Optimizing domain parameterization in isogeometric analysis based on Powell-Sabin splines

摘要: We address the problem of constructing a high-quality parameterization given planar physical domain, defined by means finite set boundary curves. look for geometry map represented in terms Powell-Sabin B-splines. splines are C 1 quadratic on triangulation, and thus parameter domain can be any polygon.The is generated following three-step procedure. First, shape corresponding triangulation determined, such way that its number corners matches domain. Second, control points related to B-spline representation chosen so they parameterize curve Third, remaining inner obtained solving nimble optimization based Winslow functional.The proposed procedure illustrated numerically context isogeometric Galerkin discretizations splines. It turns out flexibility rising from generality has beneficial effect quality also accuracy computed approximate solution.