Title of dissertation: MESHLESS COLLOCATION METHODS FOR THE NUMERICAL SOLUTION OF ELLIPTIC BOUNDARY VALUED PROBLEMS AND THE ROTATIONAL SHALLOW WATER EQUATIONS ON THE SPHERE Christopher D. Blakely, Doctor of Philosophy, 2009 Dissertation directed by: Professor John Osborn Department of Mathematics Professor Ferdinand Baer Department of Atmospheric and Oceanic Science This dissertation thesis has...

heterogeneous and dynamic problems of engineering technology and systems for industry and government. ISR is a permanent institute of the University of Maryland, within the Glenn L. Martin Institute of Technology/A. James Clark School of Engineering. It is a National Science Foundation Engineering Research Center. Web site http://www.isr.umd.edu I R INSTITUTE FOR SYSTEMS RESEARCH TECHNICAL RESE...

Fast Algorithms with Applications to PDEs

In this paper, a Jacobi-collocation spectral method is developed for Volterra integral equations of second kind with a weakly singular kernel. We use some function transformation and variable transformations to change the equation into a new Volterra integral equation defined on the standard interval [−1, 1], so that the solution of the new equation possesses better regularity and the Jacobi or...

In this paper we develop hydrodynamic models using spectral differential operators to investigate the spatial stability of swirling fluid systems. Including viscosity as a valid parameter of the fluid, the hydrodynamic model is derived using a nodal Lagrangean basis and the polynomial eigenvalue problem describing the viscous spatial stability is reduced to a generalized eigenvalue problem usin...

one of the most important and brilliant aspects in each language is the collocation that finally add up to lexical coherence . coming together in semantics considers as one of the semantic relationships at lexical level that appears at all languages , and doesnt specialize for a certain language . mean while .the study of pre-islamic period poem about coming together is a significant affair . t...

We investigate three-dimensional problems in solid mechanics with stochastic loading or material properties. To solve these problems, we use a spectral expansion of the solution and random inputs based on Askey-type orthogonal polynomials in terms of independent, identically distributed (i.i.d) random variables. A Galerkin procedure using these types of expansions, the generalized Polynomial Ch...

We consider fast solvers for the large linear systems coming from the Isogeometric Analysis (IgA) collocation approximation based on B-splines of full elliptic d-dimensional Partial Differential Equations (PDEs). We are interested in designing iterative algorithms which are optimal and robust. The former property implies that the computational cost is linear with respect to the number of degree...