Application of the LU Recombination Method to the FETI-DP Method for Solving Low-Frequency Multiscale Electromagnetic Problems

The LU recombination method is applied within a dual-primal finite element tearing and interconnecting (FETI-DP) framework to solve low-frequency multiscale electromagnetic problems. The FETI-DP method, a robust domain decomposition method, is adopted to deal with the large-scale linear system resulting from finite element modeling of multiscale problems. When frequency decreases or a highly nonuniform mesh is used, the FETI-DP method encounters a low-frequency breakdown problem. The LU recombination method is adopted to identify and eliminate dependent degrees of freedom (DOFs), so that nearly singular finite element matrices are regularized. Since it deals with matrices directly, the LU recombination method is easily combined with different types and orders of basis functions. A nested scheme is adopted to apply LU recombination within the FETI-DP framework. The proposed algorithm is applied to large-scale eddy-current, switched reluctance motor, and logging-while-drilling tool problems. With the LU recombination method, the FETI-DP method is extended down to DC, making it possible to deal with a variety of problems of practical interest.