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

被引:26
作者
Epshteyn, Yekaterina [1 ]
Phippen, Spencer [1 ]
机构
[1] Univ Utah, Dept Math, Salt Lake City, UT 84112 USA
基金
美国国家科学基金会;
关键词
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; GHOST FLUID METHOD; MATCHED INTERFACE; BOUNDARY METHOD; DISCONTINUOUS COEFFICIENTS; NUMERICAL-SOLUTION; SINGULAR SOURCES; EQUATIONS; FLOW; POISSONS; DOMAINS;
D O I
10.1016/j.apnum.2014.02.005
中图分类号
O29 [应用数学];
学科分类号
070104 ;
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.
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页码:69 / 86
页数:18
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