Jenny Suckale

Simone Marras, Michal A. Kopera, Emil M. Constantinescu et al.

The high-order numerical solution of the non-linear shallow water equations (and of hyperbolic systems in general) is susceptible to unphysical Gibbs oscillations that form in the proximity of strong gradients. The solution to this problem is still an active field of research as no general cure has been found yet. In this paper, we tackle this issue by presenting a dynamically adaptive viscosity based on a residual-based sub-grid scale model that has the following properties: $(i)$ it removes the spurious oscillations in the proximity of strong wave fronts while preserving the overall accuracy and sharpness of the solution. This is possible because of the residual-based definition of the dynamic diffusion coefficient. $(ii)$ For coarse grids, it prevents energy from building up at small wave-numbers. $(iii)$ The model has no tunable parameter. Our interest in the shallow water equations is tied to the simulation of coastal inundation, where a careful handling of the transition between dry and wet surfaces is particularly challenging for high-order Galerkin approximations. In this paper, we extend to a unified continuous/discontinuous Galerkin (CG/DG) framework a very simple, yet effective wetting and drying algorithm originally designed for DG [Xing, Zhang, Shu (2010)]. We show its effectiveness for problems in one and two dimensions on domains of increasing characteristic lengths varying from centimeters to kilometers. Finally, to overcome the time-step restriction incurred by the high-order Galerkin approximation, we advance the equations forward in time via a three stage, second order explicit-first-stage, singly diagonally implicit Runge-Kutta (ESDIRK) time integration scheme. Via ESDIRK, we are able to preserve numerical stability for an advective CFL number 10 times larger than its explicit counterpart.

Zhengyang Wei, Renzhi Jing, Yiyi He et al.

The accurate and automatic extraction of roads from satellite imagery is critical for applications in navigation and urban planning, significantly reducing the need for manual annotation. Many existing methods decompose this task into keypoint extraction and connectedness prediction, but often struggle to capture long-range dependencies and complex topologies. Here, we propose LineGraph2Road, a framework that improves connectedness prediction by formulating it as binary classification over edges in a constructed global but sparse Euclidean graph, where nodes are keypoints extracted from segmentation masks and edges connect node pairs within a predefined distance threshold, representing potential road segments. To better learn structural link representation, we transform the original graph into its corresponding line graph and apply a Graph Transformer on it for connectedness prediction. This formulation overcomes the limitations of endpoint-embedding fusion on set-isomorphic links, enabling rich link representations and effective relational reasoning over the global structure. Additionally, we introduce an overpass/underpass head to resolve multi-level crossings and a coupled NMS strategy to preserve critical connections. We evaluate LineGraph2Road on three benchmarks: City-scale, SpaceNet, and Global-scale, and show that it achieves state-of-the-art results on two key metrics, TOPO-F1 and APLS. It also captures fine visual details critical for real-world deployment. We will make our code publicly available.