Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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MULTIGRID SOLUTION OF THREE DIMENSIONAL BIHARMONIC EQUATIONS WITH DIRICHLET BOUNDARY CONDITIONS OF SECOND KIND

  • Ibrahim, S.A. Hoda (Department of Mathematics, Faculty of science, Zagazig University) ;
  • Hassan, Naglaa Ameen (Department of Mathematics, Faculty of science, Zagazig University)
  • Received : 2010.09.28
  • Accepted : 2011.07.01
  • Published : 2012.01.30
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Abstract

In this paper, we solve the three-dimensional biharmonic equation with Dirichlet boundary conditions of second kind using the full multigrid (FMG) algorithm. We derive a finite difference approximations for the biharmonic equation on a 18 point compact stencil. The unknown solution and its second derivatives are carried as unknowns at grid points. In the multigrid methods, we use a fourth order interpolation to producing a new intermediate unknown functions values on a finer grid, and the full weighting restriction operators to calculating the residuals at coarse grid points. A set of test problems gives excellent results.

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References

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