کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
520426 867718 2008 14 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Compensated optimal grids for elliptic boundary-value problems
موضوعات مرتبط
مهندسی و علوم پایه مهندسی کامپیوتر نرم افزارهای علوم کامپیوتر
پیش نمایش صفحه اول مقاله
Compensated optimal grids for elliptic boundary-value problems
چکیده انگلیسی

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.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Computational Physics - Volume 227, Issue 19, 1 October 2008, Pages 8622–8635
نویسندگان
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