Nonconformal Domain Decomposition Method Based on the Hybrid SIE-PDE Formulation for Flexible Transverse Magnetic Analysis

TL;DR

This paper introduces a flexible and efficient nonconformal domain decomposition method based on a hybrid SIE-PDE formulation for transverse magnetic electromagnetic problems, enabling better modeling of complex structures.

Contribution

It presents a novel nonconformal hybrid SIE-PDE approach with a specially designed interface coupling matrix, improving modeling flexibility and efficiency for complex electromagnetic structures.

Findings

Method is validated by three numerical examples.

Achieves higher flexibility with independent mesh generation.

Demonstrates improved efficiency over conformal mesh methods.

Abstract

A nonconformal domain decomposition method based on the hybrid surface integral equation partial differential equation (SIE-PDE) formulation is proposed to solve the transverse magnetic electromagnetic problems. In the hybrid SIE-PDE formulation, an equivalent model with only the electric current density is first constructed, and then is embedded into the inhomogeneous Helmholtz equation as an excitation. A connection matrix, which couples the interfaces of the SIE and PDE domains, is carefully designed to support nonconformal meshes. Since meshes in each domain are independently generated, it is much more efficient and flexible to model multiscale and complex structures compared with the original hybrid SIE-PDE formulation with conformal meshes. The proposed formulation is efficient, flexible and easy to implement. Its accuracy, efficiency and flexibility are validated by three numerical examples.