Theme

Geometric Numerical Integration for Differential Equations

My research interests are in applied mathematics, especially in numerical analysis for differential equations.

Differential equations often have specific geometric properties, such as symplecticity of Hamiltonian problems. Geometric numerical integration methods are numerical methods that inherit such properties in the discrete setting, and their strengths have been proved over recent decades from both practical and mathematical viewpoints. I have particularly focused on constructing and analyzing efficient high-order energy-preserving algorithms for Hamiltonian problems and structure-preserving finite difference and finite element schemes for partial differential equations.

Recently, I am also interested in numerical linear algebra, optimization on manifolds, data assimilation and uncertainty quantification.

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