The purpose of this paper is to investigate the problem of finding a common element of the set of solutions of a generalized equilibrium problem (for short, GEP) and the set of fixed points of a nonexpansive mapping in a Hilbert space. First, by using the well-known KKM technique we derive the existence and uniqueness of solutions of the auxiliary problems for the GEP. Second, on account of this result and Nadler's theorem, we introduce an iterative scheme by the viscosity approximation method for finding a common element of the set of solutions of the GEP and the set of fixed points of the nonexpansive mapping. Furthermore, it is proven that the sequences generated by this iterative scheme converge strongly to a common element of the set of solutions of the GEP and the set of fixed points of the nonexpansive mapping.

Boundary approximation method, also known as the collocation Trefftz method in engineering, is used to solve Laplace boundary value problem on rectanglular domain. Suppose the particular solutions are chosen for the whole domain. If there is no singularity on other vertices, it should have exponential convergence. Otherwise, it will degenerate to polynomial convergence. In the latter case, the order of convergence has some relation with the intensity of singularity. So, it is easy to design models with desired convergent orders. On a sectorial domain, when one side of the boundary conditions is a transcendental function, it needs to be approximated by power series. The truncation of this power series will generate an artificial singularity when solving Laplace equation on polygon. So it will greatly slow down the expected order of convergence. This thesis study how the truncation error affects the convergent speed. Moreover, we focus on the transition behavior of the convergence from one order to another. In the end, we also apply our results to boundary approximation method with enriched basis.

The dynamic solution of multiphase flow through porous media is of special interest to several fields of science and engineering, such as petroleum, geology and geophysics, bio-medical, civil and environmental, chemical engineering and many other disciplines. A natural application is the modeling of the flow of two immiscible fluids (phases) in a reservoir. Others, that are broadly based and considered in this work include the hydrodynamic dispersion (as in reactive transport) of a solute or tracer chemical through a fluid phase. Reservoir properties like permeability and porosity greatly influence the flow of these phases. Often, these vary across several orders of magnitude and can be discontinuous functions. Furthermore, they are generally not known to a desired level of accuracy or detail and special inverse problems need to be solved in order to obtain their estimates. Based on the physics dominating a given sub-region of the porous medium, numerical solutions to such flow problems may require different discretization schemes or different governing equations in adjacent regions. The need to couple solutions to such schemes gives rise to challenging domain decomposition problems. Finally, on an application level, present day environment concerns have resulted in a widespread increase in CO₂capture and storage experiments across the globe. This presents a huge modeling challenge for the future. This research work is divided into sections that aim to study various inter-connected problems that are of significance in sub-surface porous media applications. The first section studies an application of mortar (as well as nonmortar, i.e., enhanced velocity) mixed finite element methods (MMFEM and EV-MFEM) to problems in porous media flow. The mortar spaces are first used to develop a multiscale approach for parabolic problems in porous media applications. The implementation of the mortar mixed method is presented for two-phase immiscible flow and some a priori error estimates are then derived for the case of slightly compressible single-phase Darcy flow. Following this, the problem of modeling flow coupled to reactive transport is studied. Applications of such problems include modeling bio-remediation of oil spills and other subsurface hazardous wastes, angiogenesis in the transition of tumors from a dormant to a malignant state, contaminant transport in groundwater flow and acid injection around well bores to increase the permeability of the surrounding rock. Several numerical results are presented that demonstrate the efficiency of the method when compared to traditional approaches. The section following this examines (non-mortar) enhanced velocity finite element methods for solving multiphase flow coupled to species transport on non-matching multiblock grids. The results from this section indicate that this is the recommended method of choice for such problems. Next, a mortar finite element method is formulated and implemented that extends the scope of the classical mortar mixed finite element method developed by Arbogast et al [12] for elliptic problems and Girault et al [62] for coupling different numerical discretization schemes. Some significant areas of application include the coupling of pore-scale network models with the classical continuum models for steady single-phase Darcy flow as well as the coupling of different numerical methods such as discontinuous Galerkin and mixed finite element methods in different sub-domains for the case of single phase flow [21, 109]. These hold promise for applications where a high level of detail and accuracy is desired in one part of the domain (often associated with very small length scales as in pore-scale network models) and a much lower level of detail at other parts of the domain (at much larger length scales). Examples include modeling of the flow around well bores or through faulted reservoirs. The next section presents a parallel stochastic approximation method [68, 76] applied to inverse modeling and gives several promising results that address the problem of uncertainty associated with the parameters governing multiphase flow partial differential equations. For example, medium properties such as absolute permeability and porosity greatly influence the flow behavior, but are rarely known to even a reasonable level of accuracy and are very often upscaled to large areas or volumes based on seismic measurements at discrete points. The results in this section show that by using a few measurements of the primary unknowns in multiphase flow such as fluid pressures and concentrations as well as well-log data, one can define an objective function of the medium properties to be determined, which is then minimized to determine the properties using (as in this case) a stochastic analog of Newton’s method. The last section is devoted to a significant and current application area. It presents a parallel and efficient iteratively coupled implicit pressure, explicit concentration formulation (IMPEC) [52–54] for non-isothermal compositional flow problems. The goal is to perform predictive modeling simulations for CO₂sequestration experiments. While the sections presented in this work cover a broad range of topics they are actually tied to each other and serve to achieve the unifying, ultimate goal of developing a complete and robust reservoir simulator. The major results of this work, particularly in the application of MMFEM and EV-MFEM to multiphysics couplings of multiphase flow and transport as well as in the modeling of EOS non-isothermal compositional flow applied to CO₂sequestration, suggest that multiblock/multimodel methods applied in a robust parallel computational framework is invaluable when attempting to solve problems as described in Chapter 7. As an example, one may consider a closed loop control system for managing oil production or CO₂sequestration experiments in huge formations (the “instrumented oil field”). Most of the computationally costly activity occurs around a few wells. Thus one has to be able to seamlessly connect the above components while running many forward simulations on parallel clusters in a multiblock and multimodel setting where most domains employ an isothermal single-phase flow model except a few around well bores that employ, say, a non-isothermal compositional model. Simultaneously, cheap and efficient stochastic methods as in Chapter 8, may be used to generate history matches of well and/or sensor-measured solution data, to arrive at better estimates of the medium properties on the fly. This is obviously beyond the scope of the current work but represents the over-arching goal of this research. / text

In the literature, many methods are proposed to value American options. However, due to computational difficulty, there are only approximate solution or numerical method to evaluate American options. It is not easy for general investors either to understand nor to apply. In this thesis, we build up an option pricing and virtual asset model system, which provides a friendly environment for general public to calculate early exercise boundary of an American option. This system modularize the well-handled pricing models to provide the investors an easy way to value American options without learning difficult financial theories. The system consists two parts: the first one is an option pricing system, the other one is an asset model simulation system. The option pricing system provides various option pricing methods to the users; the virtual asset model system generates virtual asset prices for different underlying models.

We present an optimization procedure for solving the vehicle routing problem with a fixed heterogeneous fleet of vehicle. We want to minimize the passage price. We look and probe these methods: minimal element, Vogel’s Approximation and heuristic. The modeling vehicle routing problem is based on mathematical formulation. This paper present very well known problems – TSP Traveling Salesperson Problem and M-TSP. Vehicle routing problem is liked M-TSP with some specification, vehicle with a fixed carrying capacity must deliver order of goods to n customers from a single depot. Knowing the distance between customers, the problem is to find tours for the vehicles in such a way that: the total distance traveled by the vehicles is minimized, only one vehicle handles the deliveries for a given customer, the total quantity of goods that a single vehicle delivers cannot be larger than cars capacity.

?rea de concentra??o: Manejo florestal e silvicultura. / Submitted by Jos? Henrique Henrique (jose.neves@ufvjm.edu.br) on 2017-06-09T22:52:32Z No. of bitstreams: 2 talles_hudson_souza_lacerda.pdf: 1852089 bytes, checksum: 5f25d81aee4d02d93913bfc83196ecb3 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Approved for entry into archive by Rodrigo Martins Cruz (rodrigo.cruz@ufvjm.edu.br) on 2017-06-14T19:22:36Z (GMT) No. of bitstreams: 2 talles_hudson_souza_lacerda.pdf: 1852089 bytes, checksum: 5f25d81aee4d02d93913bfc83196ecb3 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Made available in DSpace on 2017-06-14T19:22:36Z (GMT). No. of bitstreams: 2 talles_hudson_souza_lacerda.pdf: 1852089 bytes, checksum: 5f25d81aee4d02d93913bfc83196ecb3 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2017 / Coordena??o de Aperfei?oamento de Pessoal de N?vel Superior (CAPES) / O objetivo desse trabalho foi avaliar, do ponto de vista estat?stico e biol?gico, simula??es realizadas por dois modelos de distribui??o diam?trica, ajustados pelos m?todos de aproxima??o linear e m?xima verossimilhan?a, em planta??es de eucalipto submetidos a desbaste. Os dados foram provenientes de um povoamento h?brido de Eucalyptus grandis x Eucalyptus urophylla, sob regime de desbaste, localizado no nordeste da Bahia, vinculados ? empresa BAHIA SPECIALTY CELLULOSE. Os dados utilizados neste estudo foram obtidos nas idades 27, 40, 50, 61, 76, 87, 101, 112, 122, 137, 147, 158 e 165 meses. Esse povoamento foi submetido a tratamentos de remo??o seletiva de 20%, 35% e 50%, nas idades 58 e 142 meses. Utilizou-se dois modelos de distribui??o diam?trica, empregando bases de dados observadas aos 27 meses (antes do primeiro desbaste), aos 61 meses (ap?s o primeiro desbaste) e aos 147 meses (ap?s o segundo desbaste). Por meio dos modelos gerou-se tr?s sistemas, os quais se diferiram no m?todo de ajuste da fun??o Weibull. No sistema 1 os par?metros da fun??o Weibull foram ajustados pelo m?todo de aproxima??o linear. No sistema 2 e no sistema 3, os par?metros foram ajustados pelo m?todo da m?xima verossimilhan?a. As proje??es realizadas pelos sistemas foram confrontadas com as distribui??es diam?tricas observadas, por meio do teste de ader?ncia Kolmogorov-Smirnov a 1% de signific?ncia, e pelo teste F de Graybill, com n?vel de signific?ncia de 5%. Os tr?s sistemas proporcionaram distribui??es diam?tricas projetadas estatisticamente semelhantes ?s observadas, antes e ap?s o desbastes. O sistema 2 apresentou um maior percentual de proje??es n?o significativas para os dois testes estat?sticos empregados. As simula??es realizadas pelos modelos apresentaram realismo estat?stico e tend?ncia do crescimento da distribui??o de di?metros para diferentes porcentagens de desbaste. Houve maior efici?ncia dos modelos ao se utilizar distribui??es diam?tricas observadas em idades imediatamente antes do desbaste. As proje??es das distribui??es diam?tricas, empregando-se como base inicial as distribui??es observadas antes do primeiro desbaste e imediatamente ap?s os desbastes (simula??es 1, 2 e 3), foram mais precisas do que as proje??es obtidas quando foram utilizadas somente as distribui??es diam?tricas observadas antes do primeiro desbaste como base inicial para as proje??es e, em seguida, simulados os desbastes nas idades previstas e, por ?ltimo, realizadas as proje??es empregando-se a distribui??o estimada remanescente do desbaste como base inicial para projetar as distribui??es para idades subsequentes (simula??es 4, 5 e 6). / Disserta??o (Mestrado) ? Programa de P?s-Gradua??o em Ci?ncia Florestal, Universidade Federal dos Vales do Jequitinhonha e Mucuri, 2017. / The objective of the study was evaluated from the statistical and biological point of view, simulations performed by two models of diametric distribution, adjusted by linear approximation and maximum likelihood methods, in eucalyptus plantations submitted to thinning. The data were found in a hybrid settlement of Eucalyptus grandis x Eucalyptus urophylla, under thinning regime, located in the northeast region of Bahia, linked to the company BAHIA ESPECIALIDADE CELULOSE. The data used in this study 27, 40, 50, 61, 76, 87, 101, 112, 122, 137, 147, 158 and 165 months. This population was submitted to treatments of selective removal of 20%, 35% and 50%, in the ages 58 and 142 months. Two diametric distribution models were used, using data bases observed at 27 months (before the first thinning), at 61 months (after the first thinning) and at 147 months (after the second thinning). By means of the models three systems were generated, the channels did not differ any method of adjustment of the Weibull function. No system 1 of the Weibull function parameters were adjusted by the linear approximation method. In system 2 and in system 3 the parameters were adjusted by the maximum likelihood method. As the projections performed by the systems were compared with the observed diametric distributions, using the Kolmogorov-Smirnov test at 1% significance, by the Graybill F test, with a significance level of 5%. The three systems provided by the statistically projected diametric distributions for observations, before and after the deviations. System 2 presents a higher percentage of nonsignificant projections for the two statistical tests used. As simulations of model execution demonstrated statistical realism and tendency of growth of the distribution of diameters for different percentages of thinning. There was greater efficiency of the models of use of diametric distributions observed in ages before thinning. As the projections of the diametric distributions, using as an initial basis as distributions observed before the first thinning and after the slabs (simulations 1, 2 and 3), were more accurate than the projections obtained when only diametric distributions observed before the first Thinning as the initial basis for the projections and then simulated the lagging at the predicted ages and finally performed as projections using an estimated remnant distribution of the thinning as the initial basis for designing as distributions for subsequent ages (simulations 4, 5 and 6).

Passenger ride vibration comfort is a critical aspect to consider while developing any vehicle and there is a need to understand how the occupants would be affected when driving on different road profile roughness. Hence, road profile generation is critical as road profiles are used as inputs to simulation tools to investigate vehicle dynamic behaviour in depth. At the same time, the optimisation of the vehicle characteristics can be conducted on the various road profiles in order to identify a solution that can provide enhanced ride comfort and improve vehicle handling for all the investigated road profiles. The objective of this thesis is to study ride vibrational comfort and optimise the suspension system for theNational Electric Vehicle Sweden (NEVS) vehicle model for better ride comfort and road holding. Synthetic road profiles are generated by using stochastic processes according to International Organization for Standardization (ISO) 8608 standards. Further, simulations are conducted in MSC ADAMS Car software using the generated synthetic road profiles for a rigid body NEVS vehicle model to study the vertical accelerations. The analysis includes the investigations of the acceleration Power Spectral Density (PSD) and observations are made on the peaks that appear (at Front Seat Rail (FSR) which is the sprung mass of the vehicle and Wheel centre (WC) which is the un-sprung mass of the vehicle) for different road types and vehicle velocities. It is decided that the comfort objective will be used considering the weighted Root Mean Square (RMS) accelerations. Further, the suspension system of the vehicle model is optimised for three different road profiles (A, B, and C) based on the objectives of ride comfort and handling using a suitable vehicle model with the same characteristics as theNEVScar. A multi-objective optimisation technique is used and the optimised results are observed and discussed. Optimal objectives (based on a compromise between ride comfort and road holding) for the suspension system are determined for each investigated road profile. / Vibrationskomfort för passagerare är en kritisk aspekt att tänka på när man utvecklar ett fordon och det finns ett behov av att förstå hur passagerarna kan påverkas när de åker på olika vägprofiler. Därför är vägprofilgenerering avgörande eftersom vägprofiler används som input till simuleringsverktyg för att undersöka fordonets dynamiska beteende. Samtidigt kan optimeringen av fordonets egenskaper utföras på de olika vägprofilerna för att identifiera en lösning som kan ge ökad åkkomfort och förbättra fordonshanteringen för alla undersökta vägprofiler. Syftet med detta examensarbete är att studera körvibrationskomfort och optimera fjädringssystemet för NEVS fordonsmodellen för bättre åkkomfort och väghållning. Syntetiska vägprofiler genereras genom att använda stokastiska processer enligt ISO 8608 standarder. Dessutom utförs simuleringar i MSC ADAMS programvara med hjälp av de genererade syntetiska vägprofilerna för en stelkropps NEVS fordonsmodell för att studera de vertikala accelerationerna. Analysen inkluderar undersökningar av accelerations PSD och observationer görs av topparna som visas (vid FSR och WC) för olika vägtyper och fordonshastigheter. Det beslutas att komfortmålet kommer att utvärderas med hänsyn till endast de vägda RMS accelerationerna. Dessutom är fordonsmodellens hjul upphängningssystem optimerat för tre olika vägprofiler (A, B och C) baserat på målen för åkkomfort och väghållning med hjälp av en lämplig fordonsmodell med samma egenskaper som NEVS bilen. En multi-purpose optimeringsteknik används och de optimerade resultaten observeras och diskuteras. Optimala mål (baserat på en kompromiss mellan åkkomfort och väghållning) för fjädringssystemet bestäms för varje undersökt vägprofil.