NURBS-Enhanced polygonal scaled boundary finite element method for heat diffusion in anisotropic media with internal heat sources

Abstract

We develop polygonal scaled boundary finite element method (SBFEM) with boundaries represented by non-uniform rational B-splines (NURBS) instead of standard Lagrange shape functions. The approach, coined NURBS enhanced SBFEM (NESBFEM), is able to represent the geometry exactly. For elements intersected by the boundary, NURBS basis functions are employed and for other elements, either Lagrange shape functions or NURBS functions are used. The proposed technique inherits the salient features of isogeometric analysis (IGA) and scaled boundary finite element method (SBFEM). Further, well-developed refinement strategies (h−,k−, p-refinements) of IGA are employed to generate higher order polytopal elements. The proposed approach provides a starting point to an efficient framework for practising engineers to solve heat diffusion in anisotropic media with internal heat sources, especially when the domain has internal features, viz., holes/inclusions and to obtain accurate solutions even on coarser mesh with high-order polytopal element.