Boundary Algebraic Equations for Lattice Problems
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.
KeywordsDiscrete potential theory discrete Laplace operator lattice Green’s function
Unable to display preview. Download preview PDF.
- K. E. Atkinson. The numerical solution of integral equations of the second kind. Cambridge University Press, Cambridge, 1997.Google Scholar
- 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
- 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