Design, Analysis and Implementation of Parallel Algorithms in the 3D Magnetic Field Computation

A highly parallel iterative solver on the basis of non-overlapping domain decomposition (DD) methods for large systems of equations arising in the FE-, BE- and coupled FE/BE-discretizations of two-dimensional (2D) boundary value problems has been hitherto developed. It includes a parallel nested Newton method for nonlinear electromagnetic field calculation which allows to carry over the excellent convergence properties of the Full-Multigrid-Newton method on a sequential machine into a parallel solver. Further, a parallelized modified global multigrid method applying the data structure and certain components of DD methods, produced similarly good results for FEM discretizations. Nowadays, in many technical applications the 2D model is not sufficient anymore, and a three-dimensional (3D) field calculation is required. On the basis of 3D non-overlapping DD methods, highly efficient parallel solvers can be constructed. The main points of research effort are the choice and improvement of the components of the DD preconditioner and their adaptation to the ambitious nonlinear formulation of the Maxwell equations. Since DD methods and modified multigrid methods require and stimulate each other, both methods will be subject of research. A further topic of the project will be the repeated tetrahedral meshing when parts of devices (e.g. machines) are moving.