Related papers: Maximum-principle-satisfying second-order Intrusiv…
Intrusive uncertainty quantification methods for hyperbolic problems exhibit spurious oscillations at shocks, which leads to a significant reduction of the overall approximation quality. Furthermore, a challenging task is to preserve…
In this article we study intrusive uncertainty quantification schemes for systems of conservation laws with uncertainty. Standard intrusive methods lead to oscillatory solutions which sometimes even cause the loss of hyperbolicity. We…
Methods for quantifying the effects of uncertainties in hyperbolic problems can be divided into intrusive and non-intrusive techniques. Non-intrusive methods allow the usage of a given deterministic solver in a black-box manner, while being…
We provide a framework for high-order discretizations of nonlinear scalar convection-diffusion equations that satisfy a discrete maximum principle. The resulting schemes can have arbitrarily high order accuracy in time and space, and can be…
Hyperbolic polynomials is a class of real-roots polynomials that has wide range of applications in theoretical computer science. Each hyperbolic polynomial also induces a hyperbolic cone that is of particular interest in optimization due to…
A hyperbolic system approach is proposed for robust computation of anisotropic diffusion equations that appear in quasineutral plasmas. Though the approach exhibits merits of high extensibility and accurate flux computation, the…
In this chapter, we aim at presenting the basic techniques necessary to go beyond the widely accepted paradigm of second-order numerics. We specifically focus on finite-volume schemes for hyperbolic conservation laws occuring in fluid…
Admissible states in hyperbolic systems and related equations often form a convex invariant domain. Numerical violations of this domain can lead to loss of hyperbolicity, resulting in illposedness and severe numerical instabilities. It is…
We propose a hybrid moment method for the multi-scale kinetic equations in the framework of the regularized moment method [7]. In this method, the fourth order moment system is chosen as the governing equations in the fluid region. When…
Uncertainty Quantification for nonlinear hyperbolic problems becomes a challenging task in the vicinity of shocks. Standard intrusive methods lead to oscillatory solutions and can result in non-hyperbolic moment systems. The intrusive…
The growing demand for solving large-scale, data-intensive linear and conic optimization problems, particularly in applications such as artificial intelligence and machine learning, has highlighted the limitations of classical interior…
The emergence of huge-scale, data-intensive linear optimization (LO) problems in applications such as machine learning has driven the need for more computationally efficient interior point methods (IPMs). While conventional IPMs are…
We consider hyperbolic systems of conservation laws with relaxation source terms leading to a diffusive asymptotic limit under a parabolic scaling. We introduce a new class of secondorder in time and space numerical schemes, which are…
This paper presents eigensolution and non-modal analyses for immersed boundary methods (IBMs) based on volume penalization for the linear advection equation. This approach is used to analyze the behavior of flux reconstruction (FR)…
In this paper we approximate the radiative transfer equations by the method of moments, constructing mesoscopic approximations of arbitrary order of the otherwise microscopic system. To define the necessary closure a minimum entropy…
Many interesting physical problems described by systems of hyperbolic conservation laws are stiff, and thus impose a very small time-step because of the restrictive CFL stability condition. In this case, one can exploit the superior…
In this paper we propose the first better than second order accurate method in space and time for the numerical solution of the resistive relativistic magnetohydrodynamics (RRMHD) equations on unstructured meshes in multiple space…
The continuous dynamical system approach to deep learning is explored in order to devise alternative frameworks for training algorithms. Training is recast as a control problem and this allows us to formulate necessary optimality conditions…
A new methodology is developed to integrate numerically the equations of motion for classical many-body systems in molecular dynamics simulations. Its distinguishable feature is the possibility to preserve, independently on the size of the…
It is well known that the number of particles should be scaled up to enable industrial scale simulation. The calculations are more computationally intensive when the motion of the surrounding fluid is considered. Besides the advances in…