High order entropy stable discontinuous Galerkin spectral element methods through subcell limiting

Subcell limiting strategies for discontinuous Galerkin spectral element methods do not provably satisfy a semi-discrete cell entropy inequality. In this work, we introduce an extension to the subcell limiting strategy that satisfies the semi-discrete cell entropy inequality by formulating the limiting factors as solutions to an optimization problem. The optimization problem is efficiently solved using a deterministic greedy algorithm. We also discuss the extension of the proposed subcell limiting strategy to preserve general convex constraints. Numerical experiments confirm that the proposed limiting strategy preserves high-order accuracy for smooth solutions and satisfies the cell entropy inequality

A positivity preserving strategy for entropy stable discontinuous Galerkin discretizations of the compressible Euler and Navier-Stokes equations

High-order entropy-stable discontinuous Galerkin methods for the compressible Euler and Navier-Stokes equations require the positivity of thermodynamic quantities in order to guarantee their well-posedness. In this work, we introduce a positivity limiting strategy for entropy-stable discontinuous Galerkin discretizations constructed by blending high order solutions with a low order positivity-preserving discretization. The proposed low order discretization is semi-discretely entropy stable, and the proposed limiting strategy is positivity preserving for the compressible Euler and Navier-Stokes equations. Numerical experiments confirm the high order accuracy and robustness of the proposed strategy

A Unified Framework for Mutual Improvement of SLAM and Semantic Segmentation

This paper presents a novel framework for simultaneously implementing localization and segmentation, which are two of the most important vision-based tasks for robotics. While the goals and techniques used for them were considered to be different previously, we show that by making use of the intermediate results of the two modules, their performance can be enhanced at the same time. Our framework is able to handle both the instantaneous motion and long-term changes of instances in localization with the help of the segmentation result, which also benefits from the refined 3D pose information. We conduct experiments on various datasets, and prove that our framework works effectively on improving the precision and robustness of the two tasks and outperforms existing localization and segmentation algorithms.Comment: 7 pages, 5 figures.This work has been accepted by ICRA 2019. The demo video can be found at https://youtu.be/Bkt53dAehj