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An optimizing finite difference scheme based on proper orthogonal decomposition for CVD equations
Author(s) -
Du Juan,
Zhu Jiang,
Luo Zhendong,
Navon I. M.
Publication year - 2011
Publication title -
international journal for numerical methods in biomedical engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.741
H-Index - 63
eISSN - 2040-7947
pISSN - 2040-7939
DOI - 10.1002/cnm.1295
Subject(s) - proper orthogonal decomposition , singular value decomposition , point of delivery , consistency (knowledge bases) , mathematics , finite difference , decomposition , finite difference method , finite difference scheme , finite difference coefficient , scheme (mathematics) , mathematical optimization , algorithm , mathematical analysis , finite element method , engineering , geometry , mixed finite element method , chemistry , structural engineering , organic chemistry , agronomy , biology
In this article, an optimizing reduced finite difference scheme (FDS) based on singular value decomposition (SVD) and proper orthogonal decomposition (POD) for the chemical vapor deposit (CVD) equations is presented. And the error estimates between the usual finite difference solution and the reduced POD solution of optimizing FDS are derived. At last, some examples of numerical simulation are given to demonstrate the consistency of the numerical and theoretical results. It is shown that the optimizing reduced FDS based on POD method is of great feasibility and efficiency. Copyright © 2009 John Wiley & Sons, Ltd.