A hybrid isogeometric approach on multi-patches with applications to Kirchhoff plates and eigenvalue problems

TL;DR

This paper introduces a hybrid isogeometric mortar method with penalty techniques for multi-patch discretization of high-order and eigenvalue problems, improving accuracy and implementation in complex geometries.

Contribution

It develops a systematic hybrid approach that enforces weak continuity and penalizes derivatives, enabling efficient multi-patch discretization of fourth order and eigenvalue problems.

Findings

Reduces spectrum pollution in second order eigenvalue problems.

Demonstrates effective handling of Kirchhoff plates and elasticity in complex geometries.

Shows good numerical stability and accuracy in various tests.

Abstract

We present a systematic study on higher-order penalty techniques for isogeometric mortar methods. In addition to the weak-continuity enforced by a mortar method, normal derivatives across the interface are penalized. The considered applications are fourth order problems as well as eigenvalue problems for second and fourth order equations. The hybrid coupling enables the discretization of fourth order problems in a multi-patch setting as well as a convenient implementation of natural boundary conditions. For second order eigenvalue problems, the pollution of the discrete spectrum - typically referred to as 'outliers' - can be avoided. Numerical results illustrate the good behaviour of the proposed method in simple systematic studies as well as more complex multi-patch mapped geometries for linear elasticity and Kirchhoff plates.