Space and Time Adaptive Two-Mesh hp-FEM for Transient Microwave Heating Problems

We propose a novel, highly efficient and accurate space and time adaptive higher-order finite element method (hp-FEM) for evolutionary microwave heating problems. Since the electric field E and temperature field T are very different in nature, we approximate them on individual meshes that change dynamically in time independently of each other. Although the approximations of E and T are defined on different meshes, the coupling is treated in a monolithic fashion using a complex-valued approximate temperature. We present numerical experiments showing that the novel method is clearly superior to its natural competitors – the space and time adaptive (single mesh) hpFEM and the space and time adaptive two-mesh h-FEM. In all cases, comparisons in both the number of DOF (discrete problem size) and CPU time are presented. The methodology is freely available on-line in the form of a GPL-licensed C++/Python library Hermes1. http://spilka.math.unr.edu/hermes/.