近年臺北市政府試圖藉由興建品質良好的公共住宅，解決住宅價格高漲影響人民居住的問題，然附近居民往往認為公共住宅會造成周圍住宅生活環境品質低落及房價下跌，反對其於住家鄰近興建。過去國內缺乏以實證方式計算公共住宅對周圍住宅價格之影響，亦尚未針對新推出的公營出租住宅個案深入分析；而國外相關研究雖有利用量化實證公共住宅與周圍房價關係，然多針對個別公共住宅社區為研究對象，對不同類型公共住宅及其對不同高低房價住宅之影響與差異，缺乏更全面的探討分析，且亦未釐清住宅價格的空間自相關特性及公共住宅設立的不同階段等，對周圍房價影響效果的差異。 本文應用特徵價格理論傳統迴歸模型、空間迴歸模型及分量迴歸模型，以2012年7月至2015年9月之臺北市不動產實價登錄交易資料為對象，研究整建住宅、出售國宅、出租國宅、公營出租住宅等四類不同時期公共住宅，於100~300公尺不同影響範圍下，分別對周圍住宅價格的影響效果。另外並選取興隆公共住宅作為個案研究對象，以臺北市文山區不動產實價登錄交易資料為對象，應用差異中之差異法結合空間迴歸模型，分析興隆公共住宅的興建完工與住戶入住對於周圍住宅價格之外溢效果。實證結果顯示，附近有早期興建之整建住宅及出租國宅者，其住宅總價皆呈現顯著下跌現象，分別下跌約1.7%至8.9%及1.5%至7.7%；附近有出售國宅之住宅總價漲跌情形不顯著；而近期興建之公營出租住宅則造成周圍住宅價格顯著上漲約1.7%至7.7%；又前述影響程度皆隨影響範圍擴大而隨之減輕。進一步分析不同影響範圍下對周圍高低房價住宅的影響，公營出租住宅對周圍低價住宅正向提升效果為6.2%至7.1%，皆大於高價住宅之無顯著影響至3.2%。而興隆公共住宅的興建完工確實能使周圍住宅價格較外圍地區多提升約6.5%至15.8%，惟住戶入住興隆公共住宅則未具顯著正向的價格外溢效果。由新興辦的公營出租住宅對周圍房價造成正面影響的實證結果，應可釐清公共住宅外部性之正向效果，有助後續公共住宅的興建。 / In recent years, government has tried to build the public housing with high quality to solve the living problems caused by the soaring of the house price. However, residents beside the public housing often regard them as Nimbys that will detrimentally affect property values and oppose public housing to be built nearby. There were short of empirical studies that focus on the effects of public housing on nearby property, as well as the case study of social housing newly built in Taiwan. Besides, the empirical studies in foreign only select a specific public housing as their subject, which few of them analyze different effects caused by different types of public housing, ignore different effects on nearby property with different values, and have not clarify whether the spatial autocorrelation of property values as well as the construction and operation of the social housing leads to different results. This study analyzes the effect of social housing, resettled tenement, public housing for rent and for sale on nearby property values in different ranges separately by using hedonic price theory OLS, spatial and quantile regression as model, and selecting the sale price of real estate in Taipei City from July 2012 to September 2015 as sample. Besides, Xing-Long Social housing and sale prices of real estate in Wenshan district of Taipei City are also selected for case study applying Difference in Difference method with spatial regression, in order to analyze the nearby property values changes after the construction and the move in of the residents of Xing-Long social housing. The result shows that although resettled tenement and public housing for rent detrimentally affect the property values by 1.7% to 8.9% and 1.5% to 7.7% separately, public housing for sale does not affect the property values significantly, and social housing positively affects the property values by 1.7% to 7.7% on the contrary. In addition, these effects decline with distance from public housing. With regard to the impact on high and low priced property in different ranges, social housing has positive effect on low-priced property by 6.2% to 7.1% and no significant effect to 3.2% on high-priced property. The construction of Xing-Long social housing has positive spillover effect by 6.5% to 15.8%, however, the move in of the residents does not. Empirical results show that social housing newly built are able to enhance the property values nearby, which is contributed to the follow-up construction of the public housing.

The master's thesis deals with Navier-Stokes equations in curvilinear coordinates and their solution for quasi-potential flow. The emphasis is on detailed description of curvilinear space and its expression using Bézier curves, Bézier surfaces and Bézier bodies. Further, fundamental concepts of hydromechanics are defined, including potential and quasi-potential flow. Cauchy equations are derived as a result of the law of momentum conservation and continuity equation is derived as a result of principle of mass conservation. Navier-Stokes equations are then derived as a special case of Cauchy equations using Cauchy stress tensor of Newtonian compressible fluid. Further transformation into curvilinear coordinates is accomplished through differential operators in curvilinear coordinates and by using curvature vector of space curve. In the last section we use results from previous chapters to solve boundary value problem of quasi-potential flow, which was solved by finite difference method using Matlab environment.

This thesis deals with gradient calculation in triangulation nodes using weighted average of gradients of neighboring elements. This gradient is then used for a posteriori error estimation which produce better solution of partial differential equations. This work presents two common methods - Finite elements method and Finite difference method.

This work deals with techniques of time-domain analysis of interconnects. After a studying crucial issue of time-domain analysis of interconnects methods of modeling and simulation simple interconnects in electrotechnics are described. For transient effect analysis two elementary methods can be used: the state variable method and the FDTD (Finite - Difference Time - Domain) method. The FDTD method can be used to solve partial differential equations in time domain, for instance equations of transmission lines. The method is very effective and delivers satisfactory results in case of linear and non-linear lines with a single “live” conductor. The method can be easily programmed in Matlab.

The main topic of this diploma thesis is the modeling of nonlinear effects in ultrasonic fields. The work deals with application of finite difference method (FDTD) on the Westervelt equation and the subsequent creation of the model of ultrasonic fields in MATLAB. This thesis also includes theoretical analysis of ultra-acoustic and technical aspects of diagnostic ultrasonography. In addition, this document includes verification of theoretical assumptions by using created model.

Two-stage stochastic programming problem with PDE constraint, specially elliptic equation is formulated. The computational scheme is proposed, whereas the emphasis is put on approximation techniques. We introduce method of approximation of random variables of stochastic problem and utilize suitable numerical methods, finite difference method first, then finite element method. There is also formulated a mathematical programming problem describing a membrane deflection with random load. It is followed by determination of the acceptableness of using stochastic optimization rather than deterministic problem and assess the quality of approximations based on Monte Carlo simulation method and the theory of interval estimates. The resulting mathematical models are implemented and solved in the general algebraic modeling system GAMS. Graphical and numerical results are presented.

This thesis deals with modelling of continuous casting of steel. This process of steel manufacturing has achieved dominant position not only in the Czech Republic but also worldwide. The solved casted bar cross-section shape is circular, because it is rarely studied in academical works nowadays. First part of thesis focuses on creating numerical model of thermal field, using finite difference method with cylindrical coordinates. This model is then employed in optimization part, which represents control problem of abrupt step change of casting speed. The main goal is to find out, whether the computation of numerical model and optimization both can be parallelized using spatial decomposition. To achieve that, Progressive Hedging Algorithm from the field of stochastic optimization has been used.

This dissertation deals with impedance measurements of lead-acid accumulator. Main aim was to study recent problems of impedance measurements of lead-acid accumulator and most importantly to extend difference method and also to interpret its results. The original DC difference method was developed earlier at our Power Sources Laboratory of Department of Electrical and Electronic Technology. The DC difference method and also the new AC difference method are both non-destructive, which means that experimental data can be obtained in situ. New method provides more accurate set of information because of its wide frequency range nature. Electrodes of lead-acid accumulator were analysed with special attention to collector / active mass double layer and to active mass itself. Various states and operation regimes were investigated. Obtained data contributed to better understanding of involved degradation mechanisms. Main aim of other experiment was to observe and interpret corrosion rates of electrode collector composed of various lead alloys. Last but not least charge and discharge regimes e.g. 100% deep of discharge regime, partial state of charge (PSoC) regime and pulse charge regime were analysed. BioLogic VSP was the device used for almost all experimental measurements. It takes a lot of effort to optimise VSP operation regime. Best operation regime of VSP for the difference method was suggested too.

<div>Accurate, fast, large-scale, and circuit-intuitive electromagnetic analysis is of critical importance to the design of integrated circuits (IC) and systems. Existing methods for the analysis of integrated circuits and systems have not satisfactorily achieved these performance goals. In this work, rapid modeling and simulation methods are developed for large-scale and circuit-intuitive electromagnetic analysis of integrated circuits and systems. The derived model is correct from zero to high frequencies where Maxwell's equations are valid. In addition, in the proposed model, we are able to analytically decompose the layout response into static and full-wave components with neither numerical computation nor approximation. This decomposed yet rigorous model greatly helps circuit diagnoses since now designers are able to analyze each component one by one, and identify which component is the root cause for the design failure. Such a decomposition also facilitates efficient layout modeling and simulation, since if an IC is dominated by RC effects, then we do not have to compute the full-wave component; and vice versa. Meanwhile, it makes parallelization straightforward. In addition, we develop fast algorithms to obtain each component of the inverse rapidly. These algorithms are also applicable for solving general partial differential equations for fast electromagnetic analysis.</div><div><br></div><div>The fast algorithms developed in this work are as follows. First, an analytical method is developed for finding the nullspace of the curl-curl operator in an arbitrary mesh for an arbitrary order of curl-conforming vector basis function. This method has been applied successfully to both a finite-difference and a finite-element based analysis of general 3-D structures. It can be used to obtain the static component of the inverse efficiently. An analytical method for finding the complementary space of the nullspace is also developed. Second, using the analytically found nullspace and its complementary space, a rigorous method is developed to overcome the low-frequency breakdown problem in the full-wave analysis of general lossy problems, where both dielectrics and conductors can be lossy and arbitrarily inhomogeneous. The method is equally valid at high frequencies without any need for changing the formulation. Third, with the static component part solved, the full-wave component is also ready to obtain. There are two ways. In the first way, the full-wave component is efficiently represented by a small number of high-frequency modes, and a fast method is created to find these modes. These modes constitute a significantly reduced order model of the complementary space of the nullspace. The second way is to utilize the relationship between the curl-curl matrix and the Laplacian matrix. An analytical method to decompose the curl-curl operator to a gradient-divergence operator and a Laplacian operator is developed. The derived Laplacian matrix is nothing but the curl-curl matrix's Laplacian counterpart. They share the same set of non-zero eigenvalues and eigenvectors. Therefore, this Laplacian matrix can be used to replace the original curl-curl matrix when operating on the full-wave component without any computational cost, and an iterative solution can converge this modified problem much faster irrespective of the matrix size. The proposed work has been applied to large-scale layout extraction and analysis. Its performance in accuracy, efficiency, and capacity has been demonstrated.</div>

In this thesis we look at acoustic wave propagation under water. We look in particular at waves generated by a point source and what happens with the propagation when we model the bottom as flat or as curvilinear. We assume the source to be working at a certain frequency and therefore we model this problem by solving the Helmholtz equation. Since Helmholtz equation has some unwanted numerical properties we are interested in finding new numerical methods that could accelerate the solver. In this thesis we use the Waveholtz iteration, which solves Helmholtz equation by connecting it to the time-dependent wave equation. We use finite differences and the SBP-SAT method to approximate the spatial problem numerically and for modelling the sea bottom we use curvilinear coordinates.  To compare the Waveholtz iteration we also solve Helmholtz equation with a naive solver. The naive solver consists of approximating the equation with finite differences and then solving the linear system of equation by some iterative solver, which for our tests will be GMRES. The results show that the Waveholtz iteration converges in less iterations than our naive solver. It also shows that the number of iterations stays unchanged when changing our discretization, which otherwise is a big problem for our naive solver. This allows us to increase the accuracy of our numerical solution without changing the computation time too much.  We show that the number of iterations increases according to theory for an increasing frequency, and that for open problems we even see a smaller increase. For certain resonant frequencies in Helmholtz equation we do not expect the Waveholtz iteration to converge. In the neighbourhood of these frequencies the convergence becomes slow and we need many iterations for a solution of a certain accuracy. By reformulating the Waveholtz iteration as a Krylov solution we can see that resonances in Helmholtz equation have a smaller impact of the convergence. / I detta examensarbete undersöker vi akustisk vågutbredning i vatten. Vi kollar specifikt på vågor som genereras av en punktkälla och vad som sker när vi modellerar botten som plan eller som kurvlinjär. Då vi antar att punktkällan arbetar vid en bestämd frekvens, kommer vi modellera det fysikaliska problemet genom att lösa Helmholtz ekvation. Helmholtz ekvation har dock några numeriska egenskaper som är oönskade, och därför finns ett intresse av att hitta nya numeriska metoder som löser ekvationen. I detta examensarbete undersöker vi Waveholtz iteration, som löser Helmholtz ekvation genom att koppla den till den tidsberoende vågekvationen. Vi använder finita differenser och SBP-SAT metoden för att approximera det rumsliga problemet numeriskt. För att ge en detaljerad beskrivning av botten använder vi kurvlinjära koordinater. För att jämföra Waveholtz iterationen med något löser vi även Helmholtz med hjälp av en naiv lösare. Den naiva lösaren består av att approximera problemet med finita differenser och sedan lösa det linjära systemet rakt av med en iterativ lösare (vilket för våra fall kommer vara GMRES). Resultatet visar att Waveholtz iteration konvergerar på ett lägre antal iterationer än vår naiva lösare. Det visar även att antalet iterationer inte förändras när vi ändrar diskretisering, vilket annars är ett problem för vår naiva lösare. Detta innebär att vi kan få en högre noggrannhet utan att förlänga beräkningstiden alltför mycket.  Vi visar även att antalet iterationer ökar som förväntat med en ökad frekvens, samt att för öppna problem så ökar antalet iteration mindre än enligt teorin. Vid vissa resonanta frekvenser i Helmholtz ekvation förväntar vi oss att Waveholtz iteration inte kommer konvergerar. I närheten av dessa frekvenser blir konvergensen långsam och vi behöver många iterationer för att lösa problemet. Genom att formulera Waveholtz iteration som en Krylov lösning kommer resonanser i Helmholtz ekvation ge en mindre negativ effekt på konvergensen än om den är formulerad som en fixpunkts iteration.