High-order difference potentials methods for 1D elliptic type models

作     者：Epshteyn, Yekaterina Phippen, Spencer 

作者机构：Univ Utah Dept Math Salt Lake City UT 84112 USA 

出 版 物：《APPLIED NUMERICAL MATHEMATICS》 (应用数值数学)

年 卷 期：2015年第93卷

页      面：69-86页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：National Science Foundation Grant [DMS-1112984] REU research at the Mathematics Department at the University of Utah Direct For Mathematical & Physical Scien Division Of Mathematical Sciences Funding Source: National Science Foundation 

主　　题：Difference potentials Boundary projections Cauchy's type integral Boundary value problems Variable coefficients Heterogeneous media High-order finite difference schemes Difference Potentials Method Immersed Interface Method Interface problems Parallel algorithms 

摘      要：Numerical approximations and modeling of many physical, biological, and biomedical problems often deal with equations with highly varying coefficients, heterogeneous models (described by different types of partial differential equations (PDEs) in different domains), and/or have to take into consideration the complex structure of the computational subdomains. The major challenge here is to design an efficient numerical method that can capture certain properties of analytical solutions in different domains/subdomains (such as positivity, different regularity/smoothness of the solutions, etc.), while handling the arbitrary geometries and complex structures of the domains. In this work, we employ one-dimensional elliptic type models as the starting point to develop and numerically test high-order accurate Difference Potentials Method (DPM) for variable coefficient elliptic problems in heterogeneous media. While the method and analysis are simple in the one-dimensional settings, they illustrate and test several important ideas and capabilities of the developed approach. (C) 2014 IMACS. Published by Elsevier B.V. All rights reserved.