Josh Buli | Research | UCR Mathematics Department

RESEARCH

Research Interests

My general research interest is in the design and application of computationally efficient numerical methods for partial differential equations and stochastic partial differential equations. Some specific methods and applications include:

Discontinuous Galerkin (DG) and local discontinuous Galerkin (LDG) methods
DG method applied to hyperbolic flows on networks
Intrusive and non-intrusive methods for stochastic partial differential equations: Monte-Carlo, multi-level Monte Carlo (MLMC), generalized polynomial Chaos (gPC), stochastic collocation methods
Algorithms for delay differential equations arising in traffic conngestion problems
Multi-phase flow models for blood clots

FIGURES

Buli and Xing (2018)

Figure 1. - Traveling wave solution for the BBM system.

Figure 2. - Traveling wave solution for the BBM system.

Movie 1. - Solitary Wave Collision.

Arnott and Buli (2018)

Figure 3. - Solution of a delay differential equation in heavy traffic congestion.

Figure 4. - User-cost as a function of the number of commuters derived from the bathtub model of traffic congestion.

Figure 5. - Discontinuous entry rates in the bathtub model.