Research

Research Interests

• Numerical analysis
• Scientific Computing
• Numerical analysis of differential equations ODEs, PDEs, DDEs, DPDEs, FDEs
• Iterative methods for problems with multiple scales
• Robust domain decomposition methods for problems with variable coefficients
• Multilevel methods for elliptic equations with strong convection
• Multigrid methods for time-dependent partial differential equations
• Finite difference, finite element and spectral methods
• High order time discretisation schemes for ODEs
• Delay and functional differential equations
• Functional calculi and spectral mapping theorems
• Solving differential equations using non-linear approximations and adaptive methods
• Moving mesh methods
• Numerical solution of Monge-Ampère and Monge-Kantorovich problems
• Applications of optimal transport problems
• Non-linear approximations and adaptive methods for differential equations
• Parallel Computing
• Discrete and continuous models for organisation in ant colonies
• Optimization
• Evolutionary algorithms and stochastic optimisation
• Models of computing, programming languages and paradigms