Space and Time Adaptive Two-Mesh<i>hp</i>-Finite Element Method for Transient Microwave Heating Problems

Abstract

Abstract A novel, highly efficient and accurate space and time adaptive higher-order finite element method (hp-FEM) is proposed for evolutionary microwave heating problems. Since the electric field E and temperature field T are very different in nature, they are approximated 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. Numerical experiments are presented that show the novel method is clearly superior to its natural competitors—the space and time adaptive (single mesh) hp-finite element method and the space and time adaptive two-mesh h-finite element method. In all cases, comparisons in both the number of degrees of freedom (discrete problem size) and CPU time are presented. The methodology is freely available on-line in the form of a general public licensed C++/Python library Hermes (http://hpfem.org/).