Research

Numerical partial differential equations

We develop numerical methods for time-dependent and nonlinear partial differential equations, with particular attention to operator splitting, explicit and semi-implicit time integration, and fast-sweeping ideas. Our main focus is to balance accuracy, stability, computational efficiency, and the structural properties of the underlying model.

Waves and inverse problems

We study Eulerian techniques for high-frequency wave propagation and the inverse problems that arise from indirect measurements. Our work combines eikonal and Schrödinger models, Gaussian-beam ideas, traveltime tomography, and adjoint-state methods, with an emphasis on multivalued propagation and discontinuous media.

Interfaces and evolving surfaces

We design numerical methods for moving interfaces, geometric evolution, and partial differential equations posed on surfaces. The main focus is on level-set, grid-based particle, embedding, and closest-point formulations that can handle changing geometry, implicit surfaces, and point-cloud representations without requiring a fitted mesh.

Imaging and data methods

We use variational, statistical, and optimization methods to address segmentation, denoising, restoration, and related data problems. Our current focus connects partial-differential-equation models with convex and Riemannian optimization, low-rank recovery and completion, and dimension-reduction techniques for structured data.

Computational dynamical systems

We develop Eulerian approaches for analysing Lagrangian behaviour in time-dependent flows. Our main focus is the computation of flow maps, finite-time Lyapunov exponents, and coherent structures, including settings where trajectories must be inferred from sparse measurements or are affected by uncertainty.