Near-Resonance-Informed Parallel Methods for Nonlinear Oscillatory PDE Models
Develop parallel numerical methods informed by near-resonance theory to accelerate nonlinear oscillatory PDE models. Explore how fast oscillations influence long-term dynamics and optimize algorithms for high-performance computing environments.
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Project Description
Project Overview
This project develops a new class of numerical methods tailored for modern parallel-computing architectures to solve nonlinear partial differential equations (PDEs) exhibiting significant oscillatory behavior. Such PDEs are crucial for modeling large-scale fluid phenomena, weather, and climate systems. Core to the approach is the near-resonance concept, revealing how fast oscillations impact long-term dynamics through robust nonlinear coupling.
What You Will Do
You will design, implement, and analyze near-resonance-informed parallel-in-time algorithms. This includes distributing linear subproblems across CPU cores and reconstructing their nonlinear interactions consistent with the underlying theory. Your work will rigorously assess accuracy, parallel speed-up, and energy efficiency, benchmarking performance and scalability on high-performance computing platforms.
Expected Outcomes
The project aims to deliver a general numerical framework adaptable to present and future computational hardware. Contributions will advance mathematical understanding of oscillatory PDE dynamics and improve computational tools for fluid dynamics, geophysical modeling, and related fields.
Why This Matters
Efficient and accurate nonlinear oscillatory PDE simulation is central to many scientific and engineering domains. Leveraging near-resonant coupling theory can lead to substantial improvements in speed and resource usage, impacting weather forecasting, climate prediction, and the broader study of complex wave phenomena.
Entry Requirements
How to Apply
Eligibility
Supervisor Profile
Dr Bin Cheng specializes in partial differential equations, numerical analysis, and applied mathematics with a focus on geophysical fluid dynamics. His research involves understanding complex nonlinear dynamics such as rapidly rotating shallow-water and Euler equations, underpinned by theoretical insights into oscillatory systems. He is an active researcher with contributions to developing mathematically rigorous and computationally efficient methods.