Hierarchical conformal/non‐conformal domain decomposition method for electrostatic and static magnetic field problems

Abstract

This Letter presents a hierarchical conformal/non-conformal (NC) finite element-based domain decomposition method for solving large-scale multi-region electrostatic and static magnetic field problems. In this method, an original electrically large problem is decomposed into several regions based on its geometry, and then each region is meshed and further divided into smaller sub-domains. As such, the decomposed problem is mesh-conformal within each region but could be mesh-NC between two neighbouring regions. To solve such a problem, an advanced transmission condition which was proposed by the authors recently is introduced and then imposed through an interior penalty formulation. Moreover, a type of union meshes is constructed to deal with NC mesh interfaces. Finally, the proposed method is validated with simulation of both 3D electrostatic and static magnetic models.