Numerical framework for the simulation of dielectric heating using finite and boundary element method

Abstract

This paper presents the latest development towards a software agent-based numerical framework for interdisciplinary coupled problems. The software agent framework is capable to incorporate multiple physical effects and combine multiple numerical methods through the usage of a neutral abstraction layer. The principles of software agent-based programming and the application in a numerical example are discussed. This paper focuses on dielectric heating and different methods for solving the time harmonic Maxwell equation. By reusing state of the art finite element method (FEM) and boundary element method (BEM) software tools and managing the interface between the different tools, this approach solves complicated and realistic three-dimensional problems. The functionality and efficiency of the framework are demonstrated on the dielectric heating inside a human head due to electromagnetic waves. A proper iterative coupling formulation for FEM and BEM is derived and numerically validated. The FEM-BEM coupling separates from existing approaches, because it takes advantage of new developments in the FEM, namely, the perfect handling of infinite domains through perfectly matched layers. Moreover, the simplicity and flexibility of the coupling method allow implementation in existing numerical codes.

Coupling of finite element method and integral formulation for vector Helmholtz equation

“…As mentioned above, the coupling is realized by incorporating jumps in the primary and secondary field variable. In contrast, in Grabmaier et al's (2017) study, the incorporation was approximated by the usage of point sources or dipoles. This approximation is sufficient for large distances between the point sources and the in-homogeneous objects.…”

Special issue: The 10th International Symposium on Electric and Magnetic Fields (EMF 2016)

“…The second major topic treats the numerical modelling of the electromagnetic behavior of electric and magnetic materials, with contributions on the modelling of magnetoelectric multilayer laminate composites, the magneto‐elastic behavior of steel sheets, the effect of mechanical stresses on Graphene‐based devices, and the effect of temperature on static magnetic hysteresis . The third major topic concerns fast solvers for electromagnetic applications with contributions on ultra weak variational formulations and the behavior of natural and finite element interpolation functions, domain decomposition methods for finite volume, finite element and boundary element schemes,() explicit time integration of eddy current problems, and the GPU acceleration of Maxwell solvers for differents applications. () The fourth major topic concerns the application of electromagnetic modelling, uncertainty quantification and model order reduction techniques to novel or challenging applications, with contributions to electrothermal field problems, electric machine modelling,() lightning‐produced electromagnetic fields, electronic circuits, and electrical capacitance tomography sensors …”