Eliminating spurious outlier frequencies and modes in IGA - strong and variational removal, outlier-free Bézier extraction, and advantages in explicit dynamics and nonlinear analysis

The core idea of isogeometric analysis (IGA) is to use the same smooth and higher-order spline basis functions for the exact representation of the geometry and the finite element approximation of physics-based field solutions. One of the key advantages of IGA is the accuracy and numerically favorable behavior of eigenfrequencies and eigenmodes. Unfortunately, discrete spectra of spline discretizations feature spurious frequencies and modes at the high end, denoted as “outliers”. While they do not play a role in linear static analysis, outliers unnecessarily reduce the critical time step in explicit dynamics and can affect accuracy and robustness in the presence of strong nonlinearities. To date, a practical technique for outlier removal does not exist. We recently developed new fundamental ideas on how to remove boundary outliers from a given tensor-product spline discretization, based on additional consistent higher-order boundary constraints. The overarching goal of this project is to drive forward our initial promising results towards a well-elaborated and comprehensive practical methodology for outlier removal, covering both boundary and interface outliers. To this end, we will first consolidate fundamental components of strong outlier removal for boundary outliers. In particular, we will develop an efficient algorithmic framework for generating new outlier-free basis functions and associated outlier-free Bézier extraction operators. We will then extend the outlier removal technology to interface outliers, focusing on variational strategies for removing outliers due to C^0-continuous patch interfaces. We will finally show that the resulting set of outlier removal techniques reliably eliminates outliers from given multi-patch spline discretizations. We will also demonstrate improvements in efficiency and robustness as a result of outlier removal in practical simulation scenarios, focusing on explicit dynamics and nonlinear analysis of structures. The Bézier extraction format will enable us to directly feed outlier-free spline discretizations into the commercial finite element package LS-DYNA, where numerical advantages can be studied in the context of the full range of practically relevant finite element technology, such as shell elements, large deformations, nonlinear material models, frictional contact, and mass lumping schemes. The outlier removal technology developed in this project will help fill the gap of practical outlier removal and will thus help further propel the establishment of IGA as a higher-order accurate and efficient design-through-analysis method.