Delaunay refinement for curved complexes

Abstract

This work investigates the Delaunay refinement for curved complexes. A manifold complex is defined as an unambiguous representation for the geometric objects required by a partial differential equation solver. The Chew's and Ruppert's Delaunay refinement algorithms, including an extension for curved complexes, are described under a new and arbitrary dimensional perspective. A theorem for strongly Delaunay simplicial complexes is extended to higher dimensions, as well as a fundamental theorem of the Bowyer-Watson algorithm is extended to intermediate dimensions in the simplicial complex. Some implementation points are also addressed, as the fan search in the incremental Delaunay simplicial complex update, and robust predicates in arbitrary dimensions.