SCI-Based LINUX PC-Clusters as a Platform for Electromagnetic Field Calculations

Abstract

When designing high voltage equipment like power transformers, it is of essential importance to precisely and efficiently calculate eddy-current problems in a transformer to determine possible losses. A method suitable for such simulations is the Boundary-Element method (BEM) [2]. As far as the simulation is concerned, for electrical devices operating continuously under alternating current, time-harmonic states are of interest. These lead to an elliptic transmission problem for the eddy-current Maxwell equations. With some modifications, the linear equation system resulting from the boundary element discretization is well-conditioned. For realistic problems, however, the discretization leads to very large, non-symmetric systems of linear equations. To deal with such large equation systems, iterative solution techniques such as GMRES [9] must be employed. However, for certain combinations of materials occurring in electrical engineering (such as e.g. iron and copper parts) the parallel boundary integral equation system and its discretizations are ill-conditioned, primarily caused by the physical parameters in the problem formulation. In order to cope with such problems, the Seminar for Applied Mathematics at the ETH Zürich, Switzeland has developed a preconditioner for the eddy-current system of second kind Boundary Integral Equations [4] which has been integrated into the framework of the boundary element field simulation code POLOPT [1].