Bernstein–Bézier H(curl)–conforming finite elements for time-harmonic electromagnetic scattering problems

N. Benatia, Abdellah El-Kacimi, Omar Laghrouche, A. Ratnani

Research output: Contribution to journalArticlepeer-review


This paper deals with a high-order H(curl)–conforming Bernstein–Bezier finite element method (BBFEM) to accurately solve time-harmonic Maxwell short wave problems on unstructured triangular mesh grids. We suggest enhanced basis functions, defined on the reference triangle and tetrahedron, aiming to reduce the condition number of the resulting global matrix. Moreover, element-level static condensation of the interior degrees of freedom is performed in order to reduce memory requirements. The performance of BBFEM is assessed using several benchmark tests. A preliminary analysis is first conducted to highlight the advantage of the suggested basis functions in improving the conditioning. Numerical results dealing with the electromagnetic scattering from a perfect electric conductor demonstrate the effectiveness of BBFEM in mitigating the pollution effect and its efficiency in capturing high-order evanescent wave modes. Electromagnetic wave scattering by a circular dielectric, with high wave speed contrast, is also investigated. The interior curved interface between layers is accurately described based on a linear blending map to avoid numerical errors due to geometry description. The achieved results support our expectations for highly accurate and efficient BBFEM for time harmonic wave problems.
Original languageEnglish
Article number69
JournalJournal of Scientific Computing
Issue number3
Publication statusPublished - 4 Nov 2023


  • Bernstein polynomials
  • Finite elements
  • Maxwell’s equations
  • Short wave scattering
  • Time-harmonic

ASJC Scopus subject areas

  • Software
  • General Engineering
  • Computational Mathematics
  • Theoretical Computer Science
  • Applied Mathematics
  • Numerical Analysis
  • Computational Theory and Mathematics


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