Contention resolution schemes have proven to be an incredibly powerful concept which allows to tackle a broad class of problems. The framework has been initially designed to handle submodular optimization under various types of constraints, that is, intersections of exchange systems (including matroids), knapsacks, and unsplittable flows on trees. Later on, it turned out that this framework per...

We propose Q(D)-resolution, a proof system for Quantified Boolean Formulas. Q(D)-resolution is a generalization of Q-resolution parameterized by a dependency scheme D. This system is motivated by the generalization of the QDPLL algorithm using dependency schemes implemented in the solver DepQBF. We prove soundness of Q(D)-resolution for a dependency scheme D that is strictly more general than t...

The main idea of highly accurate multioperators schemes for CFD applications is briefly outlined, their optimization being discussed.. Several examples of numerical simulations related to aeroacoustics are presented. Hybrid schemes with multioperators for shock capturing calculations are considered.

In this work, we introduce new finite-difference shock-capturing central schemes on staggered grids. Staggered schemes may have better resolution of the corresponding unstaggered schemes of the same order. They are based on high order non oscillatory reconstruction (ENO or WENO), and a suitable ODE solver for the computation of the integral of the flux. Although they suffer from a more severe s...

6 It is the purpose of this short article to analyze mass conservation in high-order rigorous 7 remapping schemes, which contrary to flux-based methods, relies on elaborate integral con8 straints over overlap areas and reconstruction functions. For applications on the sphere these 9 integral constraints may be violated primarily due to inexact or ill-conditioned integration 10 and we propose a ...

A double-GPU code is developed to accelerate WENO schemes. The test problem is a compressible viscous flow. The convective terms are discretized using third- to ninth-order WENO schemes and the viscous terms are discretized by the standard fourth-order central scheme. The code written in CUDA programming language is developed by modifying a single-GPU code. The OpenMP library is used for parall...

This article deals with a method, based on total variation diminishing (TVD) scheme, for solving three-dimensional equations of gravitational gas dynamics. For this method a parallel algorithm of the decision is offered. Equations of this kind are a powerful approach to simulating astrophysical problems. Numerical schemes applied for their solving must provide high-resolution capturing of shock...

Abstract This chapter is dedicated to the description of high-order CESE schemes. In second-order