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Numerical analysis

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Articles 31 - 41 of 41

Full-Text Articles in Applied Mathematics

Analysis Of Hdg Methods For Stokes Flow, Bernardo Cockburn, Jay Gopalakrishnan, Ngoc Cuong Nguyen, Jaume Peraire, Francisco-Javier Sayas Jan 2011

Analysis Of Hdg Methods For Stokes Flow, Bernardo Cockburn, Jay Gopalakrishnan, Ngoc Cuong Nguyen, Jaume Peraire, Francisco-Javier Sayas

Mathematics and Statistics Faculty Publications and Presentations

In this paper, we analyze a hybridizable discontinuous Galerkin method for numerically solving the Stokes equations. The method uses polynomials of degree $ k$ for all the components of the approximate solution of the gradient-velocity-pressure formulation. The novelty of the analysis is the use of a new projection tailored to the very structure of the numerical traces of the method. It renders the analysis of the projection of the errors very concise and allows us to see that the projection of the error in the velocity superconverges. As a consequence, we prove that the approximations of the velocity gradient, the …

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A Projection-Based Error Analysis Of Hdg Methods, Jay Gopalakrishnan, Bernardo Cockburn, Francisco-Javier Sayas Jan 2010

A Projection-Based Error Analysis Of Hdg Methods, Jay Gopalakrishnan, Bernardo Cockburn, Francisco-Javier Sayas

Mathematics and Statistics Faculty Publications and Presentations

We introduce a new technique for the error analysis of hybridizable discontinuous Galerkin (HDG) methods. The technique relies on the use of a new projection whose design is inspired by the form of the numerical traces of the methods. This renders the analysis of the projections of the discretization errors simple and concise. By showing that these projections of the errors are bounded in terms of the distance between the solution and its projection, our studies of influence of the stabilization parameter are reduced to local analyses of approximation by the projection. We illustrate the technique on a specific HDG …

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Determining The Orbit Locations Of Turkish Airborne Early Warning And Control Aircraft Over The Turkish Air Space, Nebi Sarikaya Mar 2009

Determining The Orbit Locations Of Turkish Airborne Early Warning And Control Aircraft Over The Turkish Air Space, Nebi Sarikaya

Theses and Dissertations

The technology improvement affects the military needs of individual countries. The new doctrine of defense for many countries emphasizes detecting threats as far away as you can from your homeland. Today, the military uses both ground RADAR and Airborne Early Warning and Control (AEW&C) Aircraft. AEW&C aircraft has become vital to detect low altitude threats that a ground RADAR cannot detect because of obstacles on the earth. Turkey has ordered four AEW&C aircraft for her air defense system because of the lack of complete coverage by ground RADAR. This research provides optimal orbit locations that can be updated according to …

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Polynomial Extension Operators. Part Ii, Leszek Demkowicz, Jay Gopalakrishnan, Joachim Schöberl Jan 2009

Polynomial Extension Operators. Part Ii, Leszek Demkowicz, Jay Gopalakrishnan, Joachim Schöberl

Mathematics and Statistics Faculty Publications and Presentations

Consider the tangential trace of a vector polynomial on the surface of a tetrahedron. We construct an extension operator that extends such a trace function into a polynomial on the tetrahedron. This operator can be continuously extended to the trace space of H(curl ). Furthermore, it satisfies a commutativity property with an extension operator we constructed in Part I of this series. Such extensions are a fundamental ingredient of high order finite element analysis.

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Hardware Algorithm Implementation For Mission Specific Processing, Jason W. Shirley Mar 2008

Hardware Algorithm Implementation For Mission Specific Processing, Jason W. Shirley

Theses and Dissertations

There is a need to expedite the process of designing military hardware to stay ahead of the adversary. The core of this project was to build reusable, synthesizeable libraries to make this a possibility. In order to build these libraries, Matlab® commands and functions, such as Conv2, Round, Floor, Pinv, etc., had to be converted into reusable VHDL modules. These modules make up reusable libraries for the Mission Specific Process (MSP) which will support AFRL/RY. The MSP allows the VLSI design process to be completed in a mere matter of days or months using an FPGA or ASIC design, as …

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Multigrid Convergence For Second Order Elliptic Problems With Smooth Complex Coefficients, Jay Gopalakrishnan, Joseph E. Pasciak Jan 2008

Multigrid Convergence For Second Order Elliptic Problems With Smooth Complex Coefficients, Jay Gopalakrishnan, Joseph E. Pasciak

Mathematics and Statistics Faculty Publications and Presentations

The finite element method when applied to a second order partial differential equation in divergence form can generate operators that are neither Hermitian nor definite when the coefficient function is complex valued. For such problems, under a uniqueness assumption, we prove the continuous dependence of the exact solution and its finite element approximations on data provided that the coefficients are smooth and uniformly bounded away from zero. Then we show that a multigrid algorithm converges once the coarse mesh size is smaller than some fixed number, providing an efficient solver for computing discrete approximations. Numerical experiments, while confirming the theory, …

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Locally Conservative Fluxes For The Continuous Galerkin Method, Bernardo Cockburn, Jay Gopalakrishnan, Haiying Wang Jan 2007

Locally Conservative Fluxes For The Continuous Galerkin Method, Bernardo Cockburn, Jay Gopalakrishnan, Haiying Wang

Mathematics and Statistics Faculty Publications and Presentations

The standard continuous Galerkin (CG) finite element method for second order elliptic problems suffers from its inability to provide conservative flux approximations, a much needed quantity in many applications. We show how to overcome this shortcoming by using a two step postprocessing. The first step is the computation of a numerical flux trace defined on element inter- faces and is motivated by the structure of the numerical traces of discontinuous Galerkin methods. This computation is non-local in that it requires the solution of a symmetric positive definite system, but the system is well conditioned independently of mesh size, so it …

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A Stochastic Model For Psa Levels: Behavior Of Solutions And Population Statistics, Pavel Bělík, P W A Dayananda, John T. Kemper, Mikhail M. Shvartsman Sep 2006

A Stochastic Model For Psa Levels: Behavior Of Solutions And Population Statistics, Pavel Bělík, P W A Dayananda, John T. Kemper, Mikhail M. Shvartsman

Faculty Authored Articles

This paper investigates the partial differential equation for the evolving distribution of prostate-specific antigen (PSA) levels following radiotherapy. We also present results on the behavior of moments for the evolving distribution of PSA levels and estimate the probability of long-term treatment success and failure related to values of treatment and disease parameters. Results apply to a much wider range of parameter values than was considered in earlier studies, including parameter combinations that are patient specific.

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Error Analysis Of Variable Degree Mixed Methods For Elliptic Problems Via Hybridization, Bernardo Cockburn, Jay Gopalakrishnan Mar 2005

Error Analysis Of Variable Degree Mixed Methods For Elliptic Problems Via Hybridization, Bernardo Cockburn, Jay Gopalakrishnan

Mathematics and Statistics Faculty Publications and Presentations

A new approach to error analysis of hybridized mixed methods is proposed and applied to study a new hybridized variable degree Raviart-Thomas method for second order elliptic problems. The approach gives error estimates for the Lagrange multipliers without using error estimates for the other variables. Error estimates for the primal and flux variables then follow from those for the Lagrange multipliers. In contrast, traditional error analyses obtain error estimates for the flux and primal variables first and then use it to get error estimates for the Lagrange multipliers. The new approach not only gives new error estimates for the new …

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A Characterization Of Hybridized Mixed Methods For Second Order Elliptic Problems, Bernardo Cockburn, Jay Gopalakrishnan Jan 2004

A Characterization Of Hybridized Mixed Methods For Second Order Elliptic Problems, Bernardo Cockburn, Jay Gopalakrishnan

Mathematics and Statistics Faculty Publications and Presentations

In this paper, we give a new characterization of the approximate solution given by hybridized mixed methods for second order self-adjoint elliptic problems. We apply this characterization to obtain an explicit formula for the entries of the matrix equation for the Lagrange multiplier unknowns resulting from hybridization. We also obtain necessary and sufficient conditions under which the multipliers of the Raviart–Thomas and the Brezzi–Douglas–Marini methods of similar order are identical.

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Mapping Efficient Numerical Methods To The Solution Of Multiple Objective Linear Programs, Michael A. Shields Mar 1991

Mapping Efficient Numerical Methods To The Solution Of Multiple Objective Linear Programs, Michael A. Shields

Theses and Dissertations

This investigation was initiated to increase the speed, accuracy and capacity of m-simplex algorithms for solving multiple objective linear programming problems. Specifically, improvements were sought through the application of general numerical techniques. It soon became apparent that the m- simplex algorithm, like the simplex algorithm, is heavily dependent upon the technology of solving related systems of linear equations. The numerical arguments for the application of LU triangular matrix factorization techniques to simplex computations are well known. OF special significance to m-simplex performance is the case of rank-k updates to basis factorizations. A stable and efficient LU approach to the rank-k …

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