Adaptive Mesh Refinement Strategies in Isogeometric Analysis - A Computational Comparison

TL;DR

This paper compares four adaptive mesh refinement strategies in isogeometric analysis using cubic splines, evaluating their performance on elliptic problems through error, degrees of freedom, and matrix properties.

Contribution

It provides a computational comparison of different adaptive refinement strategies in isogeometric analysis, including new variants of T-splines.

Findings

Different refinement strategies show varying efficiency in error reduction.

Refinement strategies impact sparsity patterns and condition numbers.

Performance varies across singular and non-singular elasticity and Poisson problems.

Abstract

We explain four variants of an adaptive finite element method with cubic splines and compare their performance in simple elliptic model problems. The methods in comparison are Truncated Hierarchical B-splines with two different refinement strategies, T-splines with the refinement strategy introduced by Scott et al. in 2012, and T-splines with an alternative refinement strategy introduced by some of the authors. In four examples, including singular and non-singular problems of linear elasticity and the Poisson problem, the H1-errors of the discrete solutions, the number of degrees of freedom as well as sparsity patterns and condition numbers of the discretized problem are compared.