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Product Gauss quadrature rules vs. cubature rules in the meshless local Petrov–Galerkin method
- Source :
- Journal of Complexity. 26:82-101
- Publication Year :
- 2010
- Publisher :
- Elsevier BV, 2010.
-
Abstract
- A crucial point in the implementation of meshless methods such as the meshless local Petrov–Galerkin (MLPG) method is the evaluation of the domain integrals arising over circles in the discrete local weak form of the governing partial differential equation. In this paper we make a comparison between the product Gauss numerical quadrature rules, which are very popular in the MLPG literature, with cubature formulas specifically constructed for the approximation of an integral over the unit disk, but not yet applied in the MLPG method, namely the spherical, the circularly symmetrical and the symmetric cubature formulas. The same accuracy obtained with 64×64 points in the product Gauss rules may be obtained with symmetric quadrature formulas with very few points.
- Subjects :
- Statistics and Probability
Regularized meshless method
Control and Optimization
Meshless Local Petrov–Galerkin method
General Mathematics
Petrov–Galerkin method
STROUD
Mathematics::Numerical Analysis
symbols.namesake
IMPLEMENTATION
Mathematics
Clenshaw–Curtis quadrature
Numerical Analysis
FINITE SPHERES
Algebra and Number Theory
NUMERICAL-INTEGRATION, FINITE SPHERES, FORMULAS, MLPG, IMPLEMENTATION, COMPILATION, MECHANICS, STROUD
Applied Mathematics
Gauss
Mathematical analysis
Cubature formulas on the disk
MLPG
Gauss–Kronrod quadrature formula
Numerical integration
Quadrature (mathematics)
MECHANICS
FORMULAS
symbols
Gaussian quadrature
NUMERICAL-INTEGRATION
COMPILATION
Subjects
Details
- ISSN :
- 0885064X
- Volume :
- 26
- Database :
- OpenAIRE
- Journal :
- Journal of Complexity
- Accession number :
- edsair.doi.dedup.....afcc7ad311b1f9742d3e7684d4d8a0cd