An Embedded Domain Decomposition Method for Electromagnetic Modeling and Design

An embedded domain decomposition method (DDM) is presented herein for solving electromagnetic problems with complex geometries. In the method, the original computational domain is decomposed into a background subdomain and multiple embedded subdomains. The subdomain problems are easier to solve than the original problem. Furthermore, the shape of the subdomains can be geometrically nonconformal, and the discretizations in the subdomains are allowed to be completely independent. Information exchange between the background and embedded subdomains are addressed in their shared regions, including four ingredients: field continuity, material difference, perfect electrical conductor (PEC), and port. Field continuity on the boundaries of the embedded subdomains is weakly enforced by employing Robin transmission condition. Modified volume sources are introduced to account for the material difference between the subdomains. For PEC and port, surface currents on them in embedded subdomains are impressed into the background subdomain in a proper way. The accuracy and flexibility of the proposed method are demonstrated through several numerical examples.