A hybrid isogeometric approach on multi-patches with applications to Kirchhoff plates and eigenvalue problems
For researchers in isogeometric analysis, this work provides a method to discretize fourth-order problems on multi-patch domains and eliminate spectral pollution, though it is an incremental improvement over existing mortar methods.
This paper introduces a hybrid isogeometric approach combining mortar methods with higher-order penalty techniques to handle multi-patch geometries for fourth-order problems and eigenvalue problems. The method avoids spectral outliers in second-order eigenvalue problems and demonstrates good performance on linear elasticity and Kirchhoff plate examples.
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.