Parametric Quadrilateral Meshes for the Design and Optimization of Superconducting Magnets

The program package ROXIE [1] has been developed at CERN for the design and optimization of the superconducting magnets for the LHC.The necessity of extremely uniform (coil dominated) fields in accelerator magnets requires very accurate methods of .eld computation. For this purpose a coupled boundary-element/ finite-element technique (BEM-FEM) is used [2]. Quadrilateral higher order finite-elements are used for the discretization of the iron domain.This is necessary for the accurate modeling of the iron contours and is favorable for 3D meshes. A new quadrilateral mesh generator using geometrically optimized domain decomposition which was developed at the University of Stuttgart, Germany [3] has been implemented into the ROXIE program providing fully automatic and user friendly mesh generation.The frequent application of mathematical optimization techniques requires parametric models which are set-up using a feature-based approach.The structure of the magnet cross-section can be modeled using parametric objects such as holes of different forms, elliptic, parabolic or hyperbolic arcs, notches, slots,etc. Investigations of the speed-up of the computations due to geometrically optimized meshes will be presented. For sensitivity analysis, point based morphing algorithms are applied to the generated mesh.