A unifying perspective on linear continuum equations prevalent in science. Part II: Canonical forms for time-harmonic equations

TL;DR

This paper reformulates various linear continuum equations, especially time-harmonic ones, using composite theory to enhance understanding and solution efficiency, focusing on canonical forms without higher order gradients.

Contribution

It introduces a unifying reformulation of time-harmonic linear continuum equations within the extended composite theory framework, simplifying analysis and solution methods.

Findings

Canonical forms for many time-harmonic equations derived

Enhanced understanding of equation structure achieved

Potential for more efficient solution techniques identified

Abstract

Following some past advances, we reformulate a large class of linear continuum science equations in the format of the extended abstract theory of composites so that we can apply this theory to better understand and efficiently solve those equations. Here in part II we elucidate the form for many time-harmonic equations that do not involve higher order gradients.