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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 655 for “"Discretization"”.
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Geometric discretization schemes and differential complexes for elasticity
… exterior calculus (DEC), we present a geometric discretization scheme for incompressible linearized elasticity. After characterizing the configuration manifold of volume- preserving discrete deformations, we use Hamilton's principle on this configuration manifold. The discrete Euler-Lagrange …
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Discretization of differential geometry for computational gauge theory
This Dissertation was approved for publication on 2018-04-13 at 12:05.
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Residual-Based Discretization Error Estimation for Unsteady Flows
… CFD. This thesis develops techniques to estimate discretization error for unsteady flows using the unsteady error transport equation (ETE) as well as defect correction. A framework to obtain exact truncation error and estimated truncation error is also presented. The technique and results for the …
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Generalized spatial discretization techniques for space-marching algorithms
Two unique spatial discretizations employing generalized indexing strategies suitable for use with space-marching algorithms are presented for the numerical solution of the equations of fluid dynamics. Both discretizations attempt to improve geometric flexibility as compared to structured indexing …
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Error behavior and optimal discretization of chaotic differential equations
… chaos introduces statistical errors alongside discretization errors. These statistical errors are generally one of two types: transient spin-up error before the system reaches the attractor (i.e. the stationary distribution of long-run states) and sampling error due to finite-time averaging of …
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Residual-based Discretization Error Estimation for Computational Fluid Dynamics
… numerical approximation error to estimate is discretization error. Residual-based discretization error estimation methods are a category of error estimators that use an estimate of the source of discretization error and information about the specific application to estimate the discretization …
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Discretization and solution of elliptic PDEs--a transform domain approach
Includes bibliographies.
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A physics-based adaptive point distribution method for computational domain discretization
Two algorithms are presented which together generate well-spaced point distributions applied to curves, surfaces, and the volume of a computational domain. The first is a force equilibrium simulation which applies a simplified direct solution of the equations of motion at each node. Inter-nodal …
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On qualitative properties and convergence of time-discretization methods for semigroups
… convergence and qualitative properties of time-discretization methods for strongly continuous semigroups. Stability, convergence, and preservation of contractivity (or norm-bound) of the semigroup under time-discretization is investigated in a Banach space setting. Preservation of positivity, …
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Extrapolation-based Discretization Error and Uncertainty Estimation in Computational Fluid Dynamics
… types of numerical error in a solution, discretization error is the largest and most difficult error to estimate. In addition, the accuracy of the discretization error estimates relies on the solution (or multiple solutions used in the estimate) being in the asymptotic range. The …
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Domain decomposition and high order discretization of elliptic partial differential equations
… has largely been based on second order accurate discretization techniques. This dissertation describes an algorithm for the numerical solution of general two-dimensional linear elliptic partial differential equations with variable coefficients which employs both a high order accurate …
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Application of r-Adaptation Techniques for Discretization Error Improvement in CFD
… the numerical error present in a solution. Discretization error is often the primary source of numerical error. Discretization error is introduced locally into the solution by truncation error. Truncation error represents the higher order terms in an infinite series which are truncated …
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Bilinear Discretization of Integrable Quadratic Vector Fields: Algebraic Structure and Algebro-Geometric Solutions
In der Arbeit werden die Integrabilitätseigenschaften der Hirota- Kimura Diskretisierungen (HK-Diskretisierungen) von algebraisch integrablen Systemen gewöhnlicher Differentialgleichungen beschrieben. Dieser Diskretisierungs-ansatz, der zuerst von Kahan beschrieben wurde und später von Hirota und …
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On the development of preconditioning the advection diffusion operators with spectral element discretization
Submission published under a 24 month embargo labeled 'U of I Access', the embargo will last until 2025-05-01
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A finite volume discretization method for flow on structured and unstructured anisotropic meshes
This project is concerned with advection discretization technology within the field of Computational Fluid Dynamics (CFD). To this end, two novel methods are proposed which are dubbed the Enhanced Taylor (ET) Schemes. The model equation for this work is the advection-diffusion equation with the …
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On the development of an efficient truly meshless discretization procedure in computational mechanics
… using numerical inf-sup tests for a variety of discretization schemes. Solutions to several example problems are presented showing the application of the method of finite spheres to problems in solid and fluid mechanics. A very specialized application of the technique to physically based real …
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Discretization Error Estimation Using the Error Transport Equations for Computational Fluid Dynamics Simulations
… nonlinear algebraic equations. Typical spatial discretization schemes include finite-difference methods, finite-volume methods, and finite-element methods. Error introduced in the discretization process is called discretization error and defined as the difference between the exact solution to …
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Polynomial Models for Systems Biology: Data Discretization and Term Order Effect on Dynamics
… modeling method: the necessity of appropriate discretization of the data and the selection of a particular polynomial model from the set of all models that fit the data. Data discretization, also known as binning, is a crucial issue for the construction of discrete models of biological …
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Linear Power Discretization and Nonlinear Formulations for Optimizing Hydropower in a Pumped Storage System
… related issues. The linear formulation uses a discretization scheme to approximate the nonlinear efficiency, pump, turbine, spillway discharge, tailrace elevation-discharge, and storage-elevation relationships. Also, there are binary unit dispatch and either/or constraints accommodating spill …
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