# Numerical methods for the construction of linear waves structures on discrete orthogonal grids

## TL;DR

This paper explores numerical methods to construct linear wave structures on discrete orthogonal grids across dimensions 1 to 4, analyzing spectral zones and validating wave propagation through simulations.

## Contribution

It introduces new numerical approaches for modeling linear waves on discrete grids, focusing on spectral regions near key frequencies, with analysis across multiple dimensions.

## Key findings

- Wave propagation is feasible in various spectral zones.
- Numerical simulations confirm theoretical predictions.
- Methods are applicable to grids up to four dimensions.

## Abstract

We study the possibility for the implementation of linear wave structures on discrete grids with various dimensions. The systems of the first order differential equations for the set of virtual functions, describing the wave propagation, are derived for different spectral zones. We are particularly interested in the spectral regions which are localized near the lowest and the maximal frequencies, as well as in the vicinity of a central frequency. The cases of discrete orthogonal grids with dimensions from 1 to 4 are analyzed. The possibility of the propagation of waves in the considered situations is substantiated by numerical simulations.