2139488
Projection method III: Spatial discretization on the staggered grid
In E & Liu (SIAM J Numer. Anal., 1995), we studied convergence and the structure of the error for several projection methods when the spatial variable was kept continuous (we call this the semi-discrete case). In this paper, we address similar questions for the fully discrete case when the spatial variables are discretized using a staggered grid. We prove that the numerical solution in velocity has full accuracy up to the boundary, despite the fact that there are numerical boundary layers present in the semi-discrete solutions.
828752
Generalized monotone schemes, discrete paths of extrema, and discrete entropy conditions
Solutions of conservation laws satisfy the monotonicity property: the number of local extrema is a non-increasing function of time, and local maximum/minimum values decrease/increase monotonically in time. This paper investigates this property from a numerical standpoint. We introduce a class of fully discrete in space and time, high order accurate, difference schemes, called generalized monotone schemes. Convergence toward the entropy solution is proven via a new technique of proof, assuming that the initial data has a finite number of extremum values only, and the flux-function is strictly convex. We define discrete paths of extrema by tracking local extremum values in the approximate solution. In the course of the analysis we establish the pointwise convergence of the trace of the solution along a path of extremum. As a corollary, we obtain a proof of convergence for a MUSCL-type scheme that is second order accurate away from sonic points and extrema.
18986222
Concepts and Application of Time-Limiters to High Resolution Schemes
A new class of implicit high-order non-oscillatory time integration schemes is introduced in a method-of-lines framework. These schemes can be used in conjunction with an appropriate spatial discretization scheme for the numerical solution of time dependent conservation equations. The main concept behind these schemes is that the order of accuracy in time is dropped locally in regions where the time evolution of the solution is not smooth. By doing this, an attempt is made at locally satisfying monotonicity conditions, while maintaining a high order of accuracy in most of the solution domain. When a linear high order time integration scheme is used along with a high order spatial discretization, enforcement of monotonicity imposes severe time-step restrictions. We propose to apply limiters to these time-integration schemes, thus making them non-linear. When these new schemes are used with high order spatial discretizations, solutions remain non-oscillatory for much larger time-steps as compared to linear time integration schemes. Numerical results obtained on scalar conservation equations and systems of conservation equations are highly promising.
10834714
Safety analysis of software product lines using state-based modeling
The analysis and management of variations (such as optional features) are central to the development of safety-critical, software product lines. However, the difficulty of managing variations, and the potential interactions among them, across an entire product line currently hinders safety analysis in such systems. The work described here contributes to a solution by integrating safety analysis of a product line with model-based development. This approach provides a structured way to construct a state-based model of a product line having significant, safety-related variations. The process described here uses and extends previous work on product-line software fault tree analysis to explore hazard-prone variation points. The process then uses scenario-guided executions to exercise the state model over the variations as a means of validating the product-line safety properties. Using an available tool, relationships between behavioral variations and potentially hazardous states are systematically explored and mitigation steps are identified. The paper uses a product line of embedded medical devices to demonstrate and evaluate the process and results
205905865
Chinese document layout analysis based on adaptive split-and-merge and qualitative spatial reasoning
The ultimate goal of automatic document processing is to understand the semantics of a document. Towards such an end, one of the primary enabling steps has been to first reason about the layout of the document by means of page segmentation and segment spatial reasoning or labeling. This, in turn, allows for the derivation of document logical organization. This paper describes a generic document segmentation and geometric relation labeling method with applications to Chinese document analysis. Unlike the previous document segmentation methods where text spacing, border lines, and/or a priori layout models based on template matching processing are performed, the present method begins with a hierarchy of partitioned image layers where inhomogeneous higher-level regions are recursively partitioned into lower-level rectangular subregions and at the same time lower-level smaller homogeneous regions are merged into larger homogeneous regions. Furthermore, the derived segment data structure readily enables efficient search for geometric relationships between identified document segments.
6371621
3D object reconstruction from a single 2D line drawing without hidden lines
The human vision system can interpret a single 2D line drawing as a 3D object without much difficulty even if the hidden lines of the object are invisible. Several reconstruction approaches have tried to emulate this ability, but they cannot recover the complete object if the hidden lines of the object are not shown. This paper proposes a novel approach for reconstructing complete 3D objects from line drawings without hidden lines. First, we develop some constraints and properties for the inference of the topology of the invisible edges and vertices of an object. Then we present a reconstruction method based on perceptual symmetry and planarity of the object. We give a number of examples to demonstrate the ability of our approach.
18277516
Mesh Optimisation Using Edge Information in Feature-Based Surface Reconstruction
One of the most challenging and fundamental problems in computer vision is to reconstruct a surface model given a set of uncalibrated 2D images. Well-established Structure from Motion (SfM) algorithms often result in a sparse set of 3D surface points, but surface modelling based on sparse 3D points is not easy. In this paper, we present a new method to refine and optimise surface meshes using edge information in the 2D images. We design a meshing – edge point detection – re-meshing scheme that can gradually refine the surface mesh until it best fits the true physical surface of the object being modelled. Our method is tested on real images and satisfactory results are obtained.
20773612
QoS-aware service location in mobile ad hoc networks
The advent of light-weight terminals (e.g., PDA) with integrated communication capabilities facilitates service access and hosting anytime, anywhere. However, effective service access requires dealing with the service's QoS, including related resource consumption. This paper introduces a comprehensive framework for QoS-aware service location in ad hoc networks. Our framework divides into: (i) QoS specification that is expressive enough to capture most significant QoS-related properties, and concise enough to have minimal computation cost associated with QoS management; and (ii) a benefit function for evaluating the overall benefit of service instances available in the network from the standpoint of QoS regarding both the user's perspective and resource consumption on hosts. Application of the proposed QoS framework is addressed in the context of the mobile ADHoc WS system, which supports QoS-aware location of Web services deployed in mobile ad hoc networks.