New solvers for electromagnetic transmission problems: Lipschitz domains, near-fields, and surface plasmon waves.

Real world boundary value problems are often set in non-smooththree-dimensional domains where they have to be solved repeatedly,rapidly, and with controlled accuracy. Integral equation based solversoffer advantages in this context. Much research on such solvers is forscattering problems for the time harmonic Maxwell equations(THME).

Hot topics include discretization techniques and findingformulations free of false resonances.Our group has in recent years developed discretization techniques forintegral equation reformulations of scattering problems in piecewisesmooth domains which, at a low cost, enable almost full machineprecision in solutions to problems for which commercial solvers mayonly reach qualitative results.

The present four-year project extendsthis work to THME-solvers with exceptional performance in plasmonics,that is, scattering against multi-dielectric objects with sharp edgesand close-to-negative permittivities. A particular focus is onaccurately computing near fields and surface plasmon waves. Theproject involves generalizations of discretization schemes and thederivation of new integral equations.

Applications of plasmonics arefound in optics, non-destructive material testing, and medicine(spectroscopy and biosensors). Our solvers can also find use in thedesign and maintenance of key accelerator equipment at MAX IV and ESSin Lund. The research covers important topics in contemporaryscientific computing and offers a PhD student a good career start.