309 research outputs found
Interval linear constraint solving in constraint logic programming.
by Chong-kan Chiu.Thesis (M.Phil.)--Chinese University of Hong Kong, 1994.Includes bibliographical references (leaves 97-103).Chapter 1 --- Introduction --- p.1Chapter 1.1 --- Related Work --- p.2Chapter 1.2 --- Organizations of the Dissertation --- p.4Chapter 1.3 --- Notations --- p.4Chapter 2 --- Overview of ICLP(R) --- p.6Chapter 2.1 --- Basics of Interval Arithmetic --- p.6Chapter 2.2 --- Relational Interval Arithmetic --- p.8Chapter 2.2.1 --- Interval Reduction --- p.8Chapter 2.2.2 --- Arithmetic Primitives --- p.10Chapter 2.2.3 --- Interval Narrowing and Interval Splitting --- p.13Chapter 2.3 --- Syntax and Semantics --- p.16Chapter 3 --- Limitations of Interval Narrowing --- p.18Chapter 3.1 --- Computation Inefficiency --- p.18Chapter 3.2 --- Inability to Detect Inconsistency --- p.23Chapter 3.3 --- The Newton Language --- p.27Chapter 4 --- Design of CIAL --- p.30Chapter 4.1 --- The CIAL Architecture --- p.30Chapter 4.2 --- The Inference Engine --- p.31Chapter 4.2.1 --- Interval Variables --- p.31Chapter 4.2.2 --- Extended Unification Algorithm --- p.33Chapter 4.3 --- The Solver Interface and Constraint Decomposition --- p.34Chapter 4.4 --- The Linear and the Non-linear Solvers --- p.37Chapter 5 --- The Linear Solver --- p.40Chapter 5.1 --- An Interval Gaussian Elimination Solver --- p.41Chapter 5.1.1 --- Naive Interval Gaussian Elimination --- p.41Chapter 5.1.2 --- Generalized Interval Gaussian Elimination --- p.43Chapter 5.1.3 --- Incrementality of Generalized Gaussian Elimination --- p.47Chapter 5.1.4 --- Solvers Interaction --- p.50Chapter 5.2 --- An Interval Gauss-Seidel Solver --- p.52Chapter 5.2.1 --- Interval Gauss-Seidel Method --- p.52Chapter 5.2.2 --- Preconditioning --- p.55Chapter 5.2.3 --- Increment ality of Preconditioned Gauss-Seidel Method --- p.58Chapter 5.2.4 --- Solver Interaction --- p.71Chapter 5.3 --- Comparisons --- p.72Chapter 5.3.1 --- Time Complexity --- p.72Chapter 5.3.2 --- Storage Complexity --- p.73Chapter 5.3.3 --- Others --- p.74Chapter 6 --- Benchmarkings --- p.76Chapter 6.1 --- Mortgage --- p.78Chapter 6.2 --- Simple Linear Simultaneous Equations --- p.79Chapter 6.3 --- Analysis of DC Circuit --- p.80Chapter 6.4 --- Inconsistent Simultaneous Equations --- p.82Chapter 6.5 --- Collision Problem --- p.82Chapter 6.6 --- Wilkinson Polynomial --- p.85Chapter 6.7 --- Summary and Discussion --- p.86Chapter 6.8 --- Large System of Simultaneous Equations --- p.87Chapter 6.9 --- Comparisons Between the Incremental and the Non-Incremental Preconditioning --- p.89Chapter 7 --- Concluding Remarks --- p.93Chapter 7.1 --- Summary and Contributions --- p.93Chapter 7.2 --- Future Work --- p.95Bibliography --- p.9
A study of domain decomposition methods applied to the discretized Helmholtz equation
In this work a domain decomposition based preconditioner of the additive Schwarz type is developed and tested on the linear systems which arise out of the application of the Green\u27s Function/Wave Expansion Discretization (GFD/WED) method to Helmholtz\u27s equation. In order to develop the additive Schwarz preconditioner, use is made of a class of one-sided Artificial Radiation Boundary Conditions (ARBC) developed during the course of this work. These ARBCs are computationally shown to be quite accurate for use on their own. The ARBC\u27s are used to radiatively couple the various sub-domains which are naturally part of domain decomposition based methods in such a manner as to ensure that the system matrix, when restricted to the subdomains, is non-singular. In addition, the inter-domain ARBC is constructed such that the solution to the global linear system is unaffected by the presence of the artificial boundaries. The efficacy and efficiency of the method is demonstrated on one, two, and three-dimensional test cases
Multilevel Preconditioning of Discontinuous-Galerkin Spectral Element Methods, Part I: Geometrically Conforming Meshes
This paper is concerned with the design, analysis and implementation of
preconditioning concepts for spectral Discontinuous Galerkin discretizations of
elliptic boundary value problems. While presently known techniques realize a
growth of the condition numbers that is logarithmic in the polynomial degrees
when all degrees are equal and quadratic otherwise, our main objective is to
realize full robustness with respect to arbitrarily large locally varying
polynomial degrees degrees, i.e., under mild grading constraints condition
numbers stay uniformly bounded with respect to the mesh size and variable
degrees. The conceptual foundation of the envisaged preconditioners is the
auxiliary space method. The main conceptual ingredients that will be shown in
this framework to yield "optimal" preconditioners in the above sense are
Legendre-Gauss-Lobatto grids in connection with certain associated anisotropic
nested dyadic grids as well as specially adapted wavelet preconditioners for
the resulting low order auxiliary problems. Moreover, the preconditioners have
a modular form that facilitates somewhat simplified partial realizations. One
of the components can, for instance, be conveniently combined with domain
decomposition, at the expense though of a logarithmic growth of condition
numbers. Our analysis is complemented by quantitative experimental studies of
the main components.Comment: 41 pages, 11 figures; Major revision: rearrangement of the contents
for better readability, part on wavelet preconditioner adde
Computer methods for design automation
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Ocean Engineering, 1992.Includes bibliographical references (leaves 142-159).by Christian Bliek.Ph.D
Parallel Solution Methods for Aerostructural Analysis and Design Optimization
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/83550/1/AIAA-2010-9308-579.pd
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