Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

Order adaptive integration rule with equivalently weighted internal nodes

Order adaptive integration rule with equivalently weighted internal nodes Purpose – To develop order adaptive integration rule without limitation requiring that the number of equally spaced nodes must be a divisible numeral. Such integration technique could be of great practical value for different engineering applications where partition adaptability is impossible and use of standard high order integration techniques is unfeasible due to the fact that a significant number of nodes at the end of the sampling sequence must be deleted until the needed divisibility of the number of nodes is achieved. Design/methodology/approach – Finite element approximation is used for the subdivision of the domain of integration and the development of order adaptive integration rule. Findings – New integration rule is developed. It has a number of interesting features. Weights of the internal nodes are equivalent and equal to one. That makes the computational implementation of the integration rule very easy. Weights not equal to one are located only at the beginning and at the end of the sequence and are symmetric. For an m ‐th order rule the number of weights not equal to one is 2 m if m is odd. Originality/value – For different engineering applications where the integration order can be controlled without changing the number of nodes, especially for real time applications where the number of discrete samples is unknown before the experiment. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Engineering Computations Emerald Publishing

Order adaptive integration rule with equivalently weighted internal nodes

Minvydas Ragulskis; Liutauras Ragulskis
Engineering Computations , Volume 23 (4): 14 – Jun 1, 2006
Download PDF
14 pages

Loading next page...
 
/lp/emerald-publishing/order-adaptive-integration-rule-with-equivalently-weighted-internal-vU8eL888Lg
Publisher
Emerald Publishing
Copyright
Copyright © 2006 Emerald Group Publishing Limited. All rights reserved.
ISSN
0264-4401
DOI
10.1108/02644400610661154
Publisher site
See Article on Publisher Site

Abstract

Purpose – To develop order adaptive integration rule without limitation requiring that the number of equally spaced nodes must be a divisible numeral. Such integration technique could be of great practical value for different engineering applications where partition adaptability is impossible and use of standard high order integration techniques is unfeasible due to the fact that a significant number of nodes at the end of the sampling sequence must be deleted until the needed divisibility of the number of nodes is achieved. Design/methodology/approach – Finite element approximation is used for the subdivision of the domain of integration and the development of order adaptive integration rule. Findings – New integration rule is developed. It has a number of interesting features. Weights of the internal nodes are equivalent and equal to one. That makes the computational implementation of the integration rule very easy. Weights not equal to one are located only at the beginning and at the end of the sequence and are symmetric. For an m ‐th order rule the number of weights not equal to one is 2 m if m is odd. Originality/value – For different engineering applications where the integration order can be controlled without changing the number of nodes, especially for real time applications where the number of discrete samples is unknown before the experiment.

Journal

Engineering Computations – Emerald Publishing

Published: Jun 1, 2006

Keywords: Numerical control; Finite element analysis; Adaptability

There are no references for this article.