Enhancing SfePy with Isogeometric Analysis

TL;DR

This paper introduces the integration of isogeometric analysis into the open-source SfePy package, enhancing its numerical discretization capabilities beyond traditional finite element methods.

Contribution

The paper adds isogeometric analysis to SfePy, enabling higher smoothness approximations and eliminating the need for domain polygonal approximation.

Findings

Implementation of isogeometric analysis in SfePy demonstrated through numerical examples.

Isogeometric analysis provides higher smoothness in solutions compared to finite element method.

Elimination of domain approximation simplifies the modeling process.

Abstract

In the paper a recent enhancement to the open source package SfePy (Simple Finite Elements in Python, http://sfepy.org) is introduced, namely the addition of another numerical discretization scheme, the isogeometric analysis, to the original implementation based on the nowadays standard and well-established numerical solution technique, the finite element method. The isogeometric removes the need of the solution domain approximation by a piece-wise polygonal domain covered by the finite element mesh, and allows approximation of unknown fields with a higher smoothness then the finite element method, which can be advantageous in many applications. Basic numerical examples illustrating the implementation and use of the isogeometric analysis in SfePy are shown.