Hybrid High‑Order Methods for the Acoustic Wave Equation in the Time Domain

作     者：Erik Burman Omar Duran Alexandre Ern Erik Burman;Omar Duran;Alexandre Ern

作者机构：Department of MathematicsUniversity College LondonLondon WC1E 6BTUK CERMICSEcole des Ponts77455 Marne la Vallée Cedex 2France INRIA Paris75589 ParisFrance 

出 版 物：《Communications on Applied Mathematics and Computation》 (应用数学与计算数学学报（英文）)

年 卷 期：2022年第4卷第2期

页      面：597-633页

核心收录：

学科分类：07[理学] 0701[理学-数学] 0702[理学-物理学] 

基　　金：The authors would like to thank L.Guillot(CEA/DAM)for insightful discussions and CEA/DAM for partial fnancial support.EB was partially supported by the EPSRC grants EP/P01576X/1 and EP/P012434/1. 

主　　题：Hybrid high-order methods Wave equation Newmark scheme Runge-Kutta scheme 

摘      要：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.