A recursive approach for the finite element computation of waveguides

TL;DR

This paper introduces a recursive method to efficiently compute the dynamic stiffness matrix of long periodic waveguides, significantly reducing computational effort for frequency response analysis.

Contribution

A novel recursive approach for finite element analysis of waveguides that decreases computation time from linear to logarithmic scale with respect to the number of periods.

Findings

Computing time scales as log2 of the number of periods.

Method effectively computes frequency response functions.

Reduces computational complexity for large structures.

Abstract

The finite element computation of structures such as waveguides can lead to heavy computations when the length of the structure is large compared to the wavelength. Such waveguides can in fact be seen as one-dimensional periodic structures. In this paper a simple recursive method is presented to compute the global dynamic stiffness matrix of finite periodic structures. This allows to get frequency response functions with a small amount of computations. Examples are presented to show that the computing time is of order $\log_2 N$ where $N$ is the number of periods of the waveguide.