# Finite Element Tearing and Interconnect for Maxwell’s equations using IGA

Master thesis, Seminar paper, Bachelor thesis

### 1. Context

Isogeometric analysis (IGA) is a finite element method (FEM) using splines for geometry description and basis functions such that the geometry can be exactly represented. Recently, an isogeometric mortar coupling [1] for electromagnetic problems was proposed. It is particularly well suited for the eigenfrequency prediction of superconducting accelerator cavities. Each cell, see Fig. 1, can be represented by a different subdomain but may still share the same discretization. The approach leads to a (stable and spectral correct) saddle-point problem. However, its numerical solution is cumbersome and iterative substructuring methods become attractive. The resulting system is available from a Matlab/Octave code. In this project the finite element tearing and interconnect method (FETI) shall be investigated and standard, possibly low-rank,preconditioners implemented and compared.

### 2. Task

First, familiarize yourself with Maxwell’s eigenvalue problem, the basics of Isogeometric Analysis and the software GeoPDEs [2]. Then understand the ideas behind FETI [3] and implement an iterative solver within the existing software. Finally, experiment with preconditioners to speed up the solution procedure.

### 3. Prerequisites

Strong background in FEM, basic knowledge of Maxwell’s equations, experience with programming in Matlab/Octave, interest in electromagnetic field simulation.

### 4. References

[1] A. Buffa et al., Isogeometric Mortar Coupling for Electromagnetic Problems, arXiv 1901.00759

[2] R. Vázquez, URL http://rafavzqz.github.io/geopdes/

[3] A. Toselli and O.B. Widlund, Domain Decomposition Methods, DOI 10.1007/b137868