Contents I. Introduction
To model an electromagnetic device, the finite element method is often used today. In order to reduce the mesh of the studied structure, numerical methods based on the domain decomposition are developed. The studied structure is divided into several sub-domains, according to their dimensions and their sizes. Each sub-domain is discretized independently. Then, the studied domain is composed of non-conforming meshes. To link these meshes, the Mortar approach can be used [1]. Applied to potential formulations in magnetostatics, the final matrix system is constituted by two sub-matrices; the first one represents the Stiffness matrix obtained from the potential formulations and the second is due to the Mortar approach. This last links on a common boundary the potentials of two non-conforming meshes. Due to the properties of the matrix system, the preconditioners and the iterative methods (CG)[2] must be adapted to solve efficiently this system. In this paper, it is proposed to study a preconditioner based on an incomplete QR decomposition approach [2]. In magneto statics, the numerical model and the Mortar approach are briefly presented. An example of application is studied to show the efficiency of the developed preconditioner.
