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 two standard Gauss-type quadrature rules. These blending rules approximate the inner products and increase the convergence rate by two extra orders when compared to those with fully-integrated inner products. To quantify the approximation errors, we generalize the Pythagorean eigenvalue error theorem of Strang and Fix. To reduce the computational cost, we further propose a two-point rule for $C^1$ quadratic isogeometric elements which produces equivalent inner products on uniform meshes and yet requires fewer quadrature...
Certain applications that analyze damping effects require the solution of quadratic eigenvalue probl...
This work studies the potential of NURBS-based IsoGeometric Analysis (IGA) for use in dynamic proble...
Certain applications that analyze damping effects require the solution of quadratic eigenvalue probl...
© 2018, Springer Nature Switzerland AG. This chapter studies the effect of the quadrature on the iso...
This chapter studies the effect of the quadrature on the isogeometric analysis of the wave propagati...
This paper introduces optimally-blended quadrature rules for isogeometric analysis and analyzes the ...
We develop quadrature rules for the isogeometric analysis of wave propagation and structural vibrati...
We develop quadrature rules for the isogeometric analysis of wave propagation and structural vibrati...
We use blended quadrature rules to reduce the phase error of isogeometric analysis discretizations. ...
We introduce the dispersion-minimized mass for isogeometric analysis to approximate the structural v...
© 2018 Elsevier B.V. We study the spectral approximation of a second-order elliptic differential eig...
International audienceA numerical technique with the optimal coefficients of the stencil equation ha...
We investigate the optimal blending in the finite element method and isogeometric analysis for wave ...
Abstract. We review the discretization properties of classical finite element and NURBS-based isogeo...
A key advantage of isogeometric discretizations is their accurate and well-behaved eigenfrequencies ...
Certain applications that analyze damping effects require the solution of quadratic eigenvalue probl...
This work studies the potential of NURBS-based IsoGeometric Analysis (IGA) for use in dynamic proble...
Certain applications that analyze damping effects require the solution of quadratic eigenvalue probl...
© 2018, Springer Nature Switzerland AG. This chapter studies the effect of the quadrature on the iso...
This chapter studies the effect of the quadrature on the isogeometric analysis of the wave propagati...
This paper introduces optimally-blended quadrature rules for isogeometric analysis and analyzes the ...
We develop quadrature rules for the isogeometric analysis of wave propagation and structural vibrati...
We develop quadrature rules for the isogeometric analysis of wave propagation and structural vibrati...
We use blended quadrature rules to reduce the phase error of isogeometric analysis discretizations. ...
We introduce the dispersion-minimized mass for isogeometric analysis to approximate the structural v...
© 2018 Elsevier B.V. We study the spectral approximation of a second-order elliptic differential eig...
International audienceA numerical technique with the optimal coefficients of the stencil equation ha...
We investigate the optimal blending in the finite element method and isogeometric analysis for wave ...
Abstract. We review the discretization properties of classical finite element and NURBS-based isogeo...
A key advantage of isogeometric discretizations is their accurate and well-behaved eigenfrequencies ...
Certain applications that analyze damping effects require the solution of quadratic eigenvalue probl...
This work studies the potential of NURBS-based IsoGeometric Analysis (IGA) for use in dynamic proble...
Certain applications that analyze damping effects require the solution of quadratic eigenvalue probl...