The scalar wave equation for a potential in a curved space time, i.e., the Laplace-Beltrami equation has been studied in this work. An action principle is used to derive a finite element algorithm for determining the modes of propagation inside a waveguide of arbitrary shape. Generalizing this idea, the Maxwell theory in a curved space time determines a set of linear partial differential equati...

It is explained how FEMLAB / COMSOL Multiphysics can be configured to calculate, the frequencies, electromagneticfield patterns, mode volumes, filling factors, radiation losses ... of the whispering-gallery modes of axisymmetric microresonators. The method exploits COMSOL’s ability to accept the definition of solutions to Maxwells equations in so-called ‘weak form’. As no transverse approximati...

We develop a new high order accurate time-integration technique for initial value problems. We focus on problems that originate from a space approximation using high order finite difference methods on summation-by-parts form with weak boundary conditions, and extend that technique to the timedomain. The new time-integration method is global, high order accurate, unconditionally stable and toget...