Parametric Quadrilateral Meshes for the Design and Optimization of Superconducting Magnets

The program package ROXIE has been developed at CERN for the design and optimization of accelerator magnets. The necessity of extremely uniform fields in the superconducting accelerator magnets for LHC requires very accurate methods of field computation. For this purpose the coupled boundary-element / finite-element technique (BEM-FEM) is used. Quadrilateral higher order finite-element meshes are generated for the discretization of the iron domain (yoke) and stainless steel collars. A new mesh generator using geometrically optimized domain decomposition which was developed at the University of Stuttgart, Germany has been implemented into the ROXIE program providing fully automatic and user friendly mesh generation. 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, .... For sensitivity analysis and parametric studies, point based morphing algorithms are applied to guarantee smooth adaptation of the mesh to geometry changes. For modeling three-dimensional iron structures, the 2D meshes can be extruded into the third dimension. This paper discusses the use of the mesh generator with examples of the computation of the LHC dipoles.