Optimum node positioning in adaptive grid refinement and the Delaunay-Voronoi algorithm [semiconductor process simulation]

Abstract

This paper presents a method for optimum placement of nodes in grid generation for process simulation together with an algorithm for updating the grid after each addition of a new node to ensure that the Delaunay property is satisfied. Placement of nodes is decided by considering the optimum error in evaluating the integral /spl int//sub V/ C(x)dx. The best error estimate is obtained when the node coincides with the centroid (the center of mass) of its own Voronoi region and moreover when the Voronoi region is symmetric. After addition of a node, the grid is updated to maintain the Delaunay property using the Delaunay-Voronoi algorithm.