Inhomogeneous dielectrics: conformal mapping and finite-element models

Abstract

Field singularities in electrostatic and magnetostatic fields require special attention in field calculations, and today finite element methods are normally used, both in homogeneous and in inhomogeneous dielectric cases. Conformal mappings are a traditional tool in the homogeneous case, but two-stage Schwarz-Christoffel + Finite Difference procedures have been proposed for a long time to solve problems in case of inhomogeneous dielectric materials too. This allowed to overcome accuracy problems caused by convex corners in the domain boundary and relevant field singularities, and to easily apply finite difference (FD) solvers in rectangular domains. In this paper, compound procedures Schwarz-Christoffel + Finite Elements Method procedures are suggested, to improve both the accuracy and the speed of second stage calculations. The results are compared to Schwarz-Christoffel + Finite Difference and to direct finite-element calculations, and the small differences analyzed considering a well know case study geometry, i.e., a shielded dielectric-supported stripline geometry.

Keywords

• inhomogeneous dielectrics
• electrostatic field singularities
• schwarz-christoffel
• finite differences
• finite elements
• 02.60.-x
• 02.70.-c
• 41.20.-q
• 84.40.-x
• 85.40.-e