Общие вопросы математики

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A Numerical Method for Anisotropic Elliptic Boundary Value Problems

Автор: Miguel Dumett
Год: 2009
Издание: LAP Lambert Academic Publishing
Страниц: 148
ISBN: 9783838322339
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 the existence of a Gerschgorin second-order scheme at a given interior grid point is found. This theorem is proved in 2D and 3D. The governing partial differential equations are discretized through a new technique which uses a linear programming approach to find the scheme at points far away from the irregular boundary. Near the irregular boundary, with the addition of boundary ...
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