Recent Advances of Isogeometric Analysis in Computational Electromagnetics

TL;DR

This paper reviews recent advances in isogeometric analysis (IGA) for electromagnetic simulations, highlighting its advantages in exact geometry representation and discussing software and benchmark applications.

Contribution

It provides a comprehensive review of IGA's benefits, challenges, and recent developments in electromagnetic simulations, including practical applications and software tools.

Findings

IGA offers exact geometry representation in CAD-based electromagnetic simulations.

It simplifies meshing by using CAD tools for implicit mesh creation.

Benchmark examples demonstrate IGA's effectiveness in optimization and uncertainty quantification.

Abstract

In this communication the advantages and drawbacks of the isogeometric analysis (IGA) are reviewed in the context of electromagnetic simulations. IGA extends the set of polynomial basis functions, commonly employed by the classical Finite Element Method (FEM). While identical to FEM with N\'ed\'elec's basis functions in the lowest order case, it is based on B-spline and Non-Uniform Rational B-spline basis functions. The main benefit of this is the exact representation of the geometry in the language of computer aided design (CAD) tools. This simplifies the meshing as the computational mesh is implicitly created by the engineer using the CAD tool. The curl- and div-conforming spline function spaces are recapitulated and the available software is discussed. Finally, several non-academic benchmark examples in two and three dimensions are shown which are used in optimization and uncertainty quantification workflows.