Interpolation Algorithms for Interfacing FDTD and FEM Meshes in Multiphysics Modeling of Microwave Sintering

Microwave sintering of powders is gaining attention in the interdisciplinary engineering community as an innovative promising technology of production of new nano-structured materials with unique physical properties. Internally dissipated microwave power allows for energy savings and fast processing of metallic, ceramic, and composite particulate materials, but the process is practically uncontrolled and is poorly understood. Modeling of microwave sintering could help clarify many issues and suggest engineering solutions for designing efficient microwave system. This project is focused on the development of a particular element of a numerical tool for comprehensive simulation of electromagnetic, thermal, and mechanical phenomena occuring during microwave sintering. Combination of the relevant solvers requires interchange of numerical data between the grids associated with the finite-difference time-domain (FDTD) technique and the finite element method (FEM). Two techniques interfacing the FDTD mesh of Cartesian cells and the FEM mesh of rectangular hexahedra are developed in this work. The algorithms are built on cubic spline interpolation and the Shamos technique for determination of areas of convex polyhedra. Computational experiments with these algorithms implemented in MATLAB show satisfactory accuracy of interfacing with the average error not more than 5%.