Near-Resonance-Informed Parallel Methods for Nonlinear Oscillatory PDE Models
Explore advanced numerical methods that leverage near-resonance theory to simulate complex nonlinear oscillatory PDEs efficiently. Develop parallel-in-time algorithms optimized for scalability and energy efficiency in high-performance computing environments.
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Project Description
Project Overview
This project focuses on developing a new class of numerical methods for nonlinear partial differential equations (PDEs) exhibiting oscillatory behavior, optimized for modern parallel computing architectures. The methods leverage the concept of near resonances to accurately capture the influence of fast oscillations on long-term dynamics, relevant in fluid dynamics, meteorology, and climate science.
What You Will Do
You will design, test, and analyze near-resonance-informed numerical schemes, including parallel-in-time algorithms that distribute linear subproblems across CPU cores and reconstruct nonlinear interactions consistent with near-resonance theory. Benchmarking against scaling laws will guide the sustainable use of high-performance computing resources.
Expected Outcomes
The project aims to deliver a general numerical framework suited to current and future computational architectures. Your work will contribute to advancing mathematical understanding and computational capabilities for oscillatory PDEs, accompanied by prototype software implementations.
Why This Matters
Nonlinear oscillatory PDEs underpin many scientific fields, including fluid mechanics and geophysical modeling. Efficient and accurate simulation methods are critical for advancing weather prediction and climate modeling, supporting better-informed decisions in science and engineering.
Entry Requirements
How to Apply
Eligibility
Supervisor Profile
Dr Bin Cheng is a researcher specializing in applied mathematics with a focus on nonlinear oscillatory partial differential equations and high-performance numerical methods. His work advances theoretical understanding and computational tools capturing essential dynamics of complex wave phenomena. He is affiliated with the University of Surrey's School of Mathematics and Physics and recognized for contributions to near-resonance theory.