition of them paves the way for automation of generating building models. This paper introduces a new logarithmically proportional objective function that can be used in both heuristic and metaheuristic (MH) algorithms to discover planar surfaces in a point cloud without exploiting any prior knowledge about those surfaces. It can also adopt itself to the structural density of a scanned construction. In this paper, a metaheuristic method, genetic algorithm (GA), is used to test this introduced objective function on a synthetic point cloud. The results obtained show the proposed method is capable to find all plane configurations of planar surfaces (with a wide variety of sizes) in the point cloud with a minor distance to the actual configurations. © 2014 IEEE.

The extended unsymmetric frontal solution for multiple-point constraints

The purpose of this paper is to discuss the linear solution of equality constrained problems by using the Frontal solution method without explicit assembling. Design/methodology/approach - Re-written frontal solution method with a priori pivot and front sequence. OpenMP parallelization, nearly linear (in elimination and substitution) up to 40 threads. Constraints enforced at the local assembling stage. Findings - When compared with both standard sparse solvers and classical frontal implementations, memory requirements and code size are significantly reduced. Research limitations/implications - Large, non-linear problems with constraints typically make use of the Newton method with Lagrange multipliers. In the context of the solution of problems with large number of constraints, the matrix transformation methods (MTM) are often more cost-effective. The paper presents a complete solution, with topological ordering, for this problem. Practical implications - A complete software package in Fortran 2003 is described. Examples of clique-based problems are shown with large systems solved in core. Social implications - More realistic non-linear problems can be solved with this Frontal code at the core of the Newton method. Originality/value - Use of topological ordering of constraints. A-priori pivot and front sequences. No need for symbolic assembling. Constraints treated at the core of the Frontal solver. Use of OpenMP in the main Frontal loop, now quantified. Availability of Software.

A logística na cadeia de frio em Portugal: transporte de produtos perecíveis congelados

Trabalho Final de Mestrado para obtenção do grau de Mestre em Engenharia Mecânica

Parallel GPU architecture for hyperspectral unmixing based on augmented Lagrangian method

Hyperspectral imaging has become one of the main topics in remote sensing applications, which comprise hundreds of spectral bands at different (almost contiguous) wavelength channels over the same area generating large data volumes comprising several GBs per flight. This high spectral resolution can be used for object detection and for discriminate between different objects based on their spectral characteristics. One of the main problems involved in hyperspectral analysis is the presence of mixed pixels, which arise when the spacial resolution of the sensor is not able to separate spectrally distinct materials. Spectral unmixing is one of the most important task for hyperspectral data exploitation. However, the unmixing algorithms can be computationally very expensive, and even high power consuming, which compromises the use in applications under on-board constraints. In recent years, graphics processing units (GPUs) have evolved into highly parallel and programmable systems. Specifically, several hyperspectral imaging algorithms have shown to be able to benefit from this hardware taking advantage of the extremely high floating-point processing performance, compact size, huge memory bandwidth, and relatively low cost of these units, which make them appealing for onboard data processing. In this paper, we propose a parallel implementation of an augmented Lagragian based method for unsupervised hyperspectral linear unmixing on GPUs using CUDA. The method called simplex identification via split augmented Lagrangian (SISAL) aims to identify the endmembers of a scene, i.e., is able to unmix hyperspectral data sets in which the pure pixel assumption is violated. The efficient implementation of SISAL method presented in this work exploits the GPU architecture at low level, using shared memory and coalesced accesses to memory.