# Dispersion optimized quadratures for isogeometric analysis

## TL;DR

This paper introduces optimized quadrature blending schemes for isogeometric analysis that significantly reduce dispersion errors, enhance eigenvalue convergence, and improve accuracy in wave propagation and eigenvalue problems.

## Contribution

The authors develop dispersion-optimized quadrature schemes for high-continuity isogeometric analysis, achieving superconvergence and improved robustness over existing methods.

## Key findings

- Two extra orders of convergence in eigenvalue errors
- Optimal convergence order in eigenfunction errors
- Validated improved accuracy through numerical examples

## Abstract

We develop and analyze quadrature blending schemes that minimize the dispersion error of isogeometric analysis up to polynomial order seven with maximum continuity in the span ($C^{p-1}$). The schemes yield two extra orders of convergence (superconvergence) on the eigenvalue errors, while the eigenfunction errors are of optimal convergence order. Both dispersion and spectrum analysis are unified in the form of a Taylor expansion for eigenvalue errors. As a consequence, the schemes increase the accuracy and robustness of isogeometric analysis for wave propagation as well as the differential eigenvalue problems. We analyze the methods' robustness and efficacy and utilize numerical examples to verify our analysis of the performance of the proposed schemes.