Please use this identifier to cite or link to this item: https://doi.org/10.1007/s10444-007-9043-6
Title: A fast finite difference method for biharmonic equations on irregular domains and its application to an incompressible Stokes flow
Authors: Chen, G.
Li, Z.
Lin, P. 
Keywords: Augmented method
Biharmonic equation
Immersed interface method
Incompressible Stokes flow
Irregular domain
Issue Date: Aug-2008
Citation: Chen, G., Li, Z., Lin, P. (2008-08). A fast finite difference method for biharmonic equations on irregular domains and its application to an incompressible Stokes flow. Advances in Computational Mathematics 29 (2) : 113-133. ScholarBank@NUS Repository. https://doi.org/10.1007/s10444-007-9043-6
Abstract: Biharmonic equations have many applications, especially in fluid and solid mechanics, but is difficult to solve due to the fourth order derivatives in the differential equation. In this paper a fast second order accurate algorithm based on a finite difference discretization and a Cartesian grid is developed for two dimensional biharmonic equations on irregular domains with essential boundary conditions. The irregular domain is embedded into a rectangular region and the biharmonic equation is decoupled to two Poisson equations. An auxiliary unknown quantity Δu along the boundary is introduced so that fast Poisson solvers on irregular domains can be used. Non-trivial numerical examples show the efficiency of the proposed method. The number of iterations of the method is independent of the mesh size. Another key to the method is a new interpolation scheme to evaluate the residual of the Schur complement system. The new biharmonic solver has been applied to solve the incompressible Stokes flow on an irregular domain. © 2007 Springer Science+Business Media, Inc.
Source Title: Advances in Computational Mathematics
URI: http://scholarbank.nus.edu.sg/handle/10635/102640
ISSN: 10197168
DOI: 10.1007/s10444-007-9043-6
Appears in Collections:Staff Publications

Show full item record
Files in This Item:
There are no files associated with this item.

SCOPUSTM   
Citations

23
checked on Oct 15, 2018

WEB OF SCIENCETM
Citations

23
checked on Oct 15, 2018

Page view(s)

31
checked on Jul 6, 2018

Google ScholarTM

Check

Altmetric


Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.