Simulation of superconducting Cavities with Isogeometric Boundary Elements (IGA-BEM)

点击翻译按钮获取中文摘要

To calculate the resonant frequencies and their deviations of superconducting cavity resonators for particle accelerators one needs numerical methods capable of achieving accuracies which push established techniques to their limit.This is mostly due to the precision the geometry of the cavities must be described with.In the project we apply for a new numerical method for the solution of Maxwell's eigenvalue problem shall be developed, which combines building blocks of state-of-the-art numerical methods.The geometry of the resonators shall be described with Non-Uniform Rational B-Splines (NURBS), which can, contrary to the usual triangulations, describe the geometry exactly. This method became popular within the framework of Isogeometric Analysis (IGA) and has proven itself already in the context of finite element methods (Buffa 2010, Corno 2016).Since the creation of a volumetric representation of this kind takes a lot of manual effort, and the boundary data of the required format is already given by CAD systems, the isogeometric approach shall be combined with a Boundary Element Method (BEM). Thanks to modern compression techniques and preconditioning, BEM is a viable alternative to a finite element method in many applications (Li 2016, Marussig 2015). In other physical domains this approach has already proven itself, (Simpson 2012). The algebraic eigenvalue problems generated by the boundary element method are nonlinear. A novel contour integral method shall be used for their solution, (Beyn 2012).In this proposal the state of the technology and properties of the mentioned methods will be discussed. A detailed outline of the project for development and prototypical implementation of the method described above will be presented.