Spatially adaptive multiwavelet representations on unstructured grids with applications to multidimensional computational modeling

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2001.Includes bibliographical references (p. 130-134).In this thesis, we develop wavelet surface wavelet representations for complex surfaces, with the goal of demonstrating their potential for 3D scientific and engineering computing applications. Surface wavelets were originally developed for representing geometric objects in a multiresolution format in computer graphics. However, we further extend the construction of surface wavelets and prove the existence of a large class of multiwavelets in Rn with vanishing moments around corners that are well suited for complex geometries. These wavelets share all of the major advantages of conventional wavelets, in that they provide an analysis tool for studying data, functions and operators at different scales. However, unlike conventional wavelets, which are restricted to uniform grids, surface wavelets have the power to perform signal processing operations on complex meshes, such as those encountered in finite element modeling. This motivates the study of surface wavelets as an efficient representation for the modeling and simulation of physical processes. We show how surface wavelets can be applied to partial differential equations, cast in the integral form. We analyze and implement the wavelet approach for a model 3D potential problem using a surface wavelet basis with linear interpolating properties.(cont.) We show both theoretically and experimentally that an O(h2/n) convergence rate, hn being the mesh size, can be obtained by retaining only O((logN)7/2 N) entries in the discrete operator matrix, where N is the number of unknowns. Moreover our theoretical proof of accuracy vs compression is applicable to a large class of Calderón-Zygmund integral operators. In principle, this convergence analysis may be extended to higher order wavelets with greater vanishing moment. This results in higher convergence and greater compression.by Julio E. Castrillón Candás.Ph.D

(Multi)wavelets increase both accuracy and efficiency of standard Godunov-type hydrodynamic models

This paper presents a scaled reformulation of a robust second-order Discontinuous Galerkin (DG2) solver for the Shallow Water Equations (SWE), with guiding principles on how it can be naturally extended to fit into the multiresolution analysis of multiwavelets (MW). Multiresolution analysis applied to the flow and topography data enables the creation of an adaptive MWDG2 solution on a non-uniform grid. The multiresolution analysis also permits control of the adaptive model error by a single user-prescribed parameter. This results in an adaptive MWDG2 solver that can fully exploit the local (de)compression of piecewise-linear modelled data, and from which a first-order finite volume version (FV1) is directly obtainable based on the Haar wavelet (HFV1) for local (de)compression of piecewise-constant modelled data. The behaviour of the adaptive HFV1 and MWDG2 solvers is systematically studied on a number of well-known hydraulic tests that cover all elementary aspects relevant to accurate, efficient and robust modelling. The adaptive solvers are run starting from a baseline mesh with a single element, and their accuracy and efficiency are measured referring to standard FV1 and DG2 simulations on the uniform grid involving the finest resolution accessible by the adaptive solvers. Our findings reveal that the MWDG2 solver can achieve the same accuracy as the DG2 solver but with a greater efficiency than the FV1 solver due to the smoothness of its piecewise-linear basis, which enables more aggressive coarsening than with the piecewise-constant basis in the HFV1 solver. This suggests a great potential for the MWDG2 solver to efficiently handle the depth and breadth in resolution variability, while also being a multiresolution mesh generator. Accompanying model software and simulation data are openly available online

Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018

This open access book features a selection of high-quality papers from the presentations at the International Conference on Spectral and High-Order Methods 2018, offering an overview of the depth and breadth of the activities within this important research area. The carefully reviewed papers provide a snapshot of the state of the art, while the extensive bibliography helps initiate new research directions

Exploiting Spatio-Temporal Coherence for Video Object Detection in Robotics

This paper proposes a method to enhance video object detection for indoor environments in robotics. Concretely, it exploits knowledge about the camera motion between frames to propagate previously detected objects to successive frames. The proposal is rooted in the concepts of planar homography to propose regions of interest where to find objects, and recursive Bayesian filtering to integrate observations over time. The proposal is evaluated on six virtual, indoor environments, accounting for the detection of nine object classes over a total of ∼ 7k frames. Results show that our proposal improves the recall and the F1-score by a factor of 1.41 and 1.27, respectively, as well as it achieves a significant reduction of the object categorization entropy (58.8%) when compared to a two-stage video object detection method used as baseline, at the cost of small time overheads (120 ms) and precision loss (0.92).</p

30th International Conference on Condition Monitoring and Diagnostic Engineering Management (COMADEM 2017)

Proceedings of COMADEM 201

Six Decades of Flight Research: An Annotated Bibliography of Technical Publications of NASA Dryden Flight Research Center, 1946-2006

Titles, authors, report numbers, and abstracts are given for nearly 2900 unclassified and unrestricted technical reports and papers published from September 1946 to December 2006 by the NASA Dryden Flight Research Center and its predecessor organizations. These technical reports and papers describe and give the results of 60 years of flight research performed by the NACA and NASA, from the X-1 and other early X-airplanes, to the X-15, Space Shuttle, X-29 Forward Swept Wing, X-31, and X-43 aircraft. Some of the other research airplanes tested were the D-558, phase 1 and 2; M-2, HL-10 and X-24 lifting bodies; Digital Fly-By-Wire and Supercritical Wing F-8; XB-70; YF-12; AFTI F-111 TACT and MAW; F-15 HiDEC; F-18 High Alpha Research Vehicle, F-18 Systems Research Aircraft and the NASA Landing Systems Research aircraft. The citations of reports and papers are listed in chronological order, with author and aircraft indices. In addition, in the appendices, citations of 270 contractor reports, more than 200 UCLA Flight System Research Center reports, nearly 200 Tech Briefs, 30 Dryden Historical Publications, and over 30 videotapes are included