Triangulation algorithm for fast elliptic solvers based on domain imbedding.
- The following triangulation problem is considered. Let R be a rectangle, and Ω an open domain whose closure is contained in R. Consider a rectangular grid covering R. Perturb this grid by shifting points close to the boundary ∂Ω onto ∂Ω. This results in a quadrilateral, almost rectangular grid. Divide each cell of this grid into two triangles along one of its diagonals. This results in a triangula... read moretion of R. A subset of this triangulation is a triangulation of an approximation Ωh to Ω. The distance between ∂Ωh and ∂Ω is required to be O(h2), where h denotes the maximum meshwidth of the rectangular grid. All triangles should be nondegenerate. Triangulations of this kind are needed for finite element domain imbedding methods for elliptic boundary value problems. A particularly simple example of such a method is reviewed. The convergence theory for this method motivates our definition of nondegeneracy of triangles. For ∂Ω member of C2, an algorithm for constructing triangulations with the desired properties is described. If the boundary has corners, the condition that the distance between ∂Ωh and ∂Ω be O(h2) cannot always be satisfied. However, domains with corners are also discussed, and a modification of the algorithm for this case is described. © 1990 Society for Industrial and Applied Mathematics.read less
- C. Börgers, "A Triangulation Algorithm for Fast Elliptic Solvers Based on Domain Imbedding," SIAM Journal on Numerical Analysis, vol. 27, no. 5, pp. 1187-1196, Oct. 1990. doi:10.1137/0727068.