Parametrization-free locally-conformal perfectly matched layer method for finite element solution of Helmholtz equation

ÖZGÜN Ö., KUZUOĞLU M., Beriot H., Mittra R.

Computer Physics Communications, vol.288, 2023 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 288
  • Publication Date: 2023
  • Doi Number: 10.1016/j.cpc.2023.108741
  • Journal Name: Computer Physics Communications
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Applied Science & Technology Source, Chemical Abstracts Core, Communication Abstracts, Computer & Applied Sciences, INSPEC, Metadex, zbMATH, Civil Engineering Abstracts
  • Keywords: Computational electromagnetics, Finite element method (FEM), Locally-conformal PML (LCPML), Mesh truncation, Perfectly matched layer (PML)
  • Hacettepe University Affiliated: Yes


We present a novel Locally-Conformal Perfectly Matched Layer (LCPML) method for mesh truncation in the Finite Element Method (FEM), to solve wave equations derived from Maxwell's equations. The original LCPML method was proposed by Ozgun and Kuzuoglu in 2006 [16] by utilizing the concept of complex elements in which nodal coordinates of elements are replaced by complex coordinates obtained by using a complex coordinate-transformation. In the proposed LCPML method, named as LCPML-log method, a more efficient coordinate-transformation is used together with new FEM formulation and implementation. The proposed method offers the advantage that only a few (or even a single) PML layer is sufficient to get reliable results. In addition, it does not require any PML parameter tuning, and hence, the decaying wave behavior in PML is achieved self-adaptively. The numerical results of some detailed and systematic performance analyses are also presented.