A Kernel-Free Boundary Integral Method for Variable Coefficients Elliptic PDEs

作     者：Wenjun Ying Wei-Cheng Wang 

作者机构：Department of MathematicsMOE-LSC and Institute of Natural SciencesShanghai Jiao Tong UniversityMinhangShanghai 200240P.R.China Department of MathematicsNational Tsing Hua Universityand National Center for Theoretical SciencesHsinChu300Taiwan 

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

年 卷 期：2014年第15卷第4期

页      面：1108-1140页

核心收录：

学科分类：07[理学] 0704[理学-天文学] 0701[理学-数学] 0702[理学-物理学] 070101[理学-基础数学] 

基　　金：supported in part by the National Science Foundation of the USA under Grant DMS-0915023 is supported by the National Natural Science Foundation of China under Grants DMS-11101278 and DMS-91130012 supported by the Young Thousand Talents Program of China supported in part by National Science Committee of Taiwan under Grant 99-2115-M-007-002-MY2 supported in part by National Center for Theoretical Sciences of Taiwan,too 

主　　题：Elliptic partial differential equation variable coefficients kernel-free boundary integral method finite difference method geometric multigrid iteration 

摘      要：This work proposes a generalized boundary integral method for variable coefficients elliptic partial differential equations(PDEs),including both boundary value and interface *** method is kernel-free in the sense that there is no need to know analytical expressions for kernels of the boundary and volume integrals in the solution of boundary integral *** of a boundary or volume integral is replaced with interpolation of a Cartesian grid based solution,which satisfies an equivalent discrete interface problem,while the interface problem is solved by a fast solver in the Cartesian *** computational work involved with the generalized boundary integral method is essentially linearly proportional to the number of grid nodes in the *** paper gives implementation details for a secondorder version of the kernel-free boundary integral method in two space dimensions and presents numerical experiments to demonstrate the efficiency and accuracy of the method for both boundary value and interface *** interface problems demonstrated include those with piecewise constant and large-ratio coefficients and the heterogeneous interface problem,where the elliptic PDEs on two sides of the interface are of different types.