| Compensated optimal grids for elliptic boundary-value problems. | |
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MedLine Citation:
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PMID: 19802366 Owner: NLM Status: Publisher |
Abstract/OtherAbstract:
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A method is proposed which allows to efficiently treat elliptic problems on unbounded domains in two and three spatial dimensions in which one is only interested in obtaining accurate solutions at the domain boundary. The method is an extension of the optimal grid approach for elliptic problems, based on optimal rational approximation of the associated Neumann-to-Dirichlet map in Fourier space. It is shown that, using certain types of boundary discretization, one can go from second-order accurate schemes to essentially spectrally accurate schemes in two-dimensional problems, and to fourth-order accurate schemes in three-dimensional problems without any increase in the computational complexity. The main idea of the method is to modify the impedance function being approximated to compensate for the numerical dispersion introduced by a small finite-difference stencil discretizing the differential operator on the boundary. We illustrate how the method can be efficiently applied to nonlinear problems arising in modeling of cell communication. |
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Authors:
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F Posta; S Y Shvartsman; C B Muratov |
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Publication Detail:
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Type: JOURNAL ARTICLE |
Journal Detail:
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Title: Journal of computational physics Volume: 227 ISSN: - ISO Abbreviation: J Comput Phys Publication Date: 2008 Oct |
Date Detail:
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Created Date: 2009-10-5 Completed Date: - Revised Date: - |
Medline Journal Info:
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Nlm Unique ID: 9883524 Medline TA: J Comput Phys Country: - |
Other Details:
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Languages: ENG Pagination: 8622-8635 Citation Subset: - |
Affiliation:
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Department of Mathematical Sciences, New Jersey Institute of Technology, University Heights, Newark, NJ 07102, USA. |
Export Citation:
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| MeSH Terms | |
Descriptor/Qualifier:
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| Grant Support | |
ID/Acronym/Agency:
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R01 GM076690-02//NIGMS NIH HHS |
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