检索结果-南通市图书馆

hybrid high‑order methods for the Acoustic Wave Equation in the Time Domain

Communications on Applied Mathematics and Computation 2022年第2期4卷 597-633页

作者： Erik Burman Omar Duran Alexandre Ern Department of Mathematics University College LondonLondon WC1E 6BTUK CERMICS Ecole des Ponts77455 Marne la Vallée Cedex 2France INRIA Paris 75589 ParisFrance

We devise hybrid high-order(HHO)methods for the acoustic wave equation in the time domain.We frst consider the second-order formulation in time.Using the Newmark scheme for the temporal discretization,we show that the resulting HHO-Newmark scheme is energy-conservative,and this scheme is also amenable to static condensation at each time step.We then consider the formulation of the acoustic wave equation as a frst-order system together with singly-diagonally implicit and explicit Runge-Kutta(SDIRK and ERK)schemes.HHO-SDIRK schemes are amenable to static condensation at each time step.For HHO-ERK schemes,the use of the mixed-order formulation,where the polynomial degree of the cell unknowns is one order higher than that of the face unknowns,is key to beneft from the explicit structure of the scheme.Numerical results on test cases with analytical solutions show that the methods can deliver optimal convergence rates for smooth solutions of order O(hk+1)in the H1-norm and of order O(h^(k+2))in the L^(2)-norm.Moreover,test cases on wave propagation in heterogeneous media indicate the benefts of using high-order methods.

关键词： hybrid high-order methods Wave equation Newmark scheme Runge-Kutta scheme

来源：

维普期刊数据库评论

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Superconvergent Interpolatory HDG methods for Reaction Difusion Equations II:HHO‑Inspired methods

引用

Communications on Applied Mathematics and Computation 2022年第2期4卷 477-499页

作者： Gang Chen Bernardo Cockburn John R.Singler Yangwen Zhang College of Mathematics Sichuan UniversityChengdu 610065SichuanChina School of Mathematics University of MinnesotaMinneapolisMNUSA Department of Mathematics and Statistics Missouri University of Science and TechnologyRollaMOUSA Department of Mathematical Science University of DelawareNewarkDEUSA

In Chen et al.(J.Sci.Comput.81(3):2188–2212,2019),we considered a superconvergent hybridizable discontinuous Galerkin(HDG)method,defned on simplicial meshes,for scalar reaction-difusion equations and showed how to defne an interpolatory version which maintained its convergence properties.The interpolatory approach uses a locally postprocessed approximate solution to evaluate the nonlinear term,and assembles all HDG matrices once before the time integration leading to a reduction in computational cost.The resulting method displays a superconvergent rate for the solution for polynomial degree k≥1.In this work,we take advantage of the link found between the HDG and the hybrid high-order(HHO)methods,in Cockburn et al.(ESAIM Math.Model.Numer.Anal.50(3):635–650,2016)and extend this idea to the new,HHO-inspired HDG methods,defned on meshes made of general polyhedral elements,uncovered therein.For meshes made of shape-regular polyhedral elements afne-equivalent to a fnite number of reference elements,we prove that the resulting interpolatory HDG methods converge at the same rate as for the linear elliptic problems.Hence,we obtain superconvergent methods for k≥0 by some methods.We thus maintain the superconvergence properties of the original methods.We present numerical results to illustrate the convergence theory.

关键词： hybrid high-order methods hybridizable discontinuous Galerkin methods Interpolatory method Superconvergence

来源：

维普期刊数据库评论

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

欢迎您,

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

在线全文

在线全文

请选择保存的检索档案：

请选择收藏分类：

通借通还

欢迎您,

建议与咨询 留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

在线全文

在线全文

请选择保存的检索档案： 新增检索档案 确定 取消

请选择收藏分类： 新增自定义分类 确定 取消

通借通还

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

请选择保存的检索档案：

请选择收藏分类：