A novel polyhedral scaled boundary finite element method solving three-dimensional heat conduction problems

In this work, we derived the three-dimensional scaled boundary finite element formulation for thermal conduction problems. By introducing Wachspress shape functions, we proposed a novel polyhedral scaled boundary finite element method (PSBFEM) to address thermal conduction problems. The proposed method effectively addresses the challenges associated with complex geometries by integrating the polyhedral mesh and the octree mesh. The presented formulation handles both steady-state and transient thermal conduction analyses. Through a series of numerical examples, the accuracy and convergence of the proposed method were validated. The results demonstrate that mesh refinement leads to superior accuracy for the PSBFEM compared to the FEM. Moreover, Polyhedral elements provide an effective and efficient approach for complex simulations that substantially reduces computational costs.