Bernstein–Bézier H(curl)-Conforming Finite Elements for Time-Harmonic Electromagnetic Scattering Problems

• Published in: Journal of scientific computing Vol. 97; no. 3; p. 69
• Main Authors: Benatia, Nawfel, El Kacimi, Abdellah, Laghrouche, Omar, Ratnani, Ahmed
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.12.2023; Springer Nature B.V
• Subjects: Algorithms; Approximation; Basis functions; Bezier patches; Computational Mathematics and Numerical Analysis; Electric conductors; Electromagnetic radiation; Electromagnetic scattering; Evanescent waves; Finite element method; Mathematical analysis; Mathematical and Computational Engineering; Mathematical and Computational Physics; Mathematical models; Mathematics; Mathematics and Statistics; Methods; Satellite communications; Tetrahedra; Theoretical; Triangles; Wave scattering; Finite elements; Time-harmonic; Short wave scattering; Bernstein polynomials; Maxwell’s equations
• ISSN: 0885-7474; 1573-7691
• DOI: 10.1007/s10915-023-02381-5

This paper deals with a high-order H ( curl ) -conforming Bernstein–Bézier 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.