46438834
Reinterpretation and simplified implementation of a discontinuous Galerkin method for Hamilton-Jacobi equations
Abstract In this note, we reinterpret a discontinuous Galerkin method originally developed by Hu and Shu [C. Hu, C.-W. Shu, A discontinuous Galerkin finite element method for Hamilton–Jacobi equations, SIAM Journal on Scientific Computing 21 (1999) 666–690] (see also [O. Lepsky, C. Hu, C.-W. Shu, Analysis of the discontinuous Galerkin method for Hamilton–Jacobi equations, Applied Numerical Mathematics 33 (2000) 423–434]) for solving Hamilton–Jacobi equations. With this reinterpretation, numerical solutions will automatically satisfy the curl-free property of the exact solutions inside each element. This new reinterpretation allows a method of lines formulation, which renders a more natural framework for stability analysis. Moreover, this reinterpretation renders a significantly simplified implementation with reduced cost, as only a smaller subspace of the original solution space in [C. Hu, C.-W. Shu, A discontinuous Galerkin finite element method for Hamilton–Jacobi equations, SIAM Journal on Scientific Computing 21 (1999) 666–690; O. Lepsky, C. Hu, C.-W. Shu, Analysis of the discontinuous Galerkin method for Hamilton–Jacobi equations, Applied Numerical Mathematics 33 (2000) 423–434] is used and the least squares procedure used in [C. Hu, C.-W. Shu, A discontinuous Galerkin finite element method for Hamilton–Jacobi equations, SIAM Journal on Scientific Computing 21 (1999) 666–690; O. Lepsky, C. Hu, C.-W. Shu, Analysis of the discontinuous Galerkin method for Hamilton–Jacobi equations, Applied Numerical Mathematics 33 (2000) 423–434] is completely avoided.
11851203
Locally Divergence-Free Discontinuous Galerkin Methods for MHD Equations
In this paper, we continue our investigation of the locally divergence-free discontinuous Galerkin method, originally developed for the linear Maxwell equations (J. Comput. Phys. 194 588–610 (2004)), to solve the nonlinear ideal magnetohydrodynamics (MHD) equations. The distinctive feature of such method is the use of approximate solutions that are exactly divergence-free inside each element for the magnetic field. As a consequence, this method has a smaller computational cost than the traditional discontinuous Galerkin method with standard piecewise polynomial spaces. We formulate the locally divergence-free discontinuous Galerkin method for the MHD equations and perform extensive one and two-dimensional numerical experiments for both smooth solutions and solutions with discontinuities. Our computational results demonstrate that the locally divergence-free discontinuous Galerkin method, with a reduced cost comparing to the traditional discontinuous Galerkin method, can maintain the same accuracy for smooth solutions and can enhance the numerical stability of the scheme and reduce certain nonphysical features in some of the test cases.
2441510
Interactive Rendering of Deforming NURBS Surfaces
The non-uniform rational B-splines (NURBS) has been widely accepted a s a standard tool f or geometry representation and design. Its r ich g eometric properties allow it t o represent both analytic shapes and free-form curves and surfaces precisely. Moreover, a set of tools is available for shape modification or more implicitly, object deformation. Existing NURBS rendering methods include de Boor algorithm, Oslo algorithm, Shantz’s adaptive forward differencing algorithm and Silbermann’s high speed implementation o f NURBS. However, these methods consider only speeding u p the rendering p rocess of individual f rames. Recently, Kumar et al. proposed an incremental method for rendering NURBS surfaces, but it is still limited to static surfaces. In realtime applications such a s virtual reality, interactive display is needed. If a virtual environment contains a lot of deforming objects, these methods cannot provide a good solution. In this paper, we propose an efficient method for interactive rendering of deformable objects by maintaining a polygon model of each d eforming NURBS surface and a daptively refining the resolution o f the polygon model. We also look at how this method may be applied to multi-resolution modelling.
4657376
Traffic Management
Quality of service in network communication is mainly assured by traffic management consisting in a variety of protocols and mechanisms whose role is to prevent the network from being congested. Traffic management has been a very active area of research for two decades following the conception of packetswitched integrated services networks, such as the Internet. This chapter provides samples of the state of the art in traffic management. It includes contributions on traffic theory, traffic and service models, quality monitoring, as well as traffic control and measurements. M. Smirnov et al. (Eds.): COST 263 Final Report, LNCS 2856, pp. 10–79, 2003. c © Springer-Verlag Berlin Heidelberg 2003 Traffic Management 11
8490960
Proof-Infused Streams: Enabling Authentication of Sliding Window Queries On Streams
As computer systems are essential components of many critical commercial services, the need for secure online transactions is now becoming evident. The demand for such applications, as the market grows, exceeds the capacity of individual businesses to provide fast and reliable services, making outsourcing technologies a key player in alleviating issues of scale. Consider a stock broker that needs to provide a real-time stock trading monitoring service to clients. Since the cost of multicasting this information to a large audience might become prohibitive, the broker could outsource the stock feed to third-party providers, who are in turn responsible for forwarding the appropriate sub-feed to clients. Evidently, in critical applications the integrity of the third-party should not be taken for granted. In this work we study a variety of authentication algorithms for selection and aggregation queries over sliding windows. Our algorithms enable the end-users to prove that the results provided by the third-party are correct, i.e., equal to the results that would have been computed by the original provider. Our solutions are based on Merkle hash trees over a forest of space partitioning data structures, and try to leverage key features, like update, query, signing, and authentication costs. We present detailed theoretical analysis for our solutions and empirically evaluate the proposed techniques.
9337355
Weather forecasting: predicting performance for streaming video over wireless LANs
The growth of wireless LANs has brought the expectation for high-bitrate streaming video to wireless PCs. However, it remains unclear how wireless channel characteristics impact the quality of streaming video sent over wireless LANs. This paper presents results from experiments that stream commercial video over a wireless campus network. By analyzing the streaming video quality and capturing wireless LAN characteristics across network and wireless link layers, "weather forecasts" are created such that selected wireless LAN performance indicators might be used to predict the streaming video quality. Furthermore, a quantified measurement of accuracy is presented to evaluate the effectiveness of individual weather forecasts. The paper evaluates six distinct weather forecasts four different streaming configurations including TCP and UDP streaming, and single and multiple-level encoded videos. The results show that the wireless Received Signal Strength Indicator (RSSI) and average wireless link capacity are the most accurate indicators to predict the performance of streaming video over wireless LANs. The weather forecast philosophy can be beneficial for adapting video streaming in wireless LAN environments.
6487445
Incremental rendering of deformable trimmed NURBS surfaces
Trimmed NURBS surfaces are often used to model smooth and complex objects. Unfortunately, most existing hardware graphics accelerators cannot render them directly. Although there are a lot of methods proposed to accelerate the rendering of such surfaces, majority of them are based on tessellation, which is developed primarily for handling non-deforming objects. For an object that may deform in run-time, such as clothing, facial expression, human and animal character, the tessellation process will need to be performed repeatedly while the object is deforming. However, as the tessellation process is very time consuming, interactive display of deforming objects is difficult. This explains why deformable objects are rarely used in virtual reality applications. In this paper, we present a efficient method for incremental rendering of deformable trimmed NURBS surfaces. This method can handle both trimmed surface deformation and trimming curve deformation. Experimental results show that our method performs significantly faster than the method used in OpenGL.