Approximate well-balanced WENO finite difference schemes using a global-flux quadrature method with multi-step ODE integrator weights

International audienceIn this work, high-order discrete well-balanced methods for one-dimensional hyperbolic systems of balance laws are proposed. We aim to construct a method whose discrete steady states correspond to solutions of arbitrary high-order ODE integrators. However, this property is embedded directly into the scheme, eliminating the need to apply the ODE integrator explicitly to solve the local Cauchy problem. To achieve this, we employ a WENO finite difference framework and apply WENO reconstruction to a global flux assembled nodewise as the sum of the physical flux and a source primitive. The novel idea is to compute the source primitive using high-order multi-step ODE methods applied on the finite difference grid. This approach provides a locally well-balanced splitting of the source integral, with weights derived from the ODE integrator. By construction, the discrete solutions of the proposed schemes align with those of the underlying ODE integrator. The proposed methods employ WENO flux reconstructions of varying orders, combined with multi-step ODE methods of up to order 8, achieving steady-state accuracy determined solely by the ODE method's consistency. Numerical experiments using scalar balance laws and shallow water equations confirm that the methods achieve optimal convergence for time-dependent solutions and significant error reduction for steady-state solutions.</div

The Graph Geometric Control Condition

Comments welcomeIn this paper, we introduce a novel concept called the Graph Geometric Control Condition (GGCC). It turns out to be a simple, geometric rewriting of many of the frameworks in which the controllability of PDEs on graphs has been studied. We prove that (GGCC) is a necessary and sufficient condition for the exact controllability of the wave equation on metric graphs with internal controls and Dirichlet boundary conditions. We then investigate the internal exact controllability of the wave equation with mixed boundary conditions and the one of the Schr\"odinger equation, as well as the internal null-controllability of the heat equation. We show that (GGCC) provides a sufficient condition for the controllability of these equations and we provide explicit examples proving that (GGCC) is not necessary in these cases

A hybridizable discontinuous Galerkin method with transmission variables for time-harmonic electromagnetic problems

The CHDG method is a hybridizable discontinuous Galerkin (HDG) finite element method suitable for the iterative solution of time-harmonic wave propagation problems. Hybrid unknowns corresponding to transmission variables are introduced at the element interfaces and the physical unknowns inside the elements are eliminated, resulting in a hybridized system with favorable properties for fast iterative solution. In this paper, we extend the CHDG method, initially studied for the Helmholtz equation, to the time-harmonic Maxwell equations. We prove that the local problems stemming from hybridization are well-posed and that the fixed-point iteration naturally associated to the hybridized system is contractive. We propose a 3D implementation with a discrete scheme based on nodal basis functions. The resulting solver and different iterative strategies are studied with several numerical examples using a high-performance parallel C++ code

On the MID Property in Planar Delay Systems. Towards a Partial Pole Placement in the Multidimensional case

International audienceIn recent works, a new stabilization paradigm called Partial Pole Placement has been set for single-delay single-input single-output systems of linear time-invariant delay differential equations. In fact, the PPP has the advantage of prescribing the closed-loop exponential decay rate since it consists in assigning the corresponding rightmost spectral value thanks to two remarkable spectral properties called respectively multiplicity-induced-dominancy (MID) and coexistant-real-roots inducing multiplicity (CRRID). In this note, we show the validity of the MID property in planar delay systems when some spectral value achieves its maximal multiplicity, thus opening new perspectives in the prescribed stabilization for delay systems with commensurate delays.</div

Withdrawal of: Solution of the Ovals problem

In the previous version of the preprint, we made a mistake in our proposed solution to the Ovals problem (formulated in [3, 24]). The erroneous claim is that the operator A_T, used in the proof of Lemma 2.4.1, is selfadjoint. But this fact is wrong, as kindly pointed out to us by Matthias Baur, Rupert L. Frank, Larry Read and Timo Weidl, whom we warmly thank. At the moment, unfortunately, this mistake seems fatal to us, so the Ovals conjecture remains open. Nevertheless, since our work contains arguments that may be useful to address the conjecture, we let it available as a preprint, with a warning on Section 2.4

What Happened in This Pipeline? Diffing Build Logs with CiDiff

Continuous integration (CI) is widely used by developers to ensure the quality and reliability of their software projects. However, diagnosing a CI regression is a tedious process that involves the manual analysis of lengthy build logs. In this paper, we explore how textual differencing can support the debugging of CI regressions. As off-the-shelf diff algorithms produce suboptimal results, in this work we introduce a new diff algorithm specifically tailored to build logs called CiDiff. We evaluate CiDiff against several baselines on a novel dataset of 17 906 CI regressions, performing an accuracy study, a quantitative study and a user-study. Notably, our algorithm reduces the number of lines to inspect by about 60 % in the median case, with reasonable overhead compared to the state-of-practice LCS-diff. Finally, our algorithm is preferred by the majority of participants in 70 % of the regression cases, whereas LCS-diff is preferred in only 5 % of the cases.</div

ProvSQL: A General System for Keeping Track of the Provenance and Probability of Data

We present the data model, design choices, and performance of ProvSQL, a general and easy-to-deploy provenance tracking and probabilistic database system implemented as a PostgreSQL extension. ProvSQL's data and query models closely reflect that of a large core of SQL, including multiset semantics, the full relational algebra, and terminal aggregation. A key part of its implementation relies on generic provenance circuits stored in memory-mapped files. We propose benchmarks to measure the overhead of provenance and probabilistic evaluation and demonstrate its scalability and competitiveness with respect to other state-of-the-art systems

Channel Simulation: Tight meta converse for error and strong converse exponents

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Periodic convergence for a class of nonlinear time-delay systems

International audienceThe new existence conditions for periodic steady-state solution in time-delay convergent systems are presented. The main advantage of this result is that highly nonlinear (without meaningful linear approximation) dynamics are allowed for analysis. These conditions are developed for Persidskii and Lotka-Volterra time-delay systems. The efficiency of the approach is demonstrated on academic examples of these models

Understanding Linux Kernel Code through Formal Verification: A Case Study of the Task-Scheduler Function select_idle_core

International audienceOn the one hand, the Linux kernel task scheduler is critical to all application performance. On the other hand, it is widely agreed that its code complexity is spiraling out of control, and only a tiny handful of kernel developers understand it. We are exploring the opportunities and challenges in applying formal verification to Linux kernel task-scheduler code. Building on a previous work focusing on the evolution of the function should_we_balance, we here consider a version of the key task-placement function select_idle_core and the evolution of the iterators on which it relies