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Boundary Algebraic Equations for Lattice Problems

  • P. G. Martinsson
  • G. J. Rodin
Conference paper
Part of the Solid Mechanics and Its Applications book series (SMIA, volume 113)

Abstract

Boundary algebraic equations corresponding to Dirichlet boundary-value problems on lattices are introduced. These equations are based on the lattice Green’s function, from which discrete single- and double-layer potentials are derived. Structurally, the boundary algebraic equations are similar to the boundary integral equations of classical potential theory. Numerical experiments indicate that boundary algebraic equations possess excellent spectral properties.

Keywords

Discrete potential theory discrete Laplace operator lattice Green’s function 

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References

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    K. E. Atkinson. The numerical solution of integral equations of the second kind. Cambridge University Press, Cambridge, 1997.Google Scholar
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    R. J. Duffin. Discrete potential theory. Duke Mathematical Journal, 20:233–251, 1953.CrossRefzbMATHMathSciNetGoogle Scholar
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    P. G. Martinsson. Fast multiscale methods for lattice equations. Ph.D. thesis, The University of Texas at Austin, Computational and Applied Mathematics, 2002.Google Scholar
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    S.G. Mikhlin. Integral equations and their applications to certain problems in mechanics, mathematical physics and technology. Pergamon Press, New York, 1957. Translated from the Russian by A. H. Armstrong.Google Scholar

Copyright information

© Kluwer Academic Publishers 2003

Authors and Affiliations

  • P. G. Martinsson
    • 1
  • G. J. Rodin
    • 2
  1. 1.Department of MathematicsYale UniversityNew HavenUSA
  2. 2.Texas Institute for Computational and Applied MathematicsThe University of Texas at AustinAustinUSA

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