Browsing by Subject "Decomposition methods"

Now showing 1 - 3 of 3

Open Access
Calculation of the scalar diffraction field from curved surfaces by decomposing the three-dimensional field into a sum of Gaussian beams
(Optical Society of America, 2013) Şahin, E.; Onural, L.
We present a local Gaussian beam decomposition method for calculating the scalar diffraction field due to a twodimensional field specified on a curved surface. We write the three-dimensional field as a sum of Gaussian beams that propagate toward different directions and whose waist positions are taken at discrete points on the curved surface. The discrete positions of the beam waists are obtained by sampling the curved surface such that transversal components of the positions form a regular grid. The modulated Gaussian window functions corresponding to Gaussian beams are placed on the transversal planes that pass through the discrete beam-waist position. The coefficients of the Gaussian beams are found by solving the linear system of equations where the columns of the system matrix represent the field patterns that the Gaussian beams produce on the given curved surface. As a result of using local beams in the expansion, we end up with sparse system matrices. The sparsity of the system matrices provides important advantages in terms of computational complexity and memory allocation while solving the system of linear equations.
Open Access
Optimizing airline operations under uncertainty
(2019-06) Aydıner, Özge Şafak
Fluctuations in passenger demand, airport congestion, and high fuel costs are the main threats to airlines' profit, thereby need to be carefully addressed in airline scheduling problems. This study takes an advantage of aircraft cruise speed control in several scheduling problems to keep the cost of fuel manageable. We first generate a flight schedule by integrating strategic departure time decisions, tactical eeting and routing decisions and more operational flight timing decisions under stochastic demand and non-cruise times. Our model differs from the existing studies by including aircraft cruise speed decisions to compensate for increase in non-cruise time variations due to the airport congestion. To e ciently solve the problem, we provide a scenario group-wise decomposition algorithm. Then, we consider a new problem which aims to accommodate new flights into an existing flight schedule in a short time. We suggest some operational changes such as controlling the aircraft cruise speed, re-timing flight departures and swapping aircraft to open up time for new flights. However, nonlinear fuel cost function, and binary assignment and swapping decisions significantly increase the computational burden of solving scheduling problems. In this thesis, we propose strong mixed integer conic quadratic formulations. Finally, we extend the problem by including a strategic decision to lease an aircraft for introducing new flights. More importantly, we consider the effects of departure time decisions on the probability distribution of random demand. We propose a bounding method based on scenario group-wise decomposition for stochastic programs with decision dependent probabilities.
Open Access
Using a variation of empirical mode decomposition to remove noise from signals
(IEEE, 2011-06) Kaleem, M. F.; Guergachi, A.; Krishnan, S.; Çetin, A. Enis
This paper will describe the application of -based decomposition, which is a variation of the empirical mode decomposition method based on modified peak selection, to de-noising and de-trending of signals. The -based decomposition method will be explained, and its application to synthetic and real-world signals in the context of de-noising and de-trending will be described. Comparison between the computational simplicity of the τ-based decomposition method to de-noising and de-trending of signals and approaches based on empirical mode decomposition will be highlighted. © 2011 IEEE.