A Multigrid Method for a Model of the Implicit Immersed Boundary Equations

作     者：Robert D.Guy Bobby Philip 

作者机构：Department of MathematicsUniversity of California DavisDavisCA 95616USA Oak Ridge National LaboratoryOak RidgeTN 37831USA 

出 版 物：《Communications in Computational Physics》 (计算物理通讯（英文）)

年 卷 期：2012年第12卷第7期

页      面：378-400页

核心收录：

学科分类：07[理学] 070102[理学-计算数学] 0704[理学-天文学] 0701[理学-数学] 0702[理学-物理学] 

基　　金：supported in part by UCOP grant 09-LR-03-116724-GUYR to RG and BP as well as NSF-DMS grant 0540779 to RG 

主　　题：Preconditioning implicit methods fluid-structure interaction 

摘      要：Explicit time stepping schemes for the immersed boundary method require very small time steps in order to maintain *** the equations that arise from an implicit discretization is ***,several different approaches have been proposed,but a complete understanding of this problem is still emerging.A multigrid method is developed and explored for solving the equations in an implicittime discretization of a model of the immersed boundary *** model problem consists of a scalar Poisson equation with conformation-dependent singular forces on an immersed *** model does not include the inertial terms or the incompressibility *** method is more efficient than an explicit method,but the efficiency gain is *** multigrid method alone may not be an effective solver,but when used as a preconditioner for Krylov methods,the speed-up over the explicit-time method is *** example,depending on the constitutive law for the boundary force,with a time step 100 times larger than the explicit method,the implicit method is about 15-100 times more efficient than the explicit method.A very attractive feature of this method is that the efficiency of the multigrid preconditioned Krylov solver is shown to be independent of the number of immersed boundary points.