Non-conforming finite element tearing and interconnecting method with one Lagrange multiplier for solving large-scale electromagnetic problems

A non-conforming finite element tearing and interconnecting method is proposed for the numerical analysis of large-scale three-dimensional electromagnetic problems. The whole computational domain is partitioned into many smaller subdomains, and a Robin-type transmission condition is introduced at the shared interfaces to exchange data among subdomains. A set of orthogonal polynomials is introduced to approximate auxiliary unknowns between adjacent subdomains. Then, a one-Lagrange multiplier scheme is applied to deal with non-conforming meshes at the interfaces. With the help of the Schur complement approach, the method formulates a reduced-order interface problem, which can be solved using an iterative algorithm. Once the resulting interface problem is solved, the unknown electric field in each subdomain can be calculated in parallel. Numerical examples are given to demonstrate the efficiency of the method.