Research Interests

Numerical Optimization

I am interested in the swarm-based algorithms for non-convex global optimizations.

Collective Dynamics of Self-Organized Systems

I am interested in the models describing the collective behavior of self-propelled particles, including the Cucker-Smale dynamics and p-alignment systems. I'm also interested in the connections between collective dynamics and data clustering.

Numerical Methods for PDEs

I am interested in the numerical methods for nonlinear conservation laws & convection-diffusion equations arising from computational fluid dynamics.

Publications

Jingcheng Lu, Eitan Tadmor, Anil Zenginoglu, Swarm-Based Gradient Descent Method for Non-Convex Optimization, preprint.

We developed a novel swarm-based approach for non-convex optimizations. The key idea is to introduce cross-individual communications such that the best agent would progressively dominate the search, helping the crowd escape from local minima.

Jingcheng Lu, Eitan Tadmor, Revisiting High-Resolution Schemes with van-Albada Slope Limiter, preprint.

We revisited the theoretical TVD stability of the smooth van Albada slope limiter.

Jingcheng Lu, Eitan Tadmor, Hydrodynamic Alignment with Pressure II. Multi-species, Quarterly of Applied Mathematics.

We provide the very first proof of hydrodynamic alignment of multi-species systems without assuming specific closure of entropic pressures.

Jingcheng Lu, James D.Baeder, Non-Oscillatory Limited-Time Integration for Conservation Laws and Covection-Diffusion equations, preprint.

We proposed a (nominally) unconditionally non-oscillatory Limited-DIRK3 scheme for conservation laws and convection-diffusion equations.

Jingcheng Lu, James D.Baeder, The High Resolution L-DIRK3 Scheme for Conservation Laws, AIAA SCITECH 2022 Forum, 2022, p. 1075.