Compensated optimal grids for elliptic boundary-value problems

Document Type

Article

Publication Date

10-1-2008

Abstract

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. © 2008 Elsevier Inc. All rights reserved.

Identifier

49349109133 (Scopus)

Publication Title

Journal of Computational Physics

External Full Text Location

https://doi.org/10.1016/j.jcp.2008.06.026

e-ISSN

10902716

ISSN

00219991

First Page

8622

Last Page

8635

Issue

19

Volume

227

Grant

R01 GM076690

Fund Ref

National Institutes of Health

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