Convergence Improvement for Domain Decomposition Method Through Corner Treatment

In complex electromagnetic simulations, domain decomposition method (DDM) has been shown to be an effective approach for discretization. However, convergence difficulty exists due to the redundant cement variables defined on the corner edges of the subdomains. In this work, we propose a solution to this issue by employing the method of Lagrange multiplier. By incorporating constraints for the corner fields and expanding the system matrix, the condition number of the DDM matrix is reduced significantly. As a result, the convergence rate of the DDM iterations is remarkably improved.