Abstract
This paper introduces optimally-blended quadrature rules for isogeometric analysis and analyzes the numerical dispersion of the resulting discretizations. To quantify the approximation errors when we modify the inner products, we generalize the Pythagorean eigenvalue theorem of Strang and Fix. The proposed blended quadrature rules have advantages over alternative integration rules for isogeometric analysis on uniform and non-uniform meshes as well as for different polynomial orders and continuity of the basis. The optimally-blended schemes improve the convergence rate of the method by two orders with respect to the fully-integrated Galerkin method. The proposed technique increases the accuracy and robustness of isogeometric analysis for wave propagation problems.
Original language | English (US) |
---|---|
Pages (from-to) | 421-443 |
Number of pages | 23 |
Journal | Computer Methods in Applied Mechanics and Engineering |
Volume | 320 |
DOIs | |
State | Published - Jun 15 2017 |
Externally published | Yes |
Keywords
- Eigenvalue problem
- Finite elements
- Isogeometric analysis
- Numerical dispersion
- Quadrature
- Wave propagation
ASJC Scopus subject areas
- Computational Mechanics
- Mechanics of Materials
- Mechanical Engineering
- General Physics and Astronomy
- Computer Science Applications