Applications of quadrilateral finite element meshes with four-node, eight-node, and twelve-node for efficient microwave energy transfer in curved waveguides

K. Lekhana; K. T. Shivaram

doi:10.46481/jnsps.2026.3412

Authors

K. Lekhana
Department of Mathematics, Dayananda Sagar College of Engineering, Visvesvaraya Technological University, Bangalore, India
K. T. Shivaram
[email protected]

Department of Mathematics, Dayananda Sagar College of Engineering, Visvesvaraya Technological University, Bangalore, India

Keywords:

Quadrilateral meshing, Multiply connected regions, Eigenvalue, Finite element method

Abstract

This study proposes a two-dimensional higher-order finite element method for computing eigenvalues in planar and multiply connected curved domains relevant to microwave energy transfer and electromagnetic waveguide problems. A fully automated quadrilateral mesh generator implemented in MAPLE-18 is used to convert triangular finite elements into quadrilateral elements with Four-node, Eight-node, and Twelve-node so that curved boundaries can be represented with improved accuracy. The formulation combines a Galerkin finite element procedure, an automated higher-order meshing strategy, and a Gauss quadrature rule to obtain numerical solutions of Helmholtz-type eigenvalue problems. Five curved waveguide domains are considered: an annular circular domain, a circular domain with a square hole, the union of two circular disks, a circular region with two unequal holes, and an L-shaped domain with a quarter-circular curved boundary. The computed eigenvalues are compared with published numerical and analytical results. The comparisons show that increasing the element order from Four-node, Eight-node, and Twelve-node improves the accuracy of the predicted eigenvalues while reducing the number of elements required to obtain comparable convergence. The proposed method therefore provides a practical and efficient finite element framework for eigenvalue estimation in curved waveguide geometries.

Dimensions

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