24 citations · 219 across the 39 of their papers we have counts for
6 papers · 1 filter
Generalized optimal transport and mean field control problems for reaction-diffusion systems with high-order finite element computation
Guosheng Fu, Stanley Osher, Will Pazner +1
We design and compute a class of optimal control problems for reaction-diffusion systems. They form mean field control problems related to multi-density reaction-diffusion systems.…
Two Finite Element Approaches For The Porous Medium Equation That Are Positivity Preserving And Energy Stable
Arjun Vijaywargiya, Guosheng Fu
In this work, we present the construction of two distinct finite element approaches to solve the Porous Medium Equation (PME). In the first approach, we transform the PME to a log-…
High order spatial discretization for variational time implicit schemes: Wasserstein gradient flows and reaction-diffusion systems
Guosheng Fu, Stanley Osher, Wuchen Li
We design and compute first-order implicit-in-time variational schemes with high-order spatial discretization for initial value gradient flows in generalized optimal transport metr…
-Multigrid preconditioner for a divergence-conforming HDG scheme for the incompressible flow problems
Guosheng Fu, Wenzheng Kuang
In this study, we present an -multigrid preconditioner for a divergence-conforming HDG scheme for the generalized Stokes and the Navier-Stokes equations using an augmented Lagr…
High-order variational Lagrangian schemes for compressible fluids
Guosheng Fu, Chun Liu
We present high-order variational Lagrangian finite element methods for compressible fluids using a discrete energetic variational approach. Our spatial discretization is mass/mome…
High order computation of optimal transport, mean field planning, and mean field games
Guosheng Fu, Siting Liu, Stanley Osher +1
Mean-field games (MFGs) have shown strong modeling capabilities for large systems in various fields, driving growth in computational methods for mean-field game problems. However,…