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Meshless collocation methods for the...

Blakely, Christopher D.

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Meshless collocation methods for the numerical solution of elliptic boundary valued problems the rotational shallow water equations on the sphere.

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Meshless collocation methods for the numerical solution of elliptic boundary valued problems the rotational shallow water equations on the sphere./
Author:	Blakely, Christopher D.
Description:	250 p.
Notes:	Source: Dissertation Abstracts International, Volume: 71-02, Section: B, page: 1091.
Contained By:	Dissertation Abstracts International71-02B.
Subject:	Applied Mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3391191
ISBN:	9781109631975

Meshless collocation methods for the numerical solution of elliptic boundary valued problems the rotational shallow water equations on the sphere.
Blakely, Christopher D.

Meshless collocation methods for the numerical solution of elliptic boundary valued problems the rotational shallow water equations on the sphere. - 250 p.

Source: Dissertation Abstracts International, Volume: 71-02, Section: B, page: 1091.

Thesis (Ph.D.)--University of Maryland, College Park, 2009.

This dissertation thesis has three main goals: (1) To explore the anatomy of meshless collocation approximation methods that have recently gained attention in the numerical analysis community; (2) Numerically demonstrate why the meshless collocation method should clearly become an attractive alternative to standard finite-element methods due to the simplicity of its implementation and its high-order convergence properties; (3) Propose a meshless collocation method for large scale computational geophysical fluid dynamics models.

ISBN: 9781109631975Subjects--Topical Terms:

1669109
Applied Mathematics.

Meshless collocation methods for the numerical solution of elliptic boundary valued problems the rotational shallow water equations on the sphere.
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020 $a 9781109631975
035 $a (UMI)AAI3391191
035 $a AAI3391191
040 $a UMI $c UMI
100 1 $a Blakely, Christopher D. $3 1669391
245 1 0 $a Meshless collocation methods for the numerical solution of elliptic boundary valued problems the rotational shallow water equations on the sphere.
300 $a 250 p.
500 $a Source: Dissertation Abstracts International, Volume: 71-02, Section: B, page: 1091.
500 $a Advisers: John E. Osborn; Ferdinand Baer.
502 $a Thesis (Ph.D.)--University of Maryland, College Park, 2009.
520 $a This dissertation thesis has three main goals: (1) To explore the anatomy of meshless collocation approximation methods that have recently gained attention in the numerical analysis community; (2) Numerically demonstrate why the meshless collocation method should clearly become an attractive alternative to standard finite-element methods due to the simplicity of its implementation and its high-order convergence properties; (3) Propose a meshless collocation method for large scale computational geophysical fluid dynamics models.
520 $a We provide numerical verification and validation of the meshless collocation scheme applied to the rotational shallow-water equations on the sphere and demonstrate computationally that the proposed model can compete with existing high performance methods for approximating the shallow-water equations such as the SEAM (spectral-element atmospheric model) developed at NCAR. A detailed analysis of the parallel implementation of the model, along with the introduction of parallel algorithmic routines for the high-performance simulation of the model will be given. We analyze the programming and computational aspects of the model using Fortran 90 and the message passing interface (mpi) library along with software and hardware specifications and performance tests. Details from many aspects of the implementation in regards to performance, optimization, and stabilization will be given.
520 $a In order to verify the mathematical correctness of the algorithms presented and to validate the performance of the meshless collocation shallow-water model, we conclude the thesis with numerical experiments on some standardized test cases for the shallow-water equations on the sphere using the proposed method.
590 $a School code: 0117.
650 4 $a Applied Mathematics. $3 1669109
650 4 $a Atmospheric Sciences. $3 1019179
650 4 $a Computer Science. $3 626642
690 $a 0364
690 $a 0725
690 $a 0984
710 2 $a University of Maryland, College Park. $b Mathematics. $3 1266601
773 0 $t Dissertation Abstracts International $g 71-02B.
790 1 0 $a Osborn, John E., $e advisor
790 1 0 $a Baer, Ferdinand, $e advisor
790 1 0 $a Fox-Rabinovitz, Michael $e committee member
790 1 0 $a Trivisa, Konstantina $e committee member
790 1 0 $a Drake, James $e committee member
790 $a 0117
791 $a Ph.D.
792 $a 2009
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3391191