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General Reproducing Kernel Element H...

Simkins, Daniel Craig, Jr.

General Reproducing Kernel Element Hierarchies.

Record Type:	Electronic resources : Monograph/item
Title/Author:	General Reproducing Kernel Element Hierarchies.
Author:	Simkins, Daniel Craig, Jr.
Description:	157 p.
Notes:	Chair: Shaofan Li.
Notes:	Source: Dissertation Abstracts International, Volume: 65-09, Section: B, page: 4722.
Contained By:	Dissertation Abstracts International65-09B.
Subject:	Engineering, Civil.
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3147005
ISBN:	0496053922

General Reproducing Kernel Element Hierarchies.
Simkins, Daniel Craig, Jr.

General Reproducing Kernel Element Hierarchies. - 157 p.

Chair: Shaofan Li.

Thesis (Ph.D.)--University of California, Berkeley, 2004.

The Reproducing Kernel Element Method (RKEM) is the first method to provide minimal higher order globally compatible basis functions in any spatial dimension. A general procedure to develop such basis functions in one and two dimensions with arbitrary Cn (n ≥ 1) continuity that are globally compatible within two different hierarchies will be presented. Further, these functions can interpolate derivatives of arbitrary mth order (Im), and can globally reproduce kth order polynomials ( Pk). These basis functions can be used in interpolation in computer graphics, or in numerical solutions of differential equations. After presenting the hierarchies, a detailed implementation scheme is presented. Formulation of a number of elements in one dimension, as well as triangular and quadrilateral elements in two dimensions are used to illustrate the theory and catalog results. Next, the performance of the RKEM functions in performing a Galerkin solution of a simple fourth-order one dimensional problem and the biharmonic equation as applied to Kirchhoff plate problems of square, circular and triangular shapes is demonstrated. Finally, RKEM interpolation capability in three dimensional geometry is displayed by rendering a full sphere using two triangular elements.

ISBN: 0496053922Subjects--Topical Terms:

212394
Engineering, Civil.

General Reproducing Kernel Element Hierarchies.
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245 1 0 $a General Reproducing Kernel Element Hierarchies.
300 $a 157 p.
500 $a Chair: Shaofan Li.
500 $a Source: Dissertation Abstracts International, Volume: 65-09, Section: B, page: 4722.
502 $a Thesis (Ph.D.)--University of California, Berkeley, 2004.
520 # $a The Reproducing Kernel Element Method (RKEM) is the first method to provide minimal higher order globally compatible basis functions in any spatial dimension. A general procedure to develop such basis functions in one and two dimensions with arbitrary Cn (n ≥ 1) continuity that are globally compatible within two different hierarchies will be presented. Further, these functions can interpolate derivatives of arbitrary mth order (Im), and can globally reproduce kth order polynomials ( Pk). These basis functions can be used in interpolation in computer graphics, or in numerical solutions of differential equations. After presenting the hierarchies, a detailed implementation scheme is presented. Formulation of a number of elements in one dimension, as well as triangular and quadrilateral elements in two dimensions are used to illustrate the theory and catalog results. Next, the performance of the RKEM functions in performing a Galerkin solution of a simple fourth-order one dimensional problem and the biharmonic equation as applied to Kirchhoff plate problems of square, circular and triangular shapes is demonstrated. Finally, RKEM interpolation capability in three dimensional geometry is displayed by rendering a full sphere using two triangular elements.
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