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Viscosity Approximation Methods for Generalized Equilibrium Problems and Fixed Point ProblemsHuang, Yun-ru 20 June 2008 (has links)
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.
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Convergence Transition of BAM on Laplace BVP with SingularitiesLin, Guan-yu 30 June 2009 (has links)
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.
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On some problems in the simulation of flow and transport through porous mediaThomas, Sunil George 20 October 2009 (has links)
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
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Option Pricing and Virtual Asset Model SystemCheng, Te-hung 07 July 2005 (has links)
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.
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Krovinių srautų modeliavimas uždaroje logistikos sistemoje / Modeling of load flows in clique logistic systemJusevičienė, Kristina 06 June 2006 (has links)
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.
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Proje??o diam?trica com base em dados observados antes e ap?s o desbaste em povoamentos de eucaliptoLacerda, Talles Hudson Souza 16 February 2017 (has links)
?rea de concentra??o: Manejo florestal e silvicultura. / Submitted by Jos? Henrique Henrique (jose.neves@ufvjm.edu.br) on 2017-06-09T22:52:32Z
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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).
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Assessment of optimal suspension systems with regards to ride under different road profiles / Bedömning av optimala fjädringssystem med avseende på komfort vid körning på olika vägprofilerMurali, Adithya, Vaje, Pratik Hindraj January 2021 (has links)
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.
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