Algorithms in ParAFEMImp: A Parallel and Wideband Impedance Extraction Program for Complicated 3-D Geometries

In this paper we describe the algorithms used in ParAFEMImp, a parallel program for wideband impedance extraction in very complicated geometries of conductors. Eddy-currents equations are solved using an adaptive finite element method. A PDE(Partial Differential Equation) based preconditioner is implemented in the program. The parallel implementation is based on the MPI (Message Passing Interface) and OpenMP (Open Multi-Processing). ParAFEMImp has the potential of good efficiency and high parallel scalability by taking the advantages of several advanced techniques, including dynamic load balancing, parallel adaptive finite element method, parallel preconditioned iterative solver and so on. Computational results of some large scale adaptive finite element simulations with up to 1 billion degrees of freedom and using up to more than 1024 CPU cores are presented to demonstrate that the ParAFEMImp is robust and scalable for analysis of verycomplicated geometries of conductors.