15045053
A monotone finite element scheme for convection-diffusion equations
A simple technique is given in this paper for the construction and analysis of a class of finite element discretizations for convection-diffusion problems in any spatial dimension by properly averaging the PDE coefficients on element edges. The resulting finite element stiffness matrix is an M-matrix under some mild assumption for the underlying (generally unstructured) finite element grids. As a consequence the proposed edge-averaged finite element scheme is particularly interesting for the discretization of convection dominated problems. This scheme admits a simple variational formulation, it is easy to analyze, and it is also suitable for problems with a relatively smooth flux variable. Some simple numerical examples are given to demonstrate its effectiveness for convection dominated problems.
7214751
A conforming finite element method for overlapping and nonmatching grids
In this paper we propose a finite element method for nonmatching overlapping grids based on the partition of unity. Both overlapping and nonoverlapping cases are considered. We prove that the new method admits an optimal convergence rate. The error bounds are in terms of local mesh sizes and they depend on neither the overlapping size of the subdomains nor the ratio of the mesh sizes from different subdomains. Our results are valid for multiple subdomains and any spatial dimensions.
2513560
An Algebraic Multigrid Method for Higher-order Finite Element Discretizations
In this paper, we will design and analyze a class of new algebraic multigrid methods for algebraic systems arising from the discretization of second order elliptic boundary value problems by high-order finite element methods. For a given sparse stiffness matrix from a quadratic or cubic Lagrangian finite element discretization, an algebraic approach is carefully designed to recover the stiffness matrix associated with the linear finite element disretization on the same underlying (but nevertheless unknown to the user) finite element grid. With any given classical algebraic multigrid solver for linear finite element stiffness matrix, a corresponding algebraic multigrid method can then be designed for the quadratic or higher order finite element stiffness matrix by combining with a standard smoother for the original system. This method is designed under the assumption that the sparse matrix to be solved is associated with a specific higher order, quadratic for example, finite element discretization on a finite element grid but the geometric data for the underlying grid is unknown. The resulting new algebraic multigrid method is shown, by numerical experiments, to be much more efficient than the classical algebraic multigrid method which is directly applied to the high-order finite element matrix. Some theoretical analysis is also provided for the convergence of the new method.
11854232
Local and parallel finite element algorithms based on two-grid discretizations
A number of new local and parallel discretization and adaptive nite element algorithms are proposed and analyzed in this paper for elliptic boundary value problems. These algorithms are motivated by the observation that, for a solution to some elliptic problems, low frequency components can be approximated well by a relatively coarse grid and high frequency components can be computed on a ne grid by some local and parallel procedure. The theoretical tools for analyzing these methods are some local a priori and a posteriori estimates that are also obtained in this paper for nite element solutions on general shape-regular grids. Some numerical experiments are also presented to support the theory. In this paper, we will propose some new parallel techniques for nite element computation. These techniques are based on our understanding of the local and global properties of a nite element solution to some elliptic problems. Simply speaking, the global behavior of a solution is mostly governed by low frequency components while the local behavior is mostly governed by high frequency compo- nents. The main idea of our new algorithms is to use a coarse grid to approximate the low frequencies and then to use a ne grid to correct the resulted residue (which contains mostly high frequencies) by some local/parallel procedures. Let us now give a somewhat more detailed but informal (and hopefully infor- mative) description of the main ideas and results in this paper. We consider the following very simple model problem posed on a convex polygonal domain R 2 : ( u + bru = f; in ;
52802993
Issues and challenges in the performance analysis of real disk arrays
The performance modeling and analysis of disk arrays is challenging due to the presence of multiple disks, large array caches, and sophisticated array controllers. Moreover, storage manufacturers may not reveal the internal algorithms implemented in their devices, so real disk arrays are effectively black-boxes. We use standard performance techniques to develop an integrated performance model that incorporates some of the complexities of real disk arrays. We show how measurement data and baseline performance models can be used to extract information about the various features implemented in a disk array. In this process, we identify areas for future research in the performance analysis of real disk arrays.
6701763
UML-based reverse engineering and model analysis approaches for software architecture maintenance
This paper proposes a UML-based software maintenance process. The process is guided by architectural descriptions and existing architectural models. The descriptions are given as variants of UML profiles describing the styles and rules relevant for a particular application domain. A reverse engineering subprocess, combining top-down and bottom-up reverse engineering activities, aims at constructing the architectural models. Resulting models are investigated in a model analysis subprocess. The models are checked against the profiles to find violations against the given architectural rules when maintaining and developing the subject system, and they are further analyzed using a set of UML model processing operations. The proposed approach is applied for maintaining a large-scale product platform architecture and real-life product-line products built on top of this platform. The model analysis results of the case study are discussed.
9110982
Modelling of Features and Feature Interactions in Nokia Mobile Phones Using Coloured Petri Nets
This paper reports on the main results from an industrial cooperation project. The project is a joint project between Nokia Research Centre and the CPN group at the University of Aarhus. The purpose of the project was to investigate features and feature interactions in development of Nokia mobile phones through construction of a Coloured Petri Nets (CPN) model. The model is extended with domain-specific graphics and Message Sequence Charts to enable mobile phone user interface designers and software developers who are not familiar with Petri Nets to work with the model. The paper presents the CPN model constructed in the project, describes how domain-specific graphics and Message Sequence Charts are used in simulations of the CPN model, and discusses how the project and in particular the construction of the CPN model has influenced the development process of features in Nokia mobile phones.
53246204
Design of a high-performance ATM firewall
A router-based packet-filtering firewall is an effective way of protecting an enterprise network from unauthorized access. However, it will not work efficiently in an ATM network because it requires the termination of end-to-end ATM connections at a packet-filtering router, which incurs huge overhead of SAR (Segmentation and Reassembly). Very few approaches to this problem have been proposed in the literature, and none is completely satisfactory. In this paper we present the hardware design of a high-speed ATM firewall that does not require the termination of an end-to-end connection in the middle. We propose a novel firewall design philosophy, called Quality of Firewalling (QoF), that applies security measures of different strength to traffic with different risk levels and show how it can be implemented in our firewall. Compared with the traditional firewalls, this ATM firewall performs exactly the same packet-level filtering without compromising the performance and has the same "look and feel" by sitting at the chokepoint between the trusted ATM LAN and untrusted ATM WAN. It is also easy to manage and flexible to use.