Now showing items 1-4 of 4
Generalization of the Pythagorean Eigenvalue Error Theorem and its Application to Isogeometric Analysis
(Numerical Methods for PDEs, 2018-10-13)
This chapter studies the effect of the quadrature on the isogeometric analysis of the wave propagation and structural vibration problems. The dispersion error of the isogeometric elements is minimized by optimally blending ...
Efficient quadrature rules for subdivision surfaces in isogeometric analysis
(Computer Methods in Applied Mechanics and Engineering, 2018-10)
We introduce a new approach to numerical quadrature on geometries defined by subdivision surfaces based on quad meshes in the context of isogeometric analysis. Starting with a sparse control mesh, the subdivision process ...
Dispersion-minimizing quadrature rules for $C^1$ quadratic isogeometric analysis
(Computer Methods in Applied Mechanics and Engineering, 2017-09-20)
We develop quadrature rules for the isogeometric analysis of wave propagation and structural vibrations that minimize the discrete dispersion error of the approximation. The rules are optimal in the sense that they only ...
Gauss-Galerkin quadrature rules for quadratic and cubic spline spaces and their application to isogeometric analysis
(Computer-Aided Design, 2016-07-01)
We introduce Gaussian quadrature rules for spline spaces that are frequently used in Galerkin discretizations to build mass and stiffness matrices. By definition, these spaces are of even degrees. The optimal quadrature ...