Numerical aspects of the PUFEM for efficient solution of Helmholtz problems

Conventional finite element methods (FEM) have been used for many years for the solution of harmonic wave problems. To ensure accurate simulation, each wavelength is discretised into around ten nodal points, with the finite element mesh being updated for each frequency to maintain adequate resolution of the wave pattern. This technique works well when the wavelength is long or the model domain is small. However, when the converse applies and the wavelength is small or the domain of interest is large, the finite element mesh requires a large number of elements, and the procedure becomes computationally expensive and impractical. The principal objective of this work is to accurately model two-dimensional Helmholtz problems with the Partition of Unity Finite Element Method (PUFEM). This will be achieved by applying the plane wave basis decomposition to the wave field. These elements allow us to relax the traditional requirement of around ten nodal points per wavelength and therefore solve Helmholtz wave problems without refining the mesh of the computational domain at each frequency. Various numerical aspects affecting the efficiency of the PUFEM are analysed in order to improve its potential. The accuracy and effectiveness of the method are investigated by comparing solutions for selected problems with available analytical solutions or to high resolution numerical solutions using conventional finite elements. First, the use of plane waves or cylindrical waves in the enrichment process is assessed for wave scattering problems involving a rigid circular cylinder in both near field and far field. In the far field, the cylindrical waves proved to be more effective in reducing the computational effort. But given that the plane waves are simpler to analytically integrate for straight edge elements, during the finite element assembling process, they are retained for the remaining of the thesis. The analysed numerical aspects, which may affect the PUFEM performance, include the conjugated and unconjugated weighting, the geometry description, the use of non-reflecting boundary conditions, and the h-, p- and q-convergence. To speed up the element assembling process at high wave numbers, an exact integration procedure is implemented. The PUFEM is also assessed on multiple scattering problems, involving sets of circular cylinders, and on exterior wave problems presenting singularities in the geometry of the scatterer. Large and small elements, in comparison to the wavelength, are used with both constant and variable numbers of enriching plane waves. Last, the PUFEM resulting system is iteratively solved by using an incomplete lower and upper based preconditioner. To further enhance the efficiency of the iterative solution, the resulting system is solved into the wavelet domain. Overall, compared to the FEM, the PUFEM leads to drastic reduction of the total number of degrees of freedom required to solve a wave problem. It also leads to very good performance when large elements, compared to the wavelength, are used with high numbers of enriching plane waves, rather than small elements with low numbers of plane waves. Due to geometry detail description, it is practical to use both large and small elements. In this case, to keep the conditioning within acceptable limits it is necessary to vary the number of enriching plane waves with the element size

Formal Analysis of MCAP Protocol Against Replay Attack

Replay attack is considered a common attacking technique that is used by adversaries to gain access to confidential information. Several approaches have been proposed to prevent replay attack in security-critical systems such as Automated Teller Machines (ATM) systems. Among those approaches is a recent one called the Mutual Chain Authentication Protocol for the Saudi Payments Network transactions (MCAP). This protocol aims to allow Saudi banking systems to overcome existing weaknesses in the currently used Two-Factor Authentication (2FA) protocols. In this paper, we analyze and verify the recent MCAP authentication protocol against replay attacks. Therefore, we examine the mutual authentication between the ATM Terminal, Sponsoring Banks (SBAT), Saudi Payments Network (SPAN) and the Issuing of Financial Bank (CIFI). The paper also provides a formal analysis of the MCAP to conduct formal proofs of the MCAP protocols against replay attacks

Right-of-Way Acquisition and Property Condemnation: A Comparison of U.S. State Laws

Recommendations for improvements in U.S. right-of-way (ROW) acquisition processes should consider the environmental, social, political, and economic characteristics of individual states. These characteristics are reflected in state statutes and constitutions, which place restrictions on ROW staff in applying recommended strategies. This work compares state condemnation statutes, noting their weaknesses and strengths. It recommends modifications to current laws to expedite the acquisition process, minimize cost, and build property owners' trust in government. It also examines how various factors are statistically significant in predicting state condemnation rates

The analysis and forecasting of male cycling time trial records established within England and Wales.

The format of cycling time trials in England, Wales and Northern Ireland, involves riders competing individually over several fixed race distances of 10-100 miles in length and using time constrained formats of 12 and 24 h in duration. Drawing on data provided by the national governing body that covers the regions of England and Wales, an analysis of six male competition record progressions was undertaken to illustrate its progression. Future forecasts are then projected through use of the Singular Spectrum Analysis technique. This method has not been applied to sport-based time series data before. All six records have seen a progressive improvement and are non-linear in nature. Five records saw their highest level of record change during the 1950-1969 period. Whilst new record frequency generally has reduced since this period, the magnitude of performance improvement has generally increased. The Singular Spectrum Analysis technique successfully provided forecasted projections in the short to medium term with a high level of fit to the time series data

Adaptive Mobility Management Scheme for Mobile IP using Ad Hoc Networks.

Mobile IP has been developed to handle global mobility of mobile hosts. Mobile IP suffers from a number of drawbacks such as frequent location update, high signaling overhead, high handover latency, high packet loss rate, and requirement of infrastructure change. To treat these problems, we propose a new mobility management scheme by constructing dynamic service regions of Ad Hoc networks for roaming mobile host without location update to reduce signaling overhead and packets loss. Analytical analysis and simulation results are shown in this paper to demonstrate that the proposed scheme performs better performance than other schemes

Crystalline Electric Field and Kondo Effect in SmOs4Sb12

Our ultrasound results obtained in pulsed magnetic fields show that the filled-skutterudite compound SmOs$_4$Sb$_{12}$ has the $\Gamma_{67}$ quartet crystalline-electric-field ground state. This fact suggests that the multipolar degrees of freedom of the $\Gamma_{67}$ quartet play an important role in the unusual physical properties of this material. On the other hand, the elastic response below $\approx$ 20 T cannot be explained using the localized 4$f$-electron model, which does not take into account the Kondo effect or ferromagnetic ordering. The analysis result suggests the presence of a Kondo-like screened state at low magnetic fields and its suppression at high magnetic fields above 20 T even at low temperatures.Comment: 4 pages, 4 figure