Asvadurov, S.; Druskin, V.; Moskow, S.

Optimal grids for anisotropic problems

ETNA, Electron. Trans. Numer. Anal. 26, 55-81, electronic only (2007)


Summary: 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.

Mathematics Subject Classification

65M06, 65N06


finite differences, dtn maps, anisotropy, spectral approximation