A Numerical Method for Anisotropic Elliptic Boundary Value Problems
Miguel Dumett
Broschiertes Buch

A Numerical Method for Anisotropic Elliptic Boundary Value Problems

on Irregular Domains in Two and Three Dimensions

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We present a new second-order stable Cartesian grid algorithm for solving anisotropic elliptic boundary value problems on bounded irregular domains in two dimensions (2D) and three dimensions (3D). The irregular domain is embedded in a uniform Cartesian mesh, but grid points outside of the domain are not used. Second- order local truncation error and the sufficient Gerschgorin criterion for stability impose some conditions to be satisfied by the weights of the discretization scheme at a particular interior grid point. A necessary and sufficient condition, in terms of the anisotropy matrix, for...