Mathematics for energy systems: Methods, modeling strategies, and simulation

TL;DR

This paper reviews mathematical methods and modeling strategies used to analyze and simulate energy systems, covering charge transport, storage, markets, and collective behaviors with advanced analytical and computational tools.

Contribution

It introduces a comprehensive framework combining well-posed models, analysis techniques, and simulation tools for understanding complex energy systems.

Findings

Development of deterministic and stochastic models

Application of homogenization and averaging techniques

Implementation of high-performance computational simulations

Abstract

We offer an insight into our mathematical endeavors, which aim to advance the foundational understanding of energy systems in a broad context, encompassing facets such as charge transport, energy storage, markets, and collective behavior. Our working techniques include a combination of well-posed mathematical models (both deterministic and stochastic), mathematical analysis arguments (mostly concerned with model dimension reduction and averaging, periodic homogenization), and simulation tools (numerical approximation techniques, computational statistics, high-performance computing).