Geometric Numerical Integration for Differential Equations

I specialize in applied mathematics, with a particular emphasis on numerical analysis of differential equations.

Differential equations frequently exhibit important geometric properties. An example of this is the symplecticity in Hamiltonian problems. Geometric numerical integration methods are designed to retain these properties even in discrete settings. Over recent decades, the efficacy of these methods has been established both from practical and theoretical perspectives. My work mainly revolves around the construction and analysis of efficient high-order energy-preserving algorithms for Hamiltonian problems. Additionally, I have developed structure-preserving finite difference and finite element schemes for partial differential equations.

Recently, my interests have also expanded to include numerical linear algebra, continuous optimization, data assimilation, and uncertainty quantification. These areas have promising applications across diverse fields, such as science, engineering, and informatics.