arXiv subjects

Jovan Žigić

Publications and source records attributed to Jovan Žigić.

2 recordsLinked to original sources

arXiv2025

Time-Dependent Solutions to the 2D Kuramoto-Sivashinsky Equation via Pseudospectral Method on a Rectangular Domain

This report provides an investigation into solving the Kuramoto-Sivashinsky equation in two spatial dimensions (2DKS) using a pseudo-spectral method on various rectangular periodic domains. The Kuramoto-Sivashinsky equation is a fluid dynamics model that exhibits dynamical features that are highly dependent on the length of the periodic domain. The goals of this report are to describe the mathematical problem; explain the details of the chosen numerical method; inspect solutions and dynamical features for varying grid sizes, step sizes, and domains; and summarize the findings.

math.NA↗

arXiv2023

A Splitting Approach to Dynamic Mode Decomposition of Nonlinear Systems

Reduced-order models have long been used to understand the behavior of nonlinear partial differential equations (PDEs). Naturally, reduced-order modeling techniques come at the price of computational accuracy for a decrease in computation time. Optimization techniques are studied to improve either or both of these objectives and decrease the total computational cost of the problem. This paper focuses on the dynamic mode decomposition (DMD) applied to nonlinear PDEs with periodic boundary conditions. It provides a study of a newly proposed optimization framework for the DMD method called the Split DMD.

math.NA↗