Volume 26, pp. 55-81, 2007.

Optimal grids for anisotropic problems

S. Asvadurov, V. Druskin, and S. Moskow


Spectral convergence of optimal grids for anisotropic problems is both numerically observed and explained. For elliptic problems, the gridding algorithm is reduced to a Stieltjes rational approximation on an interval of a line in the complex plane instead of the real axis as in the isotropic case. We show rigorously why this occurs for a semi-infinite and bounded interval. We then extend the gridding algorithm to hyperbolic problems on bounded domains. For the propagative modes, the problem is reduced to a rational approximation on an interval of the negative real semiaxis, similarly to in the isotropic case. For the wave problem we present numerical examples in 2-D anisotropic media.

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Key words

finite differences, DtN maps, anisotropy, spectral approximation

AMS subject classifications

65M06, 65N06

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