Local RBF Algorithms for Elliptic Boundary Value Problems in Annular Domains  

作　　者：C.S.Chen Andreas Karageorghis 

机构地区：[1]School of Civil Engineering and Architecture,Nanchang University,Nanchang,China,and School of Mathematics and Natural Sciences,University of Southern Mississippi,Hattiesburg,MS 39406,USA [2]Department of Mathematics and Statistics,University of Cyprus,P.O.Box 20537,1678 Nicosia,Cyprus

出　　处：《Communications in Computational Physics》2019年第1期41-67,共27页计算物理通讯（英文）

基　　金：acknowledges HPC at The University of Southern Mississippi supported by the National Science Foundation under the Major Research Instrumentation(MRI)program via Grant#ACI 1626217.

摘　　要：A local radial basis function method(LRBF)is applied for the solution of boundary value problems in annular domains governed by the Poisson equation,the inhomogeneous biharmonic equation and the inhomogeneous Cauchy-Navier equations of elasticity.By appropriately choosing the collocation points we obtain linear systems in which the coefficient matrices possess block sparse circulant structures and which can be solved efficiently using matrix decomposition algorithms(MDAs)and fast Fourier transforms(FFTs).The MDAs used are appropriately modified to take into account the sparsity of the arrays involved in the discretization.The leave-one-out cross validation(LOOCV)algorithm is employed to obtain a suitable value for the shape parameter in the radial basis functions(RBFs)used.The selection of the nearest centres for each local influence domain is carried out using a modification of the kdtree algorithm.In several numerical experiments,it is demonstrated that the proposed algorithm is both accurate and capable of solving large scale problems.

关 键 词：Radial basis functions Kansa method Poisson equation biharmonic equation Cauchy-Navier equations of elasticity matrix decomposition algorithms fast Fourier transforms 

分 类 号：O17[理学—数学]