Near-Resonance-Informed Parallel Methods for Nonlinear Oscillatory PDE Models
Explore numerical methods that exploit near-resonance theory to accelerate nonlinear oscillatory PDE simulations in parallel computing. Develop and test algorithms that improve speed and accuracy for applications in fluid dynamics and climate modelling.
AI-generated overview
Project Description
Project Overview
This PhD project aims to develop near-resonance-informed parallel numerical methods to solve nonlinear partial differential equations (PDEs) featuring oscillatory behavior, which are prevalent in fluid simulation, weather and climate models. Leveraging recent theoretical insights on near resonances by Dr Bin Cheng and collaborators, the research focuses on designing numerical schemes that capture essential fast oscillation interactions influencing long-term dynamics.
What You Will Do
You will design, implement, and rigorously evaluate new parallel-in-time algorithms that distribute sub-problems across CPU cores while reconstructing nonlinear interactions consistent with near-resonance theory. Benchmarking will involve performance evaluation through scaling laws to optimize high-performance computing resources with attention to accuracy, parallel speed-up, and energy/hardware efficiency.
Expected Outcomes
The project will produce a general numerical framework tailored to modern and emerging computational architectures, enhancing simulation capability for nonlinear oscillatory PDEs. The outcomes will include robust algorithmic design, theoretical analysis, and prototype software for broader use in fluid dynamics, geophysical, and related fields.
Why This Matters
The developed methods will enable faster, more accurate, and resource-efficient simulation of complex wave phenomena critical in climate and environmental science. By advancing computational methods aligned with near-resonance theory, the project addresses challenges in modeling nonlinear dynamics vital for scientific and engineering applications.
Entry Requirements
How to Apply
Eligibility
Supervisor Profile
Dr Bin Cheng is a specialist in partial differential equations, geophysics, numerical analysis, and applied mathematics, based at the University of Surrey. His research focuses on capturing complex nonlinear dynamics in oscillatory PDEs, leveraging analytical insights into near resonances to design efficient, scalable numerical methods. Cheng is a recognized expert with a strong publication record and collaborations with leading mathematicians such as Eitan Tadmor.