Enriched finite elements for initial-value problem of transverse electromagnetic waves in time domain

Mayank Drolia, M Shadi Mohamed, Omar Laghrouche, Mohammed Seaid, Jon Trevelyan

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)
85 Downloads (Pure)


This paper proposes a partition of unity enrichment scheme for the solution of the electromagnetic wave equation in the time domain. A discretization scheme in time is implemented to render implicit solutions of systems of equations possible. The scheme allows for calculation of the field values at dierent time steps in an iterative fashion. The spatial grid is partitioned into a finite number of elements with intrinsic shape functions to form the bases of solution. Furthermore, each finite element degree of freedom is expanded into a sum of a slowly varying term and a combination of highly oscillatory functions. The combination consists of plane waves propagating in multiple directions, with a fixed frequency. This signicantly reduces the number of degrees of freedom required to discretize the unknown field, without compromising on the accuracy or allowed tolerance in the errors, as compared to that of other enriched FEM approaches. Also, this considerably reduces the computational costs in terms of memory and processing time. Parametric studies, presented herein, confirm the robustness and eciency of the proposed method and the advantages compared to another enrichment method.
Original languageEnglish
Pages (from-to)354–367
Number of pages14
JournalComputers and Structures
Early online date7 Jan 2017
Publication statusPublished - 1 Apr 2017


  • Electromagnetic Wave Equation
  • Finite Element
  • Partition of Unity
  • Time Domain Wave Problems
  • Enrichment Methods


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