Numerical Implementation of Grid Generator
The comprehensive system of the generalized Laplace equations in the boundary value problem (5.4) allows one to generate grids on surfaces or in domains in a unified manner, regardless of their dimension. In particular, the transformed elliptic equations obtained from the generalized Laplace equations by changing mutually dependent and independent variables can be applied to produce grids in spatial blocks by means of the successive generation of grids on curvilinear edges, faces, and parallelepipeds, using the solution at a step i < n as the Dirichlet boundary condition for the following step i + 1 ≤ n. Thus both the interior and the boundary grid points of a domain or surface can be calculated by the similar elliptic solver.
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