Elliptic Grid Control on a Discrete Level

Abstract

Considering a grid cell with a single central point the solution of the discretized Laplace equation may be conceived as a weighted average of points on the cell boundary. Our grid control method is based on a local perturbation of the numerical solution to the Laplace equation by specifying line-wise central target points relative to the orientation of and the distance from the cell's bounding faces. Simple one-dimensional weighting functions allow to extend the overall control of grid line spacing and direction from the boundaries into the field.