Performance analysis of the ultra weak variational formulation to compute electromagnetic fields on nonuniform meshes

Abstract

The purpose of this work is to apply a previously developed ultra weak variational formulation (UWVF) to the solution of the Helmholtz equation in electromagnetic scattering problems. The variational form is based on discontinuous Galerkin with plane wave basis functions in 2-dimensional finite element mesh. We present a general strategy, which allows to adjust the number of wave directions based on both the element size and the local conditioning number. This provides a cost-effective mechanism for application of UWVF using nonuniform meshes. Through simulation of scattering of a dielectric-coated circular cylinder, it is shown that the process significantly improves the UWVF performance. KEYWORDS electrically large domains, electromagnetic scattering, nonuniform mesh, plane wave basis, ultra weak variational formulation

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 …”