Vortrag
Handling Magnetic Field Integral Operators at Extremely Low Frequency
Vortrag von Prof. Dr. Francesco Andriulli
Datum: 02.05.18 Zeit: 16.15 - 17.45 Raum: Y27H25
When solving electromagnetic scattering problems with the boundary element method, the Electric Field and the Magnetic Field Integral Operators are the building blocks for a large number of formulations in literature. When modelling increasingly low frequency scenarios, however, the electric operator is known to give rise, upon discretization, to increasingly ill-conditioned problems whose iterative solution converges very slowly (a problem traditionally handled by leveraging on Helmholtz-Hodge decompositions). The magnetic operator, instead, gives rise to uniformly well-conditioned matrices (on simply connected geometries) independently of the frequency. At low-frequency, when the magnetic operator associated problems are solved via an iterative procedure, they converge rapidly but, lamentably, this rapid convergence is towards a severely incomplete solution since numerical cancellations occur in finite precision. We will discuss several aspects of this issue in detail delineating effective strategies to handle it and to obtain electromagnetic full-wave solvers providing stable solutions from high to arbitrarily low frequency.