Abstract
We propose a reproducing kernel triangular B-spline-based finite element method (FEM) as an improvement to the conventional triangular B-spline element for solving partial differential equations (PDEs). In the latter, unexpected errors can occur throughout the analysis domain mainly due to the excessive flexibilities in defining the B-spline. The performance therefore becomes unstable and cannot be controlled in a desirable way. To address this issue, the proposed improvement adopts the reproducing kernel approximation in the calculation of B-spline kernel function. Three types of PDE problems are tested to validate the present element and compare against the conventional triangular B-spline. It has been shown that the improved triangular B-spline satisfies the partition of unity condition even for extreme conditions including corners and holes.
Original language | English |
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Pages (from-to) | 342-358 |
Number of pages | 17 |
Journal | Computer Methods in Applied Mechanics and Engineering |
Volume | 267 |
DOIs | |
Publication status | Published - 2013 Dec 1 |
Bibliographical note
Funding Information:The authors thank the support by the European Union through the FP7-grant ITN (Marie Curie Initial Training Networks) INSIST (Integrating Numerical Simulation and Geometric Design Technology), the US Office of Navy Research through the ONR-YIP award N00014–10-1–0698, the NSFC (41130751), National Basic Research Program of China (973 Program: 2011CB013800) and Shanghai Pujiang Program (12PJ1409100), the Nature Science Foundation of China (Nos. 61272390 , 61004117 , 61211130103 ) and the Scientific Research Foundation for the Returned Overseas Chinese Scholars from State Education Ministry.
Keywords
- Finite element method
- Poisson's equations
- Reproducing kernel approximation
- Reproducing kernel triangular B-spline
- Triangular B-spline
ASJC Scopus subject areas
- Computational Mechanics
- Mechanics of Materials
- Mechanical Engineering
- General Physics and Astronomy
- Computer Science Applications