Efficient Local Refinement Near Parametric Boundaries Using kd-Tree Data Structure and Algebraic Level Sets

In analysis of problems with parametric spline boundaries that are immersed or inserted into an underlying domain, the discretization on domain usually does not conform to boundaries. While fixed is great convenience as evolve, field approximations near require refinement in do quadrature cells. this paper, a kd-tree data structure together sign-based and/or distance-based strategy proposed for local well adaptive The developed algorithms construct and utilize implicit forms Non-Uniform Rational B-Spline (NURBS) surfaces algebraically (and non-iteratively) estimate distance sign relative boundary. demonstrated produce fewer sub-cells same accuracy solution compared classical quad/oct tree-based subdivision. Consistent structure, we describe new priori algorithm based signed unsigned from We first demonstrate coupled by constructing Truncated Hierarchical B-spline (THB-spline) “meshes”. next efficiency through NURBS within volumetric three-dimensional discretizations.