Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 20 of 60 for “"spectral method"”.
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A multidomain spectral method for computational aeroacoustics
This thesis presents a method for computational aeroacoustics, primarily aimed at computing sound propagation in, and radiation from, turbofan inlets. The physics of sound propagation is modeled by the system of partial differential equations that describe conservation of mass, momentum and energy …
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Solution of non-linear partial differential equations with the Chebyshev Spectral method
The Spectral method is a powerful numerical technique for solving engineering differential equations. The method is a specialization of the method of weighted residuals. Trial functions that are easily and exactly differentiable are used. Often the functions used also satisfy an orthogonality …
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Semiconductor device simulation : a spectral method for solution of the Boltzmann transport equation
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1988.
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Krylov Subspace Spectral Method with Multigrid for a Time-Dependent, Variable-Coefficient Partial Differential Equation
<p>Krylov Subspace Spectral (KSS) methods are traditionally used to solve time-dependent, variable-coefficient PDEs. They are high-order accurate, component-wise methods that are efficient with variable input sizes.</p> <p>This thesis will demonstrate how one can make KSS methods even more …
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Chebyshev spectral method for incompressible viscous flow with boundary layer control via suction or blowing
… code implements a two-equation integral method with empirical closure relations to solve the boundary layer flow problem with or without suction, but lacks the option of flow control via blowing. The integral method is parameterized with the shape parameter H _ 6*/0 which cannot be …
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A spectral method determination of the first critical Rayleigh number for a low-Prandtl number crystal melt in a cylindrical container
… and insulated surfaces. A Chebyshev Galerkin spectral model is used to reduce the governing Boussinesq system to a first-order system of ordinary differential equations. A local stability analysis using the linearized system determines the first critical Rayleigh number. The results are …
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Deterministic numerical simulation of the Boltzmann and kinetic model equations for classical and quantum dilute gases
… accurate and efficient deterministic numerical method to solve the Boltzmann equation. The fast spectral method [1], originally developed by Mouhot and Pareschi for the numerical approximation of the collision operator, is extended to deal with other collision kernels, such as those …
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Simulation of Turbulent Flows Using Nodal Integral Method
… compared with those obtained using the pseudo spectral method. The comparison shows good agreement and also shows that results obtained with similar grid sizes and time steps match very well with those obtained using pseudo spectral method. New results are obtained for k = 2, and the …
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Chebyshev spectral methods for potential field computation
We investigate Chebyshev spectral methods for solving Poisson's equation and the generalized Poisson's equations and apply them to 3-D gravity and DC resistivity modeling. When we approximate a function by a finite sum of Chebyshev polynomials, there are two kinds of errors: truncation and …
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Efficient Spectral-Element Methods For Acoustic Scattering And Related Problems
… on the development of high-order numerical methods for acoustic and electromagnetic scattering problems, and nonlinear fluid-structure interaction problems.</p> <p>For the scattering problems, two cases are considered: 1) the scattering from a doubly layered periodic structure; and 2) the …
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Multilevel spectral clustering : graph partitions and image segmentation
While the spectral graph partitioning method gives high quality segmentation, segmenting large graphs by the spectral method is computationally expensive. Numerous multilevel graph partitioning algorithms are proposed to reduce the segmentation time for the spectral partition of large graphs. …
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A new numerical method for the problem of nonlinear long-short wave interactions
… thesis is the development of a new numerical method to address the problem of nonlinear interactions of free-surface gravity waves. More specifically, this study addresses the case of wave interactions of short waves ridding on longer waves up to second order of nonlinearity M. The study of …
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Topological solitons of the nonlinear Dirac equation in 2+1 dimensional space time
… use of the sine series expansion and Chebyshev spectral method, where the author is the first to present this work. The Chebyshev spectral method was found to outperform the sine series expansion in terms of computation times. However, the drawback of Chebyshev differentiation matrices is that …
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Time Spectral Adjoint Based Design for Flutter and Limit Cycle Oscillation Suppression
… Traditionally, frequency domain based methods have been used to predict flutter characteristics and its sensitivity. However, this approach is only applicable for linear or linearized models and cannot be applied to systems undergoing LCO or other nonlinear effects. Though the time …
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Approximation of wave packets on the whole real line
… L₂(R) which can be used in the construction of a spectral method for solving the semi-classically scaled time dependent linear Schrödinger equation (TDSE) on the real line. All bases have banded skew-symmetric (or skew-Hermitian) differentiation matrices, which greatly simplifies their …
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SOLVING THE CABLE EQUATION, A SECOND-ORDER TIME DEPENDENT PDE FOR NON-IDEAL CABLES WITH ACTION POTENTIALS IN THE MAMMALIAN BRAIN USING KSS METHODS
… perform the comparisons of a Krylov Subspace Spectral method with Forward Euler, Backward Euler and Crank-Nicolson to solve the Cable Equation. The Cable Equation measures action potentials in axons in a mammalian brain treated as an ideal cable in the first part of the study. We shall subject …
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Numerical Investigation of turbulent coupling boundary layer of air-water interaction flow
… stress condition across the interface. Pseudo-spectral method is used in each flow subdomain with Fourier expansion in streamwise and spanwise directions and finite difference in vertical direction. Statistically quasi-steady flow properties, such as mean velocity profiles, turbulent …
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Option pricing in a path integral framework
This dissertation is an examination of methods for computing an option price using a path integral framework. The framework, developed by Chiarella, El-Hassan and Kucera, is based on the Black and Scholes paradigm. The path integral is backward recursive with the payoff known at expiry and has no …
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Coupled Adjoint-based Sensitivity Analysis using a FSI Method in Time Spectral Form
A time spectral and coupled adjoint based sensitivity analysis of rotor blade is carried out in this study. The time spectral method is an efficient technique to solve unsteady periodic problems by transforming unsteady equation of motion to a steady state one. Due to the availability of the …
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Spectral Estimation of Hidden Markov Models
This thesis extends and improves methods for estimating key quantities of hidden Markov models through spectral method-of-moments estimation. Unlike traditional estimation methods like EM and Gibbs sampling, the set of estimation methods, which we call spectral HMMs (sHMMs), are incredibly fast, do …
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