Higher-Order Accurate Meshing of Nonsmooth Implicitly Defined Surfaces and Intersection Curves

Abstract

A higher-order accurate meshing algorithm for nonsmooth surfaces defined via Boolean set operations from smooth surfaces is presented. Input data are a set of level-set functions and a bounding box containing the domain of interest. This geometry definition allows the treatment of edges as intersection curves. Initially, the given bounding box is partitioned with an octree that is used to locate corners and points on the intersection curves. Once a point on an intersection curve is found, the edge is traced. Smooth surfaces are discretized using marching cubes and then merged together with the advancing-front method. The piecewise linear geometry is lifted by projecting the inner nodes of the Lagrangian elements onto the surface or intersection curve. To maintain an accurate mesh, special attention is paid to the accurate meshing of tangential intersection curves. Optimal convergence properties for approximation problems are confirmed in numerical studies.