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A numerical method based on boundary integral equations and radial basis functions for plane anisotropic thermoelastostatic equations with general variable coefficients

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Applied Mathematics and Mechanics(English Edition) 2020年第4期41卷 551-566页

作者： W.T.ANG X.WANG School of Mechanical and Aerospace Engineering Nanyang Technological UniversitySingapore 639798Singapore Department of Mechanical Engineering National University of SingaporeSingapore 117575Singapore

A boundary integral method with radial basis function approximation is proposed for numerically solving an important class of boundary value problems governed by a system of thermoelastostatic equations with variable coe?cients. The equations describe the thermoelastic behaviors of nonhomogeneous anisotropic materials with properties that vary smoothly from point to point in space. No restriction is imposed on the spatial variations of the thermoelastic coe?cients as long as all the requirements of the laws of physics are satis?ed. To check the validity and accuracy of the proposed numerical method, some speci?c test problems with known solutions are solved.

关键词： elliptic partial differential equation variable coefficient boundary element method radial basis function anisotropic thermoelastostatics

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THE SINGULARLY PERTURBED BOUNDARY VALUE PROBLEMS FOR HIGHER ORDER SEMILINEAR elliptic equationS

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Acta Mathematica Scientia 1997年第1期17卷 44-50页

作者：莫嘉琪许玉兴 Dept. of Math. Anhui Normal University Wuhu 241000 China

In this paper a singular perturbation of boundary value problem for elliptic partial differential equations of higher order is considered by using the differential inequalities. The uniformly valid asymptotic expansio... 详细信息

关键词： differential inequality singular perturbation asymptotic expansion elliptic partial differential equation boundary value problem

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

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Communications in Computational Physics 2014年第4期15卷 1108-1140页

作者： Wenjun Ying Wei-Cheng Wang Department of Mathematics MOE-LSC and Institute of Natural SciencesShanghai Jiao Tong UniversityMinhangShanghai 200240P.R.China Department of Mathematics National Tsing Hua Universityand National Center for Theoretical SciencesHsinChu300Taiwan

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.

关键词： elliptic partial differential equation variable coefficients kernel-free boundary integral method finite difference method geometric multigrid iteration

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