相关论文: Error estimate of a bi-fidelity method for kinetic…

Uniform error estimates of a bi-fidelity method for a kinetic-fluid coupled model with random initial inputs in the fine particle regime are proved in this paper. Such a model is a system coupling the incompressible Navier-Stokes equations…

In this paper, we introduce a bi-fidelity algorithm for velocity discretization of Boltzmann-type kinetic equations under multiple scales. The proposed method employs a simpler and computationally cheaper low-fidelity model to capture a…

The construction of efficient methods for uncertainty quantification in kinetic equations represents a challenge due to the high dimensionality of the models: often the computational costs involved become prohibitive. On the other hand,…

In this paper we study the effect of randomness in kinetic equations that preserve mass. Our focus is in proving the analyticity of the solution with respect to the randomness, which naturally leads to the convergence of numerical methods.…

We introduce in this paper a new approach to the problem of the convergence to equilibrium for kinetic equations. The idea of the approach is to prove a 'weak' coercive estimate, which implies exponential or polynomial convergence rate. Our…

In traffic flow modeling, incorporating uncertainty is crucial for accurately capturing the complexities of real-world scenarios. In this work we focus on kinetic models of traffic flow, where a key step is to design effective numerical…

In this paper, we study the multiscale Boltzmann equation with multi-dimensional random parameters by a bi-fidelity stochastic collocation (SC) method developed in [A. Narayan, C. Gittelson and D. Xiu, SIAM J. Sci. Comput., 36 (2014); X.…

In this paper, we consider the development of efficient numerical methods for linear transport equations with random parameters and under the diffusive scaling. We extend to the present case the bi-fidelity stochastic collocation method…

We develop a new method for proving hypocoercivity for a large class of linear kinetic equations with only one conservation law. Local mass conservation is assumed at the level of the collision kernel, while transport involves a confining…

We overview some recent results in the field of uncertainty quantification for kinetic equations and related problems with random inputs. Uncertainties may be due to various reasons, such as lack of knowledge on the microscopic interaction…

We obtain an error estimate between viscosity solutions and \delta-viscosity solutions of nonhomogeneous fully nonlinear uniformly elliptic equations. The main assumption, besides uniform ellipticity, is that the nonlinearity is…

A new framework is introduced for constructing interpretable and truly reliable reduced models for multiscale problems in situations without scale separation. Hydrodynamic approximation to the kinetic equation is used as an example to…

We discuss kinetic-based particle optimization methods and variable-sample strategies for problems where the cost function represents the expected value of a random mapping. Kinetic-based optimization methods rely on a consensus mechanism…

A general lattice Boltzmann method for simulation of fluids with tailored transport coefficients is presented. It is based on the recently introduced quasi-equilibrium kinetic models, and a general lattice Boltzmann implementation is…

In some recent works [G. Dimarco, L. Pareschi, Hybrid multiscale methods I. Hyperbolic Relaxation Problems, Comm. Math. Sci., 1, (2006), pp. 155-177], [G. Dimarco, L. Pareschi, Hybrid multiscale methods II. Kinetic equations, SIAM…

In this paper, we establish optimal hypoelliptic estimates for a class of kinetic equations, which are simplified linear models for the spatially inhomogeneous Boltzmann equation without angular cutoff.

Bicoherence analysis is a well established method for identifying the quadratic nonlinearity of stationary processes. However, it is often applied without checking the basic assumptions of stationarity and convergence. The classic…

In a recent paper we presented a new ultra efficient numerical method for solving kinetic equations of the Boltzmann type (G. Dimarco, R. Loubere, Towards an ultra efficient kinetic scheme. Part I: basics on the 689 BGK equation, J. Comp.…

In this work, we prove rigorous convergence properties for a semi-discrete, moment-based approximation of a model kinetic equation in one dimension. This approximation is equivalent to a standard spectral method in the velocity variable of…

This article is a review on basic concepts and tools devoted to a posteriori error estimation for problems solved with the Finite Element Method. For the sake of simplicity and clarity, we mostly focus on linear elliptic diffusion problems,…