ESAIM: Mathematical Modelling and Numerical Analysis最新文献_第2页

High order asymptotic preserving scheme for diffusive scaled linear kinetic equations with general initial conditions 具有一般初始条件的扩散比例线性动力学方程的高阶渐近保全方案

ESAIM: Mathematical Modelling and Numerical Analysis Pub Date : 2024-04-18 DOI: 10.1051/m2an/2024028

Megala Anandan, Benjamin Boutin, Nicolas Crouseilles

{"title":"High order asymptotic preserving scheme for diffusive scaled linear kinetic equations with general initial conditions","authors":"Megala Anandan, Benjamin Boutin, Nicolas Crouseilles","doi":"10.1051/m2an/2024028","DOIUrl":"https://doi.org/10.1051/m2an/2024028","url":null,"abstract":"Diffusive scaled linear kinetic equations appear in various applications, and they contain a small parameter $epsilon$ that forces a severe time step restriction for standard explicit schemes. Asymptotic preserving (AP) schemes are those schemes that attain asymptotic consistency and uniform stability for all values of ε, with the time step restriction being independent of ε. In this work, we develop high order AP scheme for such diffusive scaled kinetic equations with both well-prepared and non-well-prepared initial conditions by employing IMEX-RK time integrators such as CK-ARS and A types. This framework is also extended to a different collision model involving advection-diffusion asymptotics, and the AP property is proved formally. A further extension of our framework to inflow boundaries has been made, and the AP property is verified. The temporal and spatial orders of accuracy of our framework are numerically validated in different regimes of ε, for all the models. The qualitative results for diffusion asymptotics, and equilibrium and non-equilibrium inflow boundaries are also presented.","PeriodicalId":505020,"journal":{"name":"ESAIM: Mathematical Modelling and Numerical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140687855","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

New pipe element based on Hermite-Jackson interpolation 基于 Hermite-Jackson 插值法的新型管道元件

ESAIM: Mathematical Modelling and Numerical Analysis Pub Date : 2024-04-12 DOI: 10.1051/m2an/2024027

E. Zafati, K. Le Nguyen

引用次数: 0

Structure-preserving reduced order model for cross-diffusion systems 交叉扩散系统的结构保持减阶模型

ESAIM: Mathematical Modelling and Numerical Analysis Pub Date : 2024-04-12 DOI: 10.1051/m2an/2024026

Jad Dabaghi, Virginie Ehrlacher

{"title":"Structure-preserving reduced order model for cross-diffusion systems","authors":"Jad Dabaghi, Virginie Ehrlacher","doi":"10.1051/m2an/2024026","DOIUrl":"https://doi.org/10.1051/m2an/2024026","url":null,"abstract":"In this work, we construct a structure-preserving Galerkin reduced-order model for the resolution\u0000of parametric cross-diffusion systems. Cross-diffusion systems are often used to model the evolution of\u0000the concentrations or volumic fractions of mixtures composed of different species, and can also be used\u0000in population dynamics (as for instance in the SKT system). These systems often read as nonlinear\u0000degenerated parabolic partial differential equations, the numerical resolutions of which are highly ex-\u0000pensive from a computational point of view. We are interested here in cross-diffusion systems which\u0000exhibit a so-called entropic structure, in the sense that they can be formally written as gradient flows\u0000of a certain entropy functional which is actually a Lyapunov functional of the system. In this work, we\u0000propose a new reduced-order modelling method, based on a reduced basis paradigm, for the resolution\u0000of parameter-dependent cross-diffusion systems. Our method preserves, at the level of the reduced-order\u0000model, the main mathematical properties of the continuous solution, namely mass conservation, non-\u0000negativeness, preservation of the volume-filling property and entropy-entropy dissipation relationship.\u0000The theoretical advantages of our approach are illustrated by several numerical experiments.","PeriodicalId":505020,"journal":{"name":"ESAIM: Mathematical Modelling and Numerical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140710085","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

An optimization-based method for sign-changing elliptic PDEs 基于优化的符号变化椭圆 PDE 方法

ESAIM: Mathematical Modelling and Numerical Analysis Pub Date : 2024-04-04 DOI: 10.1051/m2an/2024013

A. Abdulle, Simon Lemaire

引用次数: 0

An exact in time Fourier pseudospectral method with multiple conservation laws for three-dimensional Maxwell’s equations 针对三维麦克斯韦方程的具有多重守恒定律的精确时间傅立叶伪谱法

ESAIM: Mathematical Modelling and Numerical Analysis Pub Date : 2024-03-25 DOI: 10.1051/m2an/2024022

Bin Wang, Yao-Lin Jiang

引用次数: 0

Optimized Schwarz Waveform Relaxation method for the incompressible Stokes problem 不可压缩斯托克斯问题的优化施瓦茨波形松弛法

ESAIM: Mathematical Modelling and Numerical Analysis Pub Date : 2024-03-18 DOI: 10.1051/m2an/2024020

Duc Quang Bui, C. Japhet, P. Omnes

引用次数: 0

Existence and uniqueness of the motion of a particle subject to a unilateral constraint and friction 受单边约束和摩擦力作用的质点运动的存在性和唯一性

ESAIM: Mathematical Modelling and Numerical Analysis Pub Date : 2024-03-12 DOI: 10.1051/m2an/2024018

Christopher Roger Dance

引用次数: 0

Unconditionally optimal error estimates of linearized Crank-Nicolson Virtual element methods for quasilinear parabolic problems on general polygonal meshes 一般多边形网格上准线性抛物问题的线性化 Crank-Nicolson 虚拟元素方法的无条件最优误差估计

ESAIM: Mathematical Modelling and Numerical Analysis Pub Date : 2024-03-11 DOI: 10.1051/m2an/2024017

Yang Wang, Huaming Yi, Xiaohong Fan, Guanrong Li

引用次数: 0

Multi-step variant of the parareal algorithm: convergence analysis and numerics 准噶尔算法的多步变体：收敛分析和数值计算

ESAIM: Mathematical Modelling and Numerical Analysis Pub Date : 2024-03-06 DOI: 10.1051/m2an/2024014

Katia Ait-Ameur, Y. Maday

{"title":"Multi-step variant of the parareal algorithm: convergence analysis and numerics","authors":"Katia Ait-Ameur, Y. Maday","doi":"10.1051/m2an/2024014","DOIUrl":"https://doi.org/10.1051/m2an/2024014","url":null,"abstract":"In this paper, we consider the problem of accelerating the numerical simulation of time dependent problems involving a multi-step time scheme by the parareal algorithm. The parareal method is based on combining predictions made by a coarse and cheap propagator, with corrections\u0000computed with two propagators: the previous coarse and a precise and expensive one used in a parallel way over the time windows. A multi-step time scheme can potentially bring higher approximation orders than plain one-step methods but the initialisation of each time window needs to be appropriately chosen. Our main contribution is the design and analysis of an algorithm adapted to this type of discretisation without being too much intrusive in the coarse or fine propagators. At convergence, the parareal algorithm provides a solution that coincides with the solution of the fine solver. In the classical version of parareal, the local initial condition of each time window is corrected at every iteration. When the fine and/or coarse propagators is a multi-step time scheme, we need to choose a consistent approximation of the solutions involved in the initialisation of the fine solver at each time windows. Otherwise, the initialisation error will prevent the parareal algorithm to converge towards the solution with fine solver’s accuracy. In this paper, we develop a variant of the algorithm that overcome this obstacle. Thanks to this, the parareal algorithm is more coherent with the underlying time scheme and we recover the properties of the original version. We show both theoretically and numerically that the accuracy and convergence of the multi-step variant of parareal algorithm are preserved when we choose carefully the initialisation of each time window.","PeriodicalId":505020,"journal":{"name":"ESAIM: Mathematical Modelling and Numerical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140262486","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Solving reaction-diffusion problems with explicit Runge-Kutta exponential methods without order reduction 用不降阶的显式 Runge-Kutta 指数法解决反应扩散问题

ESAIM: Mathematical Modelling and Numerical Analysis Pub Date : 2024-02-08 DOI: 10.1051/m2an/2024011

Begoña Cano, María Jesús Moreta

引用次数: 0