A Multilevel Method With Novel Correction Strategy for Parallel Finite-Element Analysis of Electromagnetic Problems

Adaptive process of finite-element method always needs to solve a set of linear systems repeatedly. This communication proposes an accurate and efficient domain decomposition method (DDM) based on a multilevel algorithm and a coarse-level correction strategy. Our developed algorithm facilitates the adaptive refinement process utilizing dynamic coarse-level correction, exploits the hierarchical feature of the refined systems through p-type multigrid method in subdomains, then solves the lowest order system through algebraic multigrid method in auxiliary and node-based spaces. The numerical results show that with this effective coarse-level correction, the residual errors introduced by adaptive refined systems can be eliminated quickly by the DDM. Besides, optimal performance in terms of simulation time is achieved, regardless of workload imbalances during the adaptive steps. Several large-scale electromagnetic problems are analyzed for accuracy as well as performance evaluation of the proposed method.