%0 PDF
%T Triangulation algorithm for fast elliptic solvers based on domain imbedding.
%A Börgers, Christoph.
%D 2018-04-05T10:20:46.473-04:00
%8 2018-04-05
%I Tufts University. Tisch Library.
%R http://localhost/files/fq9786215
%X 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 triangulation 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.
%[ 2018-10-10
%9 Text
%~ Tufts Digital Library
%W Institution