Third-order triangular finite elements for waveguiding problems

TL;DR

This paper introduces simplified explicit matrix relations for third-order triangular finite elements, enhancing waveguiding problem simulations in both isotropic and anisotropic materials with improved accuracy.

Contribution

It provides new, simpler explicit matrix relations for third-order triangular finite elements, facilitating easier implementation in waveguiding simulations.

Findings

Third-order elements improve accuracy over second-order.

Explicit matrix relations are simpler than previous methods.

Numerical examples demonstrate effectiveness in waveguide problems.

Abstract

Explicit relations of matrices for two-dimensional finite element method with third-order triangular elements are given. They are more simple than relations presented in other works and could be easily implemented in new algorithms for both isotropic and anisotropic materials. Numerical examples are given comparatively using second-order and third-order triangular elements for problems of wave propagation in rectangular waveguides which have analytic solutions.