Application of Extended Multi-Branch Basis Functions in Non-Conformal Meshes

Accurate solution of real-life electromagnetic problems via surface integral equations commonly requires handling a large number of unknowns and multi-scale features, for which methods such as the domain decomposition method significantly improve convergence and enable efficient parallelization on supercomputers. In this context, generating computer-aided design and mesh models in separate subdomains and then connecting them to analyze the entire problem without concern for mesh conformity is highly advantageous. While solutions based in multiple traces are well-suited for scenarios with different dielectric materials, single-trace solutions are better suited for analyzing perfect electric conductor problems or homogeneous dielectric materials without increasing the number of unknowns. Some existing solutions for non-conformal mesh problems are the Multi-Branch basis functions, limited by their need for partial node conformity, or the Integral Equation Discontinuous Galerkin method, which does not require partial node conformity, however the calculation of the stabilization parameter complicates its application to realistic problems. This work introduces a new approach, the Extended Multi-Branch basis functions, which combines the advantages of both methods: it does not require partial node conformity and eliminates the stabilization parameter calculation, thus streamlining the analysis process for non-conformal meshes.