arXiv subjects

Yunhong Deng

Publications and source records attributed to Yunhong Deng.

4 recordsLinked to original sources

arXiv2026

Efficient Primal-dual Forward-backward Splitting Method for Wasserstein-like Gradient Flows with General Nonlinear Mobilities

We construct an efficient primal-dual forward-backward (PDFB) splitting method for computing a class of minimizing movement schemes with nonlinear mobility transport distances, and apply it to computing Wasserstein-like gradient flows. This approach introduces a novel saddle point formulation for the minimizing movement schemes, leveraging a support function form from the Benamou-Brenier dynamical formulation of optimal transport. The resulting framework allows for flexible computation of Wasserstein-like gradient flows by solving the corresponding saddle point problem at the fully discrete level, and can be easily extended to handle general nonlinear mobilities. We also provide a detailed convergence analysis of the PDFB splitting method, along with practical remarks on its implementation and application. The effectiveness of the method is demonstrated through several challenging numerical examples.

math.NA↗

arXiv2026

Homogenization of Time-Discrete Gradient Flows

In this work, we study the homogenization limit for Fokker--Planck equations on the flat torus with rapidly oscillating diffusion coefficients at the time-discrete level. We discretize the equation in time using a minimizing movement scheme and compare two choices of metric: a transport-type metric and a weighted L2 metric. We prove that this choice is crucial: the two schemes lead to different homogenization limits as the scaling parameter tends to zero, and consequently to different evolution equations as the time step is sent to zero. In particular, only the scheme based on the weighted L2 metric recovers the correct effective dynamics.

math.AP↗

arXiv2025

A Primal-dual Forward-backward Splitting Method for Cross-diffusion Gradient Flows with General Mobility Matrices

In this work, we construct a primal-dual forward-backward (PDFB) splitting method for computing a class of cross-diffusion systems that can be formulated as gradient flows under transport distances induced by matrix mobilities. By leveraging their gradient flow structure, we use minimizing movements as the variational formulation and compute these cross-diffusion systems by solving the minimizing movements as optimization problems at the fully discrete level. Our strategy to solve the optimization problems is the PDFB splitting method outlined in our previous work \cite{PDFB2024}. The efficiency of the proposed PDFB splitting method is demonstrated on several challenging cross-diffusion equations from the literature.

math.NA↗

arXiv2024

Adaptive Hyperbolic-cross-space Mapped Jacobi Method on Unbounded Domains with Applications to Solving Multidimensional Spatiotemporal Integrodifferential Equations

In this paper, we develop a new adaptive hyperbolic-cross-space mapped Jacobi (AHMJ) method for solving multidimensional spatiotemporal integrodifferential equations in unbounded domains. By devising adaptive techniques for sparse mapped Jacobi spectral expansions defined in a hyperbolic cross space, our proposed AHMJ method can efficiently solve various spatiotemporal integrodifferential equations such as the anomalous diffusion model with reduced numbers of basis functions. Our analysis of the AHMJ method gives a uniform upper error bound for solving a class of spatiotemporal integrodifferential equations, leading to effective error control.

math.NA↗