Colloquium, Mathematical Sciences

Abstrakt: Maxwell's equations describe electromagnetic wave propagation and the most dominant force in our world. These fundamental equations can be handled in a natural way by a hypercomplex algebra due to W. K. Clifford, a contemporary of J. C. Maxwell.

We shall survey this kind of non-commutative complex analysis, that is useful in solving Maxwell's equations. Making use of a Cauchy integral formula for time-harmonic Maxwell's equations advocated by Alan McIntosh, we describe a recent boundary integral equation reformulation for Maxwell scattering. In recent joint work with Johan Helsing and Anders Karlsson, Lund, we have achieved an efficient solver, with almost down to machine precision, for computationally challenging plasmonic and eddy current electromagnetic scattering problems.