Purpose

This paper aims to solve inhomogeneous dielectric problems by matching boundary conditions at the interfaces among homogeneous subdomains. The capabilities of Hilbert transform computations are deeply investigated in the case of limited numbers of samples, and a refined model is presented by means of investigating accuracies in a case study with three subdomains.

Design/methodology/approach

The accuracies, refined by Richardson extrapolation to zero error, are compared to finite element (FEM) and finite difference methods. The boundary matching procedures can be easily applied to the results of a previous Schwarz–Christoffel (SC) conformal mapping stage in SC + BC procedures, to cope with field singularities or with open boundary problems.

Findings

The proposed field computations are of general interest both for electrostatic and magnetostatic field analysis and optimization. They can be useful as comparison tools for FEM results or when severe field singularities can impair the accuracies of other methods.

Research limitations/implications

This static field methodology, of course, can be used to analyse transverse electro magnetic (TEM) or quasi-TEM propagation modes. It is possible that, in some case, these may make a contribution to the analysis of axis symmetrical problems.

Originality/value

The most relevant result is the possible introduction of SC + BC computations as a standard tool for solving inhomogeneous dielectric field problems.

中文翻译：

---

非均匀域中场分析的另一种方法

目的

本文旨在通过匹配均匀子域之间界面处的边界条件来解决非均匀介电问题。在样本数量有限的情况下，深入研究了 Hilbert 变换计算的能力，并通过在具有三个子域的案例研究中研究精度来提出改进的模型。

设计/方法/方法

将通过 Richardson 外推法细化到零误差的精度与有限元 (FEM) 和有限差分方法进行比较。边界匹配程序可以很容易地应用于 SC + BC 程序中先前 Schwarz-Christoffel (SC) 共形映射阶段的结果，以处理场奇点或开放边界问题。

发现

所提出的场计算对于静电和静磁场分析和优化都具有普遍意义。它们可用作 FEM 结果的比较工具，或者当严重的场奇异性会损害其他方法的准确性时。

研究限制/影响

当然，这种静态场方法可用于分析横向电磁 (TEM) 或准 TEM 传播模式。在某些情况下，这些可能有助于轴对称问题的分析。

原创性/价值

最相关的结果是可能引入 SC + BC 计算作为解决非均匀介电场问题的标准工具。