Computational Science

Permanent URI for this collection

http://etd.aau.edu.et/handle/12345678/147

Browse

Now showing 1 - 7 of 7

Application of Newton and Quasi-Newton Techniques to Non-Linear Problems in Computational Mechanics
(Addis Ababa University, 2020-11-12) Habtamu, Fikru; Oseloka, Okey (Professor)
In the field of engineering, researches often come across strong nonlinear boundary value problems (BVPs) that cannot solve easily. Numerical convergence for many problems, typically solved by the Newton-Raphson algorithm, is sensitive to the initial guess and need computations of Jacobi and its inverse at each iteration. Emphasis in the present work is placed on the alternative approach, such as quasi-Newton, HM and optimization method. Many problems in applied mechanics are reduced to the solutions of systems of nonlinear algebraic, transcendental equations containing an explicit parameter. These are problems in the areas of thermo-fluids, gas dynamics, deformable solids, heat transfer, biomechanics, optimal control and others. A parameter found in these models is not unique, and may be easily identified artificially. An important aspect of these problems is a question of the variation of the solution when parameter is incrementally changed. The numerical solution of BVPs of ordinary differential equations (ODE‟s) relies heavily on methods for solving systems of algebraic equations. The choice of the optimal numerical method, which ensures the best convergence rate with minimum error for the corresponding system of nonlinear equations, is discussed. Some modifications of quasi-Newton‟s method for systems of ordinary nonlinear differential equations are apply and suggested. Effectiveness of the method is demonstrated by comparing the results with the analytic solution for model boundary value problem implemented using a MATLAB Program. The objective of the research is to investigate applicability of the method to the wide range of nonlinear boundary value problems in different areas of mechanics. Different problems of applied mechanics and physics with dominant nonlinearities due to constituent models, and others are analyzed and solve in the present work. In this paper, the Newton‟s Homotopy analysis method (NHAM) is also applied on nonlinear boundary value problems(BVPs) of mechanics problems. The result from the method prove NHAM with Runge-Kutta steps, were significantly reliable and more accurate however, computation cost is high.
Debt Collection Optimization: Commercial Bank of Ethiopia’s case
(Addis Ababa University, 2015-02) Girma, Benyam; Teklu, Tilahun (PhD)
This thesis develops and analyzes a finite horizon Markov decision process model for commercial bank of Ethiopia’s debt collection optimization problem. Two sectors namely domestic trade and services (DTS) and foreign trade (FT) have been studied primarily because of loan turnover rates and economic policy focus. A 2 years long data are used to determine cost of holding an outstanding loan in a certain state or delinquency status on a log scale where each state/status is scaled by the percentage of provision allocated to the states. Conclusions are made in terms of which loan segments banks need treat with more caution. Simple but important suggestions on ways of improving the operations of banks are made in the end.
Epidemiological Modeling of Measles Disease with Optimal Control of Vaccination Strategy
(Addis Ababa University, 2015-04) Zewdie Esayas; Oseloka Okey (Professor)
Epidemiological models provide a powerful tool for investigating the dynamics and control of infectious diseases, but quantifying the underlying epidemic structure can be challenging especially for new and under-studied diseases. Measles is a highly infectious disease which has a major impact on child survival, particularly in developing countries. The importance of understanding the epidemiology of this disease is underlined by its ability to change rapidly in the face of increasing immunization coverage with proper cost effectiveness. Much is still to be learned about its epidemiology and the best strategies for administering measles vaccines. However, it is clear that tremendous progress can be made in preventing death and disease from measles with existing knowledge about the disease, and by using the presently available vaccines and applying well-tried methods of treating cases. Since vaccination turned out to be the most effective strategy against childhood disease, developing a framework that would predict an optimal vaccine coverage level needed to control the spread of these diseases is crucial. We consider an optimal control problem subject to an SEIR measles epidemic model with vaccination controls. Our aim is find the best optimal control strategies to make the number of infectious individuals as small as possible and to keep the vaccination ratio of measles as low as possible during a certain vaccination period that will minimize the cost of control. We used Pontryagin’s maximum principle to characterize the optimal levels of the controls. The resulting optimality system is solved numerically by forward-backward sweep method. The results show that the optimal vaccination policy differs according to the controlled and uncontrolled individuals and has a very desirable effect upon the population for reducing the number of infected individuals. The effect of vaccination on transmission dynamics of measles is studied. The resulting optimality system also showed that, the use of vaccinating at the highest possible rate to the population as early as possible is essential for controlling an epidemic of the measles disease. Finally, we use our model to simulate the data of measles cases in the Ethiopia from 2004 to 2014 and design a control strategy (optimal vaccination policy) of the country to eliminate the epidemic for the future course with optimal control theory. The results from our simulation are discussed.
The Influence of Nonlinear Reaction, Memory and A Heaviside Function Source Term on Scalar Transport
(Addis Ababa University, 2016-06) Bekele Habtamu; Oseloka Okey (Professor)
In this study, a numerical method based on finite difference is presented for the numerical solution of a generalized Fisher-Integro differential equation. A composite weighted trapezoidal rule is manipulated to handle the numerical integrations which results in a closed difference scheme. The non-linear terms are linearized by one of the finite difference linearization techniques. Three different methods are used; Left end point rule, right end point rule and trapezoidal end point rule. The numerical solutions obtained for the three methods indicate that, the approach is reliable and yields results compatible. The discretization of the governing equation is made by explicit, Implicit and Crank-Nicolson method time scheme. The flow of an incompressible viscous fluid between a uniformly porous upper plate and a lower impermeable plate that is subjected to a FKPP is modeled and analyzed in this study. The Model equations are presented in terms of Left end point rule, Right end point rule and trapezoidal end point rule. For the Left end point rule, we are using the explicit method, for the right end point rule we are using the implicit method and for the trapezoidal end point rule we are using both implicit and explicit (Crank-Nicolson) method. In this study, the researcher looked how to discretize integro-partial differential equation (memory term) using trapezoidal, left endpoints, right endpoints and Simpson’s rule. The literature highlights how the Fisher Kolomogrov-Petrovskii-Piskunov Equation is developed and used. The main part of this paper is dedicated in discretizing FKPP and developing a computer program to compute the solution.
Modeling Traffic Flow Problem: Comparison of Multilane Roundabout Versus Traffic Light Control
(Addis Ababa University, 2009-07) Yoseph, Dagim; Mitiku, Semu (PhD)
The vehicular traffic is controlled by a self-organized scheme in which traffic lights are absent at traffic junctions. This controlling method incorporates a yield-at-entry strategy for the vehicles approaching to the circulating traffic flow in the roundabout. Vehicular dynamics are simulated within the framework of the probabilistic cellular automata and the throughputs experienced at each individual street are evaluated for specified time intervals to determine the performance of the roundabout. We used Multi-stream Minimum Acceptable Space (MMAS) Cellular Automata (CA) model for the description of vehicular traffic at a roundabout. In this thesis inconsistency of driver behavior and interactions in cross traffic at entrances of roundabouts are simulated by incorporation of four different categories of driver behavior (i.e., conservative, moderate, urgent and radical). Our results give the critical throughput in which the intersection should be controlled in a self-organized manner is approximately 4500vph. This proves that below certain congestion, the roundabout efficiency is higher than fixed-time signalized junction point. In general, average throughputs for two-lane roundabout are lower than the signalized intersection, even for a fixedtime signalization.
Optimal Project Selection and Budget Allocation for the Selected Project
(Addis Ababa University, 2011-06) Taye, Nuhamin; Guta, Berhanu (PhD)
Project Selection is the process of evaluating individual projects, to choose the right project based on an analysis so that the objectives of the company will be achieved. It involves a thorough analysis including the most important nancial aspect to determine the most optimum project among all the alternatives. LINGO optimization tool has been adopted to determine the optimal project. The model presented in the paper shows a special tool for project selection based on in uences that govern the project selection process. Finally, an optimal budget is allocated to the selected project using a dynamic programming. The result showed that optimal project selection and optimal budget allocation should be used by organization to maximize their return.
Seismicity of Afar and the Main Ethiopian Rift From 2000 - 2002 G.C.
(Addis Ababa University, 2011-06) Alemayehu, Sisay; Ayele, Atalay (PhD)
Earthquakes data recorded between 2000 and 2002 are used to study the seismicity of Ethiopia mainly focused around Afar and the Main Ethiopian rift. The locations of 238 local earthquake are determined using P- and S- wave arrival times recorded on three or more stations that resulted to a maximum of 1.5 root mean square (RMS). Previous studies of seismicity by Brazier et al., 2006 has been revisited using the same data from IRIS/PASSCAL broadband seismic experiments and adding more from ESSN (Ethiopian Seismic Station Network) sources. Comparing the results in this study with Brazier et al., 2006's, it is found that eight bogus events (earthquakes that didn't occur in the real world) and six more teleseismic earthquakes are reported as if they occurred in the Ethiopian neighborhood. On the other hand, it is observed that Brazier et al's work, which is published in Bulletins of Seismological Society of America (BSSA), reported 25 earthquakes that are located with readings from seismic stations less than three which puts doubt on the accuracy of the seismicity study. Another 53 new earthquakes are identi ed in the database and located in this study which has improved details of the seismicity of the region for the time period considered. A Fortran program is written in 0.5 by 0.5 degree window and with 0.5 degree sliding window in order to map the seismic energy release. The distribution of epicenter in this study shows high seismic activity around 90N and 40:500E; 9:500N and 39:500E during the study period, these epicenters are close to the N - S trending Ankober region, Kessem area and Dofen volcano. Coda magnitudes are also estimated for the reported events. Similarly b-values are estimated using both the least squares method and the maximum likelihood method. b-value of 0.9 0.09 and 1.10 were obtained using the maximum-likelihood method and using least square method determined respectively for the highly seismic Ankober-Dofen region during the study period. On the other hand, seismic energy map is developed for the whole region. The relatively high b-value estimated and the seismic energy mapping showed that seismic energy are released in the form of small magnitude.

Browse

Browsing Computational Science by Subject "Computational"

Results Per Page

Sort Options